An experimental analysis of the CGPS algorithm for the three-machine flow shop scheduling with minimum makespan criterion

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An experimental analysis of the CGPS algorithm for thethree-machine flow shop scheduling with minimummakespan criterionHui-Chin Tang aa Department of Industrial Engineering and Management Cheng Shiu Institute ofTechnology Kaohsiung 83305 Taiwan Republic of ChinaPublished online 18 Jun 2013

To cite this article Hui-Chin Tang (2002) An experimental analysis of the CGPS algorithm for the three-machine flowshop scheduling with minimum makespan criterion Journal of Information and Optimization Sciences 232 323-344 DOI10108002522667200210699531

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An experimental analysis of the CGPS algorithm for the three-machine flow shop scheduling with minimum makespan criterion

Hui-Chin Tang

Department of Industrial Engineering and Management

Cheng Shiu Institute of Technology

Kaohsiung 83305

Taiwan

Republic of China

ABSTRACT The algorithm developed by Chen Glass Potts and Strusevich (CGPS) is by far

the best one in terms of the worst-case perfurmance ratio for the three-machine flow shop scheduling (3FSS) with minimum makespan criterion This paper focuses on the experimental analysis of the CGPS algorithm Three simulation experiments are conshyducted to compare and evaluate its performance in terms of six evaluation measures It is shown that the CGPS algorithm is not empirically preferred for the 3FSS with minimum makespan criterion

1 INTRODUCTION

Since the publication of Johnsons 1954 paper on the two-machine flow shop scheduling (FSS) [6] the growth in interest in the FSS problem has been quite dramatic [3 4 8 12] The FSS is a productionshyplanning problem that schedules 11 jobs on m sequential machines At any time each machine processes at most one job and each job is processed on at most one machine The uninterrupted processing time of each job on each machine is given Among many regular criteria this paper is concerned with the makespan Since it is the easiest crishyterion to use and represents other beneficial characteristics such as maximum machine utilization of a production line [4] Thus this paper considers the FSS with minimum makespan criterion

An intfgtresting special case is the three-machine FSS (3FSS) [2 17] The 3FSS has many properties One property is that there exists an

Journal of Information amp Optimization Sciences Vol 23 (2002) No2 pp 323-344 copy Analytic Publishing Co 0252middot266702 $200+25

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324 H C TANG

optimal schedule that is a permutation schedule viz schedule with the same processing order on each machine [3 12] Another property is that the 3FSS with minimum makespancriterion is a strongly NPshyhard problem [5 9] while the two-machine FSS with minimum makespan criterion has a computational time complexity of O(n log n) [6J Therefore much research has been devoted to proposing heuristic algorithms yielding near-optimal schedules in a quick time Two heuristic algorithms are distinguished constructive algorithms and improvement algorithms For more details see Smutnicki [14] Sullman [15] and the references cited there In this paper we restrict overselves to the constructive algorithms for the 3FSS with minimum makespan criterion

Moreover the measures of a heuristic algorithm performance can be investigated either experimentally or analytically (worst-case analysis or probability analysis) As the worst-case analysis is concerned the heuristic algorithm developed by Chen Glass Potts and Strusevich (CGPS) [2J is the best one so far This is very inspiring However no experimental analysis of its performance has been reported to date

The primary purpose of this paper is to measure the CGPS alshygorithm performance by the experimental analysis In the following sections we first recall the CGPS algorithm for the 3FSS with minimum makespan criterion A number of evaluation measures are proposed in section 3 Detailed evaluations and comparisons are performed in section 4 Finally some concluding remarks are made

2 THE CGPS ALGORITHM

The CGPS algorithm is an O(n log n) time heuristic algorithm which has a worst-case performance ratio of 53 for the 3FSS with minimum makespan criterion There are two main stages for the CGPS algorithm Firstly the construction of an initial permutation schedule 1tl involves creating an artificial two-machine FSS problem by the machine aggregation heuristic of ROck and Schmidt [13] and then applying Johnsons algorithm [6] to obtain 1tl The second stage is attempting to improve 1tl by partitioning the middle jobs into subshyjects and then rescheduling the jobs The resulting permutation schedule is 1t2 Of the two perm utation schedules 1tl and 1t2 the CGPS algorithm is shown that at least one of these permutation schedules has makespan which is at most 53 times that of an optimal schedule

For notational convenience we adopt the same notations as Chen et al [2] Let ai hi and ci be the uninterrupted processing times of job i E N I 2 n on machines A Band C respectively Also let 1t

0 deshynote an optimal permutation schedule that minimizes the makespan

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325 ANALYSIS OF THE CGPS ALGORITHM

For N ~ N we define a(N) =L ai The notation B(N) and c(N) are iEN

defined similarly For the 1tl obtained by applying Johnsons algorithm [6] we assume that Il and v are critical jobs where 1 S Il S v s n We also assume that

Nl = I 2 Il- I Nz = Il + 1 v - I and

N3 =v+ 1 n

Then the makespan of 1tl is rewritten as

a(Nl) + aJ1 + bfl + cJ1 + c(Ns) if Il v Cmax(n l ) (1)

ja(Nl ) + aJ1 + bJ1 + b(N2) + bv + Cv + c(Ns) if Il v

In the following we present two lemmas that are useful in the subsequent analysis

V It

LEMMA 1 Cmain) ~ L ak + bv + L Ck for v == 1 2 n (2) k=l k=y

PROOF See p 893 in Chen et a1 [2] 0

Next Chen et a1 [2] applied one value of v in (2) to establish conditions under which the schedule 1tl has a worst-case performance ratio of 53

LEMMA 2 If Il and v are critical jobs in 1tgt then

(a) If Il == v then 1tl is an optimal permutation schedule (b) If Il lt v and

beNz) + minbJ1 by S 23 beN) (3)

then we have Cmax(1tl)Cmax(1t) S 53 (4)

PROOF See p 893 11 Chen et a1 [2] 0

If Il lt v and (3) is violated Chen et a1 [2] constructed a schedule 1t2 such that the better of 1tl and 1t2 has a worst-case performance ratio of 53

LEMMA 3 If Il lt v (3) is violated a(N1) + aJ1 ~ Cy + c(N3) and (nl)Cmax (1t) ~ 53 then the permutation schedule 1tz generatedCmax

by the CGPS algorithm satisfies

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326 HCTANG

Cmax(1ti)ICmax(1tmiddot) ~ 53 (5)

PROOF See p 895 in Chen et al [2) 0

Two notable observations are obtained from the CGPS algorithm One is that the desired performance (4) sometimes holds but (3) violates The other is that the schedule 1t2 does not necessarily represent an imshyprovement on 1t1 in its makespan Detailed descriptions are presented in the following

We now concern the necessary and sufficient conditions for the desired performance (4) In Lemma 2 we can recognize that condition (3) is a sufficient for the desired performance (4) However as Chen et al [2) point out (4) sometimes holds also when (3) is violated since the lower bound used in Lemma 2 is not sufficient sharp In other words (3) is a sufficient but not necessary condition for (4) Thus we propose a modification to the CGPS algorithm by changing condition (3) While we derive new lower bounds we shall be concerned with the trade-off between the sharpness of lower bounds and their computashytional requirements As indicated in Chen et al [2] the lower bounds used in the analysis are not sufficient strong Then we shall propose some stronger lower bounds with a little extra computational requirement One way improving upon lower bound of the optimal schedule is to apply two values of v in (2)

LEMMA 4 If fl and v are critical jobs in 1t1 and fl lt v then

(a) Cmai1tmiddot) ~ plusmnak + i Ck + max b~ + ~ Ck plusmnak + bv ) (6) kl kv k=1l k=~+l

(b) We can replace (3) by

b(Ni) + bll + bv - maX[bll + ~ Ck plusmnak + b) ~ 23 beN) (7) k=~ k=IHl

(c) If condition (3) holds then (7) holds

PROOF After applying (2) with v fl and v v gives

Inequality (6) is now derived

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To prove part (b) we subtract (6) from (1) to obtain

Cmai 1t l) - Cmai 1tmiddot) $ a(N1) + all + bit + b(Nz + by + cy+ c(Na)

Substituting (7) yields

Cmai1tl) - Cmai1tmiddot)$ 23 b(N)

The desired inequality (4) is now deduced from C (1t) b(N) Somax that we can replace (3) by (7)

Finally since

b(N2) + bit + bv - maxi bit + ~ Ck I ak + by ) w1t kdegIt+1

$ b(N2) + bit + by - max blL by)

== b(N2) + min bit by

it follows that if (3) holds then (7) holds This completes the proof of the lemma 0

Another approach for deriving a sharper lower bound of the optimal schedule is using (2) From the proof of Lemma 1 in Chem et al [2] the lower bound of an optimal schedule is

(8)

Iy n )where max L (Jk + L Pk 11 $ v $ n is the makespan of the artificial

k=l k=y

two-machine FSS with processing times Ctk == ak + bk and Pk = bk + Ck

for kEN It follows that condition (3) can be replaced by

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328 H C TANG

It is recognized that the lower bound (8) considers all values of v in (2) but the lower bound (6) only considers two of its values This implies that the lower bound (8) is stronger than (6) Therefore condition (9) is less restrictive than condition (7) This result is stated formally below

LEMMA 5 If condition (7) holds then (9) holds

Therefore among the three conditions condition (9) is the least restrictive from Lemma 4 and Lemma 5

The second notable observation is that the schedule 1t2 does not always improve the makespan of the schedule 1tl In other words the makespan of1t2 sometimes is larger than or equal to the makespan Of1tl

Taking into consideration the above pieces of information our conclusion is that eight cases arise through the various possible comshybinations For condition (3) ~s an example these cases are

(C1) 11 =v

(C2) 11 lt v and (3) holds

(C3) 11 lt v (3) is violated Cmai1tl) gt Cmai1t0 and (4) holds

(C4) 11 lt v (3) is violated Cmai1tl) gt Cmai1t2) and (4) is violated (10)

(C5) 11 lt v (3) is violated Cmai1tl) = Cmai1t2) and (4) holds

(C6) 11 lt v (3) is violated Cmai1tl) = Cmai1t0 and (4) is violated

(C7) 11 lt v (3) is violated Cmai1tl) lt Cmai1t2) and (4) holds

(C8) 11 lt v (3) is violated Cmai1tl) lt Cmai1t2) and (4) is violated

Similarly for other two proposed conditions we replace (3) by (7) and (9) respectively

3 EVALUATION MEASURES

To evaluate the performance of the CGPS algorithm this paper provides a number of evaluation measures in three respects The first respect refers to the effectiveness of the CGPS algorithm The second respect is concerned with the comparison of the three conditions satisfyshying the desired performance (4) The final respect is apout comparing with the heuristics developed by Nawaz Enscore and Ham (NEH) [10] and by Campbell Dudek and Smith (CDS) [1] which are the best two among the constructive algorithms for the FSS with minimum makespan criterion

Firstly to measure the effectiveness of the CGPS algorithm two evaluation measures are adopted In Lemma 2 for the case that

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l == v an optimal schedule is found from the CGPS algorithm It follows that the percentage of schedules that are equal to the optimal ones is used to measure its effectiveness This proportional optimum is defined as

P [(C1)Tl 100 (11)

where (C1) denotes the number of times the schedule Xl that is equal to an optimal one in T problem instances Another evaluation measshyure is the empirical average-case performance ratio For the algorithm A and problem instance Z its quality is measured by the ratio

(12)

It is recognized that the worst-case performance ratio provides a performance guarantee which is valid for all problem instances As stated in Chen et al [2] the CGPS algorithm is by far the best one with the worst-case performance ratio as the performance measure However the Operations Research practitioners also concern the comshyputational experience of the CGPS algorithm Thus we adopt the empirical average-case performance ratio

T

~A L llA(Zi)T (13) i=l

to measure its performance empirically For notational convenience the argument Z will be omitted in Cmaix Z) and Cmax(x Z) if it is not necessary in the following

Secondly to compare conditions (3) (7) and (9) satisfying the deshysired performance (4) three evaluation measures are proposed We only consider condition (3) since the other conditions are treated simishylarly It is recognized that the desired performance (4) sometimes holds but condition (3) violates This implies that the percentage of equivalent relation between condition (3) and the desired performance (4) can be used as an evaluation measure This proportional equivashylency can be defined as

i _[ (C2) + (C4) +(C6) + (C8) ] E - (C2)+(C3)+(C4)+(C5)+(C6)+(C7)+(C8) 100

for i == 3 7 9 (14)

where (C2) + (C4) + (C6) + (C8) is thee number of times the equivalent relation between the desired performance (4) and condition (3) The other evaluation measures concern an improvement on the makespan of the schedule Xl Two evaluation measures are distinshy

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330 HCTANG

guished One is the relative error of the schedule 1tl from the schedule 1tH in terms of the 11Z)

i [ Cmax(1tH Z)Cmax(1t Z) 1R 1- 100 Cmax(1tl Z)CmaxC1t Z)

Cmax(1tH Z) ] (15) 1 - C ( l Z) 100 for pound 3 7 9[ 1tmax

The other is an improvement on the makespan of the schedule 1t1 in terms of the problem instance The definition of this proportional imshyprovement is

Ii _ [ (C3) + (C4) ] - (C3) +(C4) +(C5) +(C6) +(C7) +(C8) 100

for i 3 7 9 (16)

where (C3) + (C4) is the number of times the schedule 1tH that imshyproves the makespan of the schedule 1tl

Finally in concern with the comparison of the CGPS NEH and CDS algorithms two evaluation measures are adopted One measure is based on the empirical average-case performance ratio (13) The other measure is that the percentage of problem instances that the A algorithm is superior to the B algorithm in its makespan This proporshytional superiority can be defined as

A _[ (A) ] (17)SB - (A) +(AB) + (B) 100

where (A) and (B) are the number of times the makespan better by A and B algorithms respectively and (AB) is the number of times the makespan equal by A and B algorithms Denote E~ the percentage of problem instances that the A algorithm is equal to the B algorithm

Therefore there are six evaluation measures adopted in this paper We use (11) and (13) to measure the effectiveness of the CGPS algoshyrithm To compare conditions (3) (7) and (9) satisfying the desired pershyformance (4) three evaluation measures (14) (15) and (16) are adopted To compare the CGPS algorithm with the NEH algorithm as well as the CDS algorithm two evaluation measures (13) and (17) are used

4 SIMULATION EXPERIMENTS

To get an idea of the CGPS algorithm from the empirical perspecshytive three simulation experiments are conducted in this paper The first simulation experiment examines the effectiveness of the CGPS algoshy

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rithm The second simulation experiment concerns the empirical comparishyson of conditions (3) (7) and (9) which are the sufficient for the desired performance (4) The third simulation experiment conducts the comparison of the CGPS algorithm with the NEH and CDS algorithms

The number of machines considered is three and the numbers of jobs considered are 3 4 5 6 7 8 9 10 15 20 30 40 50 100 200 300 400 500 600 700 800 900 and 1000 The problem size is dishyvided into two classes One is the small problem for the 3 4 5 6 7 8 9 and 10 job problems The other is the large problem for the 15 20 30 40 50 100 200 300 400 500 600 700 800 900 and 1000 job problems One hundred problems are generated for each job The processing times for each problem are randomly generated integers uniformly distributed between 1 and 100 A more portable random number generator Xn == 16807xH(mod 231

- 1) is adopted using same to generate the random values for each problem The whole simushy

lation experiments are subjected to extensive testing 13800 problems A number of evaluation measures described in previous section

are used for the three simulation experiments We adopt the evaluation measures (11) and (13) for the first simulation experiment (14) (15) and (16) for the second simulation experiment (13) and (17) for the third simulation experiment respectively The whole computation is conducted on a 266 MHz Pentinum II PC using Microsoft Visual C++ compiler under Microsoft Windows 98 operating system

To obtain an optimal schedule for the empirical average-case pershyformance ratio the branch-and-bound algorithm with two-machine lower bound rule proposed by Tang [16] is applied This proposed twoshymachine lower bound is a modification to the algorithms of Lageweg et al [7] and Potts [11] and is shown to be more efficient Whenever a problem is not solved after 100000 nodes have been generated comshyputation is stopped In this case the optimal makespan is replaced by the best-known makespan Thus the empirical average-case pershyformance ratio is underestimated

The first simulation experiment is concerned with the effectiveness of the CGPS algorithm Detailed results are presented in Table 1 where Min denotes the minimum value of proportional optimum or empirical average-case performance ratio Max and Avg the corresshyponding maximum and average values respectively The proportional optimum is 503478 on the average In other words 503478 of the initial permutation schedules generated by the CGPS algorithm are the optimal schedules especially for the large problems the empirical average-case performance ratio is concerned Table 1 lists the percentage POP of problem instances that the optimal schedules are found by the

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332 H C TANG

branch-and-bound algorithm with Tangs two-machine lower bound rule [16] The average percentage Popt is 962609 Especially in the case of small problems the branch-and-bound algorithm can always find the optimal schedules within 100000 nodes generated Therefore it is appropriate to adopt the empirical average-ca~e performance ratio to measure the effectiveness of the CGPS algorithm The empirical average-case performance ratio of the initial permutation schedule is in the range of 10011 and 10355 and is 10156 on the average While the empirical average-case performance ratio of the CGPS algorithm is in the range of 10001 and 10282 and is 10115 on the average These values are always smaller than the performance guarantee 53 of the CGPS algorithm

Table 1 Results of simulations for the effectiveness of the COPS

Job P Popt ~1t1

3 59 100 10139 4 53 100 10185 10148 5 40 100 10309 10264 6 40 100 10317 10282 7 33 100 10318 10262 8 26 100 10355 10270 9 36 100 10355 10282 10 35 100 10337 10255 15 44 84 10299 10243 20 42 82 10300 10183 30 53 90 10157 10106 40 51 94 10132 10085 50 48 95 10128 10065 100 51 93 10083 10032 200 56 97 10040 10017 300 69 99 10021 10007 400 62 98 10022 10004 500 57 96 10018 10002 600 57 99 10017 10002 700 64 96 10013 10001 800 60 99 10012 10002

(Table 1 Contd)

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lOOO 60 97 10001

Small problems Max

Avg 59

402500 lOO lOO

10355 10289

10139 10282 10238

Large problems

Min Max

42 82 10011 10300

10001 10243 10050

Overall problems Max 69

503478 100

922609 10355 10156

10001 10282 10115

The second experiment refers to the comparison of conditions (3) (7) and (9) in terms of the proportional equivalency (14) the relative error (15) and the proportional improvement (16) Table 2 gives the reshysults Notably the number of times of the cases C3 C4 C5 C6 C7 and C8 for conditions (7) and (9) are all zeros In other words the CGPS algorithm with condition (7) or (9) only generates the initial permutashytion schedule It follows that the proportional equivalency is lOO the relative error is zero and the proportional improvement is not availshyable (NA) for each problem These results indicate that the initial pershymutation schedule never violates the worst-case performance ratio of 53 if we adopt the CGPS algorithm with condition (7) or (9)

In the case of condition (3) viz the original CGPS algorithm the proportional equivalency is 2695 on the average This value indicates that 7305 of the desired performance (4) holds also when condition (3) is violated Therefore condition (3) is too restrictive especially for the large problems In concern with the improvement on the makesshypan of 1tl the relative error is 03940 and the proportional improveshyment is 647152 on the average This implies that 647154 of the permutation schedule 1t2 has improved on the initial permutation schedule in its makespan However the quality of improvement made by 1t2 over 1tl is only 03940 in terms of the empirical average-case performance ratio Therefore condition (3) in the CGPS algorithm is more restrictive and the improvement in the average-case performance ratio is so marginal from the empirical point of view

The third experiment concerns the comparison of the CGPS algoshyrithm with the NEH algorithm as well as the CDS algorithm Comparashytive results are shown in Table 3 On basis of the empirical

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ltgtl

ltgtl

Tab

le 2

C

om

para

tiv

e r

esu

lts

for

co

nd

itio

ns

(3)

(7)

an

d (

9)

--------------shy

Job

C

ondi

tion

s E

i R

i Ii

C

1 C

2 C

3 C

4 C

5 C

6 C

7 C

8 -----shy

(3)

59

39

0 0

2 0

0 0

951

220

0

0000

000

00

3 (7

) 59

41

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 59

41

0

0 0

0 0

0 10

000

00

0

0000

NA

-shy

(3)

53

39

4 0

0 0

4 0

829

787

0

3633

500

000

4 (7

) 53

47

0

0 0

0 0

0 10

000

00

0

0000

NA

53

47

0

0 0

0 0

0 10

000

00

0

0000

NA

---shy

-----------shy

(3)

40

44

9 0

1 0

6 0

733

333

0

4365

562

500

5 (7

) 40

60

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 40

eo

0

0 0

0 0

0 10

000

00

0

0000

NA

(3

) 40

4

7

5 0

0 0

8 0

783

333

0

3392

384

600

6 (7

) 40

6

0

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

40

60

0

0 0

0 0

0 10

000

00

0

000

0

NA

-----------shy

(3)

33

37

10

0

0 0

20

0 55

223

9

054

27

33

330

0

7 (7

) 33

6

7

0 0

0 0

0 0

100

0000

000

00

N

A

p (9

) 33

6

7

0 0

0 0

0 0

100

0000

000

00

N

A

0 ------~

(Tab

le 2

Con

td)

gtshy Z

C

)

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Con

diti

ons

~ z

Job

E

i R

i Ii

gt

C

l C

2 C

3 C

4 C

5 C

6 C

7 C

8 S CD

26

40

16

0 1

0 17

0

540

541

0

8209

470

600

CD

0 gt1j

8 (7

) 26

74

0

0 0

0 0

0 10

000

00

0

0000

NA

gt-3 r

(9)

26

74

0 0

0 0

0 0

100

0000

000

00

N

A

ttl

()

36

29

12

0 1

0 22

0

453

125

0

7050

342

900

0 0

9

(7)

36

64

0 0

0 0

0 0

100

0000

000

00

N

A

CD

t

(9)

36

64

0 0

0 0

0 0

100

0000

000

00

N

A

0 ~

0 0(3

) 35

29

19

0

0 0

17

0 44

615

4

079

33

52

780

0

gt-3 r10

(7

) 35

65

0

0 0

0 0

0 10

000

00

0

0000

NA

s

(9

) 35

65

0

0 0

0 0

0 10

000

00

0

0000

NA

(3

) 44

12

20

0

0 0

24

0 21

428

6

054

37

45

450

0

15

(7)

44

56

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

44

56

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

42

9 27

0

0 0

22

0 15

517

2

113

59

55

100

0

20

(7)

42

58

0 0

0 0

0 0

100

0000

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101

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-----

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average-case performance ratio the NEH algorithm is the best one folshylowed by the CDS algorithm and then by the CGPS algorithm As comshypared with the CDS algorithm in terms of the proportional superiority 87391 of problem instances better by the CGPS algorithm 694348 of problem instances equal by the CGPS and CDS algorithms and 218261 of problem instances better by the CDS algorithm on the average It follows that the CDS algorithm is better than the CGPS alshygorithm especially for the large problems Similarly the NEH algorithm is better than the CGPS algorithm and the NEH algorithm is better than the CDS algorithm especially for the small problems Therefore we have the same conclusion about these heuristics in terms of the empirishycal average-case performance ratio and proportional superiority

To sum up 503478 ofthe initial permutation schedules generated by the CGPS algorithm are the optimal schedules Among the 496522 of non-optimal schedules 647154 of the permutation schedules 1t2 improve the makespan of the initial permutation schedule However the improvement made by 1t2 is only 03940 over 1tl in terms of the empirical average-case performance ratio Moreover compared with the NEH and CDS algorithms the CGPS algorithm is the worst one in terms of the empirical average-case performance ratio and proportional superiority These imply that the CGPS algorithm is not good enough for applications

5 CONCLUSION

In this paper the 3FSS with minimum makespan criterion is considered Theoretically the heuristic algorithm proposed by Chen et a1 [2] has the best worst-case performance ratio of 53 This paper evaluates the performance of the CGPS algorithm from the empirical perspective Three simulation experiments are performed to analyze its performance in terms of the six evaluation measures on a total of 13800 problems Four conclusions can be drawn from this paper Firstly in the CGPS algorithm 503478 of the initial permutation schedules are the optimal ones 321326 of the permutation schedshyules 1t2 improve the makespan of nl and 175196 of the permutation schedules n2 do not improve their makespan Secondly the empirical average-case performance ratio of initial permutation schedule genershyated by the CGPS algorithm is always smaller than the performance guarantee 53 developed by Chen et al [2] Its empirical average-case performance ratio is in the range of 10011 and 10355 and is 10156 on the average Thirdly the permutation schedule 1t2 improves 1tl in terms of the empirical average-case performance ratio by the non-significant percentage 03940 Fourthly among the three heuristic algorithms the

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344 H C TANG

NEH algorithm is the best one in terms of both empirical average-case performance ratio and proportional superiority followed by the CDS alshygorithm and then by the CGPS algorithm Consequently the CGPS algoshyrithm is not suitable for the 3FSS with minimum makespan criterion

REFERENCES

l H G Campbell R A Dudek and M L Smith A heuristic algorithm for the n-job tn-machine sequencing problem Management Science Vol 16 (1970) pp 630-637

2 B Chen C A Glass C N Potts and V A Strusevich A new heuristic for threeshymachine flow shop scheduling Operations Research Vol 44 (1996) pp 891-898

3 R W Conway W L Maxwell and L W Miller Theory of Scheduling AddisonshyWesley Reading MA 1967

4 R A Dudek S S Panwalkar and M L Smith The lessons of flowshop scheduling research Operations Research Vol 40 (1992) pp 7-13

5 M R Garey D S Johnson and R Sethi The complexity of flowshop and jobshop scheduling Mathematics Operations Research Vol 1 (1976) pp 117-129

6 S M Johnson Optimal two- and three-stage production schedules with setup times included Naval Research Logistic Quarterly Vol 1 (1954) pp 61-68

7 B J Lageweg J K Lenstra and A H G Rinnooy Kan A general bounding scheme for the permutation flow-shop problem Operations Research Vol 26 (1978) pp 53-67

8 E L Lawler J K Lenstra A H G Rinnooy Kan and D B Shmoys Sequencing and Scheduling Algorithms and Complexity in S C Graves A H G Rinnooy

-Kan and P H Zipkin Handbooks in Operations Research and Management Science Vol 4 Logistics of Production and Inventory North Holland Amsterdam 1993 pp 445-522

9 J K Lenstra A H G Rinnooy Kan and P Brucker Complexity of machine scheduling problems Annals Discrete Mathematics Vol 1 (1977) pp 343-362

10 M Nawaz E E Enscore Jr and I Ham A heuristic algorithm for the m-machine n-job flow-shop sequencing problem OMEGA Vol 11 (1983) pp 91-95

II C N Potts An Adaptive branching rule for the permutation flow-shop problem European Journal of Operational Research Vol 5 (1980) pp 19-25

12 A H G Rinnooy Kan Machine scheduling problems classification complexity and computations Nijhoff The Hague 1976

13 H Rock and G Schmidt Machine aggregation heuristics in shop scheduling Methods of Operations Research Vol 45 (1983) pp 303-314

14 C Smutnicki Some results of the worst-case analysis for flow shop scheduling European Journal of Operational Research Vol 109 (1998) pp 66-87

15 S M A Suliman A two-phase heuristic approach to the permutation flow-shop scheduling problem International Journal of Production Economics Vol 64 (2000) pp 143-152

16 H C Tang A new lower bonding rule for permutation flow shop scheduling Journal of Information amp Optimization Sciences Vol 22 (2001) pp 249-257

17 H C Tang A modification to the CGPS algorithm for three-machine flow shop scheduling Journal of Information amp Optimization Sciences Vol 22 (2001) pp 321-331

Received January 2001

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An experimental analysis of the CGPS algorithm for the three-machine flow shop scheduling with minimum makespan criterion

Hui-Chin Tang

Department of Industrial Engineering and Management

Cheng Shiu Institute of Technology

Kaohsiung 83305

Taiwan

Republic of China

ABSTRACT The algorithm developed by Chen Glass Potts and Strusevich (CGPS) is by far

the best one in terms of the worst-case perfurmance ratio for the three-machine flow shop scheduling (3FSS) with minimum makespan criterion This paper focuses on the experimental analysis of the CGPS algorithm Three simulation experiments are conshyducted to compare and evaluate its performance in terms of six evaluation measures It is shown that the CGPS algorithm is not empirically preferred for the 3FSS with minimum makespan criterion

1 INTRODUCTION

Since the publication of Johnsons 1954 paper on the two-machine flow shop scheduling (FSS) [6] the growth in interest in the FSS problem has been quite dramatic [3 4 8 12] The FSS is a productionshyplanning problem that schedules 11 jobs on m sequential machines At any time each machine processes at most one job and each job is processed on at most one machine The uninterrupted processing time of each job on each machine is given Among many regular criteria this paper is concerned with the makespan Since it is the easiest crishyterion to use and represents other beneficial characteristics such as maximum machine utilization of a production line [4] Thus this paper considers the FSS with minimum makespan criterion

An intfgtresting special case is the three-machine FSS (3FSS) [2 17] The 3FSS has many properties One property is that there exists an

Journal of Information amp Optimization Sciences Vol 23 (2002) No2 pp 323-344 copy Analytic Publishing Co 0252middot266702 $200+25

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324 H C TANG








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N3 =v+ 1 n





V It












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326 HCTANG












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Finally since






(8)


k=l k=y



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328 H C TANG






(C1) 11 =v












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P [(C1)Tl 100 (11)


(12)


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i _[ (C2) + (C4) +(C6) + (C8) ] E - (C2)+(C3)+(C4)+(C5)+(C6)+(C7)+(C8) 100

for i == 3 7 9 (14)


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330 HCTANG





Ii _ [ (C3) + (C4) ] - (C3) +(C4) +(C5) +(C6) +(C7) +(C8) 100

for i 3 7 9 (16)



A _[ (A) ] (17)SB - (A) +(AB) + (B) 100





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t 22

24 2

1 D

ecem

ber

2014









Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

332 H C TANG



Job P Popt ~1t1

3 59 100 10139 4 53 100 10185 10148 5 40 100 10309 10264 6 40 100 10317 10282 7 33 100 10318 10262 8 26 100 10355 10270 9 36 100 10355 10282 10 35 100 10337 10255 15 44 84 10299 10243 20 42 82 10300 10183 30 53 90 10157 10106 40 51 94 10132 10085 50 48 95 10128 10065 100 51 93 10083 10032 200 56 97 10040 10017 300 69 99 10021 10007 400 62 98 10022 10004 500 57 96 10018 10002 600 57 99 10017 10002 700 64 96 10013 10001 800 60 99 10012 10002

(Table 1 Contd)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014


lOOO 60 97 10001

Small problems Max

Avg 59

402500 lOO lOO

10355 10289

10139 10282 10238

Large problems

Min Max

42 82 10011 10300

10001 10243 10050


503478 100

922609 10355 10156

10001 10282 10115




Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

ltgtl

ltgtl

Tab

le 2

C

om

para

tiv

e r

esu

lts

for

co

nd

itio

ns

(3)

(7)

an

d (

9)

--------------shy

Job

C

ondi

tion

s E

i R

i Ii

C

1 C

2 C

3 C

4 C

5 C

6 C

7 C

8 -----shy

(3)

59

39

0 0

2 0

0 0

951

220

0

0000

000

00

3 (7

) 59

41

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 59

41

0

0 0

0 0

0 10

000

00

0

0000

NA

-shy

(3)

53

39

4 0

0 0

4 0

829

787

0

3633

500

000

4 (7

) 53

47

0

0 0

0 0

0 10

000

00

0

0000

NA

53

47

0

0 0

0 0

0 10

000

00

0

0000

NA

---shy

-----------shy

(3)

40

44

9 0

1 0

6 0

733

333

0

4365

562

500

5 (7

) 40

60

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 40

eo

0

0 0

0 0

0 10

000

00

0

0000

NA

(3

) 40

4

7

5 0

0 0

8 0

783

333

0

3392

384

600

6 (7

) 40

6

0

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

40

60

0

0 0

0 0

0 10

000

00

0

000

0

NA

-----------shy

(3)

33

37

10

0

0 0

20

0 55

223

9

054

27

33

330

0

7 (7

) 33

6

7

0 0

0 0

0 0

100

0000

000

00

N

A

p (9

) 33

6

7

0 0

0 0

0 0

100

0000

000

00

N

A

0 ------~

(Tab

le 2

Con

td)

gtshy Z

C

)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

Con

diti

ons

~ z

Job

E

i R

i Ii

gt

C

l C

2 C

3 C

4 C

5 C

6 C

7 C

8 S CD

26

40

16

0 1

0 17

0

540

541

0

8209

470

600

CD

0 gt1j

8 (7

) 26

74

0

0 0

0 0

0 10

000

00

0

0000

NA

gt-3 r

(9)

26

74

0 0

0 0

0 0

100

0000

000

00

N

A

ttl

()

36

29

12

0 1

0 22

0

453

125

0

7050

342

900

0 0

9

(7)

36

64

0 0

0 0

0 0

100

0000

000

00

N

A

CD

t

(9)

36

64

0 0

0 0

0 0

100

0000

000

00

N

A

0 ~

0 0(3

) 35

29

19

0

0 0

17

0 44

615

4

079

33

52

780

0

gt-3 r10

(7

) 35

65

0

0 0

0 0

0 10

000

00

0

0000

NA

s

(9

) 35

65

0

0 0

0 0

0 10

000

00

0

0000

NA

(3

) 44

12

20

0

0 0

24

0 21

428

6

054

37

45

450

0

15

(7)

44

56

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

44

56

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

42

9 27

0

0 0

22

0 15

517

2

113

59

55

100

0

20

(7)

42

58

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

42

58

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

53

6 19

0

0 0

22

0 12

766

0

050

21

46

340

0

30

(7)

53

47

0 0

0 0

0 0

100

0000

000

00

N

A

53

47

0 ()

0 0

0 0

100

0000

000

00

N

A

CJ

) C

J)

Of

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

w

Job

--~~

~~-

~--

Ri

Ii

w

CIl

Cl

C2

C

3 C

4

C5

C6

C7

C

8 -----------shy

(3)

51

3 21

0

1 0

24

0

61

22

4

0

46

39

456

500

40

(7

) 51

4

9

0 0

0 0

0 0

10

00

00

0

0

00

00

NA

(9

) 51

4

9

0 -----_

_

-shy

0 0

0 --shy-----~~~~

0 0

-----------shy

10

00

00

0

0

00

00

---------shy

NA

(3

) 4

8

4 33

0

0 0

15

0

769

23

0

62

20

68

75

00

50

(7

) 4

8

52

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

48

5

2

0 0

0 0

0 0

100

0000

00

00

0

N

A

51

4 3

7

0 0

0 8

0 8

16

33

05

05

8

8

22

20

0

10

0

(7)

51

49

0

0 0

0 0

0 10

000

00

0

00

00

NA

(9

) 51

4

9

0 0

0 0

0 0

100

0000

00

00

0

N

A

----------shy

(3)

56

0

35

0 0

0 9

0 0

00

00

02

29

1

79

550

0

20

0

(7)

56

4

4

0 0

0 0

0 0

100

0000

00

00

0

N

A

(9)

56

4

4

0 0

0 0

0 0

100

0000

00

00

0

N

A

69

2

24

0

0 0

5 0

64

51

6

0

13

97

82

76

00

30

0

(7)

69

31

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

(9)

69

31

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

(3)

62

1

35

0

0 0

2 0

26

31

6

0

17

96

94

59

00

~

40

0

(7)

62

3

8

0 0

0 0

0 0

10

00

00

0

0

00

00

NA

0

(9)

62

3

8

0 0

0 0

0 0

100

0000

00

00

0

N

A

fja

tJte

2-C

onat

)

gt-3

)shy z Cl

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

0gtshy

Con

diti

ons

Job

E

i R

i Ii

C

l C

2 C

3 C

4 C

5 C

6 C

7 C

8 ~ rt

J gt-

lt57

0

38

0 0

0 5

0 0

0000

015

97

88

370

0

rtJ

j

500

(7)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

0 3

(9)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

tr1

tlj

0(3

) 57

1

39

0 0

0 3

0 2

3256

014

97

92

860

0

0 rtJ

60

0

(7)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

~ 57

43

0

0 0

0 0

0 10

000

00

0

0000

NA

0 0

1 34

0

gt-lt

(3)

64

0 0

1 0

277

78

0

1198

971

400

tO

3

700

(7)

64

36

0 0

0 0

0 0

100

0000

000

00

N

A

tr1 ~

(9)

64

36

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

60

2 38

0

0 0

0 0

500

00

0

0999

100

0000

800

(7)

60

40

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

60

40

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

62

0 38

0

0 0

0 0

000

00

0

0999

100

0000

900

(7)

62

38

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

62

38

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

60

0 39

0

0 0

1 0

000

0

010

99

97

500

0

1000

(7

) 60

40

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 60

40

0

0 0

0 0

0 10

000

00

0

0000

NA

w

w

(T

able

2 C

ontd

)

-l

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

------

CIJ

Con

diti

ons

CIJ

Job

E

i R

i Ii

O

J

C1

C2

C3

C4

C

5 C

6 C

7

C8

Min

44

615

4

000

00

0

0000

Sm

all

(3

) M

ax

951

220

0

8209

562

500

pro

ble

ms

Avg

66

121

6

050

01

39

021

3

_

Min

0

0000

009

99

45

450

0

Lar

ge

(3

) M

ax

214

286

1

1359

100

0000

p

rob

lem

s A

vg

605

84

0

3374

784

187

--

-_

__

---

Min

0

0000

000

00

0

0000

Ov

eral

l

(3)

Max

95

122

0

113

59

10

000

00

pro

ble

ms

Avg

26

950

0

039

40

64

715

2

tr1

()

gt-3 ~ Q

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

gtshyT

able

3

z C

om

par

ativ

e re

sult

s fo

r th

e C

GP

S

CD

S

an

d N

EH

alg

ori

thm

s ~

Job 3

4

5

6

7

8

9

10

15

20

30

40

50

100

200

101

39

101

48

102

64

102

82

102

62

102

7

102

82

102

55

102

43

101

83

101

06

100

85

100

65

100

32

100

17

~CDS

100

96

101

28

102

14

102

32

102

46

102

15

102

04

102

04

101

78

101

53

100

99

100

63

100

55

100

35

100

17

~~--------------

~NElI

100

1

100

39

100

53

100

54

100

48

100

72

100

50

100

47

100

25

100

33

100

08

100

05

100

06

100

02

100

01

(Tab

le 3

Con

td)

lfl

gt-

lfl

0 tJ r t=J

0 0 i


w

w

to

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

-----

---

co

jgt

~CGPS

~CDS

~NE

H 0

300

100

07

100

11

100

00

400

100

04

100

06

100

00

500

100

02

100

06

100

00

600

100

02

100

03

100

00

700

100

01

100

02

100

00

800

100

02

100

02

100

00

900

100

01

100

04

100

00

1000

1

0001

1

0003

1

0000

Min

1

0139

1

0096

1

0010

Sm

all

pro

ble

ms

Max

1

0282

1

0246

1

0072

Avg

1

0238

1

0192

1

0047

Min

1

0001

1

0002

1

0000

Lar

ge

pro

ble

ms

Max

1

0243

1

0178

1

0033

Avg

1

0050

1

0042

1

0005

Min

1

0001

1

0002

1

0000

r

Ov

eral

l p

rob

lem

s M

ax

102

82

102

46

100

72

0 -3A

vg

101

15

100

95

100

20

p Z

(Tab

le 3

Con

td)

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

lgtT

able

3 (

Con

td)

Z

--------

_shy

SCG

PS

EQ

CG

PS

SCD

S SC

GP

S E

QC

GP

S SN

EH

SN

EH

EQ

IjE

H

SCD

S --

~ Jo

b C

DS

CDS

CG

PS

NEH

N

EH

CG

PS

CD

S CD

S N

EH

en

en

3 0

91

9

0

83

17

12

88

0

0 gtzj

4 2

8

7

11

2

70

28

21

76

3

gt-l

[1j

5 2

82

16

4

58

38

28

66

6

0 0 1

j6

3

77

20

1

51

48

40

56

4

en

7 5

75

20

5

43

52

45

50

5

~ 0 0

8 6

70

24

8

35

57

44

47

9

~

gt-l

9 5

6

7

28

2

40

58

46

46

8

10

7

68

25

5

40

55

42

50

8

15

7

70

23

2

45

53

46

50

4

20

8

65

27

4

46

50

37

58

5

30

8

74

18

0

57

43

35

63

2

40

7

72

21

3

53

44

29

62

9

50

13

62

25

4

49

47

31

59

10

10

0

15

6

0

25

1

52

47

27

71

2

20

0

17

64

19

2

55

43

26

68

6

30

0

12

74

14

7

63

30

17

74

9

w

(T

able

3 C

ontd

)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

Job

S

co

Ps

CD

S E

QC

GP

SC

DS

SCD

S C

GPS

SC

GP

S N

EH

E

QC

GP

SN

EH

S

NE

H

CG

PS

NE

H

SCD

S E

Q

EH

CD

S SC

DS

NE

Il

N

400

14

63

23

5

58

37

14

81

5

500

13

62

25

1

57

42

20

78

2

60

0

9

61

30

4

54

42

12

82

6

700

11

66

23

8

56

36

13

79

8

80

0

10

63

27

4

57

39

14

82

4

900

16

63

21

2

60

38

17

81

2

1000

11

61

28

4

57

39

12

82

6

Sm

all

pro

ble

ms

Min

Max

Avg

0

67

9

7

91

28

375

00

77

125

0

191

250

0

8

337

50

35

17

83

58

525

000

44

1250

12

46

347

500

46

88

598

750

0

9

537

50

Lar

ge

pro

ble

ms

Min

Max

7

17

60

74

14

30

0

8

45

63

30

53

12

46

50

82

2

10

114

00

65

3333

2

326

67

3

4000

546

000

42

0000

233

333

71

333

3

533

33

Ov

eral

l p

rob

lem

s

Min

Max

Avg

0

60

9

17

91

30

873

91

69

434

8 2

182

61

0

8

339

13

35

17

83

58

538

696

42

739

1

12

46

273

043

~~~--~--

46

0

88

10

673

478

5

3478

c 0 ~ gtshy L

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014




5 CONCLUSION


Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

344 H C TANG


REFERENCES




















Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

324 H C TANG








Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014





N3 =v+ 1 n





V It












Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

326 HCTANG












Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014







Finally since






(8)


k=l k=y



Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

328 H C TANG






(C1) 11 =v












Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014



P [(C1)Tl 100 (11)


(12)


T




i _[ (C2) + (C4) +(C6) + (C8) ] E - (C2)+(C3)+(C4)+(C5)+(C6)+(C7)+(C8) 100

for i == 3 7 9 (14)


Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

330 HCTANG





Ii _ [ (C3) + (C4) ] - (C3) +(C4) +(C5) +(C6) +(C7) +(C8) 100

for i 3 7 9 (16)



A _[ (A) ] (17)SB - (A) +(AB) + (B) 100





Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014









Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

332 H C TANG



Job P Popt ~1t1

3 59 100 10139 4 53 100 10185 10148 5 40 100 10309 10264 6 40 100 10317 10282 7 33 100 10318 10262 8 26 100 10355 10270 9 36 100 10355 10282 10 35 100 10337 10255 15 44 84 10299 10243 20 42 82 10300 10183 30 53 90 10157 10106 40 51 94 10132 10085 50 48 95 10128 10065 100 51 93 10083 10032 200 56 97 10040 10017 300 69 99 10021 10007 400 62 98 10022 10004 500 57 96 10018 10002 600 57 99 10017 10002 700 64 96 10013 10001 800 60 99 10012 10002

(Table 1 Contd)

Dow

nloa

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by [

Uni

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ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014


lOOO 60 97 10001

Small problems Max

Avg 59

402500 lOO lOO

10355 10289

10139 10282 10238

Large problems

Min Max

42 82 10011 10300

10001 10243 10050


503478 100

922609 10355 10156

10001 10282 10115




Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

ltgtl

ltgtl

Tab

le 2

C

om

para

tiv

e r

esu

lts

for

co

nd

itio

ns

(3)

(7)

an

d (

9)

--------------shy

Job

C

ondi

tion

s E

i R

i Ii

C

1 C

2 C

3 C

4 C

5 C

6 C

7 C

8 -----shy

(3)

59

39

0 0

2 0

0 0

951

220

0

0000

000

00

3 (7

) 59

41

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 59

41

0

0 0

0 0

0 10

000

00

0

0000

NA

-shy

(3)

53

39

4 0

0 0

4 0

829

787

0

3633

500

000

4 (7

) 53

47

0

0 0

0 0

0 10

000

00

0

0000

NA

53

47

0

0 0

0 0

0 10

000

00

0

0000

NA

---shy

-----------shy

(3)

40

44

9 0

1 0

6 0

733

333

0

4365

562

500

5 (7

) 40

60

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 40

eo

0

0 0

0 0

0 10

000

00

0

0000

NA

(3

) 40

4

7

5 0

0 0

8 0

783

333

0

3392

384

600

6 (7

) 40

6

0

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

40

60

0

0 0

0 0

0 10

000

00

0

000

0

NA

-----------shy

(3)

33

37

10

0

0 0

20

0 55

223

9

054

27

33

330

0

7 (7

) 33

6

7

0 0

0 0

0 0

100

0000

000

00

N

A

p (9

) 33

6

7

0 0

0 0

0 0

100

0000

000

00

N

A

0 ------~

(Tab

le 2

Con

td)

gtshy Z

C

)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

Con

diti

ons

~ z

Job

E

i R

i Ii

gt

C

l C

2 C

3 C

4 C

5 C

6 C

7 C

8 S CD

26

40

16

0 1

0 17

0

540

541

0

8209

470

600

CD

0 gt1j

8 (7

) 26

74

0

0 0

0 0

0 10

000

00

0

0000

NA

gt-3 r

(9)

26

74

0 0

0 0

0 0

100

0000

000

00

N

A

ttl

()

36

29

12

0 1

0 22

0

453

125

0

7050

342

900

0 0

9

(7)

36

64

0 0

0 0

0 0

100

0000

000

00

N

A

CD

t

(9)

36

64

0 0

0 0

0 0

100

0000

000

00

N

A

0 ~

0 0(3

) 35

29

19

0

0 0

17

0 44

615

4

079

33

52

780

0

gt-3 r10

(7

) 35

65

0

0 0

0 0

0 10

000

00

0

0000

NA

s

(9

) 35

65

0

0 0

0 0

0 10

000

00

0

0000

NA

(3

) 44

12

20

0

0 0

24

0 21

428

6

054

37

45

450

0

15

(7)

44

56

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

44

56

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

42

9 27

0

0 0

22

0 15

517

2

113

59

55

100

0

20

(7)

42

58

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

42

58

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

53

6 19

0

0 0

22

0 12

766

0

050

21

46

340

0

30

(7)

53

47

0 0

0 0

0 0

100

0000

000

00

N

A

53

47

0 ()

0 0

0 0

100

0000

000

00

N

A

CJ

) C

J)

Of

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

w

Job

--~~

~~-

~--

Ri

Ii

w

CIl

Cl

C2

C

3 C

4

C5

C6

C7

C

8 -----------shy

(3)

51

3 21

0

1 0

24

0

61

22

4

0

46

39

456

500

40

(7

) 51

4

9

0 0

0 0

0 0

10

00

00

0

0

00

00

NA

(9

) 51

4

9

0 -----_

_

-shy

0 0

0 --shy-----~~~~

0 0

-----------shy

10

00

00

0

0

00

00

---------shy

NA

(3

) 4

8

4 33

0

0 0

15

0

769

23

0

62

20

68

75

00

50

(7

) 4

8

52

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

48

5

2

0 0

0 0

0 0

100

0000

00

00

0

N

A

51

4 3

7

0 0

0 8

0 8

16

33

05

05

8

8

22

20

0

10

0

(7)

51

49

0

0 0

0 0

0 10

000

00

0

00

00

NA

(9

) 51

4

9

0 0

0 0

0 0

100

0000

00

00

0

N

A

----------shy

(3)

56

0

35

0 0

0 9

0 0

00

00

02

29

1

79

550

0

20

0

(7)

56

4

4

0 0

0 0

0 0

100

0000

00

00

0

N

A

(9)

56

4

4

0 0

0 0

0 0

100

0000

00

00

0

N

A

69

2

24

0

0 0

5 0

64

51

6

0

13

97

82

76

00

30

0

(7)

69

31

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

(9)

69

31

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

(3)

62

1

35

0

0 0

2 0

26

31

6

0

17

96

94

59

00

~

40

0

(7)

62

3

8

0 0

0 0

0 0

10

00

00

0

0

00

00

NA

0

(9)

62

3

8

0 0

0 0

0 0

100

0000

00

00

0

N

A

fja

tJte

2-C

onat

)

gt-3

)shy z Cl

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

0gtshy

Con

diti

ons

Job

E

i R

i Ii

C

l C

2 C

3 C

4 C

5 C

6 C

7 C

8 ~ rt

J gt-

lt57

0

38

0 0

0 5

0 0

0000

015

97

88

370

0

rtJ

j

500

(7)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

0 3

(9)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

tr1

tlj

0(3

) 57

1

39

0 0

0 3

0 2

3256

014

97

92

860

0

0 rtJ

60

0

(7)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

~ 57

43

0

0 0

0 0

0 10

000

00

0

0000

NA

0 0

1 34

0

gt-lt

(3)

64

0 0

1 0

277

78

0

1198

971

400

tO

3

700

(7)

64

36

0 0

0 0

0 0

100

0000

000

00

N

A

tr1 ~

(9)

64

36

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

60

2 38

0

0 0

0 0

500

00

0

0999

100

0000

800

(7)

60

40

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

60

40

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

62

0 38

0

0 0

0 0

000

00

0

0999

100

0000

900

(7)

62

38

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

62

38

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

60

0 39

0

0 0

1 0

000

0

010

99

97

500

0

1000

(7

) 60

40

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 60

40

0

0 0

0 0

0 10

000

00

0

0000

NA

w

w

(T

able

2 C

ontd

)

-l

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

------

CIJ

Con

diti

ons

CIJ

Job

E

i R

i Ii

O

J

C1

C2

C3

C4

C

5 C

6 C

7

C8

Min

44

615

4

000

00

0

0000

Sm

all

(3

) M

ax

951

220

0

8209

562

500

pro

ble

ms

Avg

66

121

6

050

01

39

021

3

_

Min

0

0000

009

99

45

450

0

Lar

ge

(3

) M

ax

214

286

1

1359

100

0000

p

rob

lem

s A

vg

605

84

0

3374

784

187

--

-_

__

---

Min

0

0000

000

00

0

0000

Ov

eral

l

(3)

Max

95

122

0

113

59

10

000

00

pro

ble

ms

Avg

26

950

0

039

40

64

715

2

tr1

()

gt-3 ~ Q

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

gtshyT

able

3

z C

om

par

ativ

e re

sult

s fo

r th

e C

GP

S

CD

S

an

d N

EH

alg

ori

thm

s ~

Job 3

4

5

6

7

8

9

10

15

20

30

40

50

100

200

101

39

101

48

102

64

102

82

102

62

102

7

102

82

102

55

102

43

101

83

101

06

100

85

100

65

100

32

100

17

~CDS

100

96

101

28

102

14

102

32

102

46

102

15

102

04

102

04

101

78

101

53

100

99

100

63

100

55

100

35

100

17

~~--------------

~NElI

100

1

100

39

100

53

100

54

100

48

100

72

100

50

100

47

100

25

100

33

100

08

100

05

100

06

100

02

100

01

(Tab

le 3

Con

td)

lfl

gt-

lfl

0 tJ r t=J

0 0 i


w

w

to

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

-----

---

co

jgt

~CGPS

~CDS

~NE

H 0

300

100

07

100

11

100

00

400

100

04

100

06

100

00

500

100

02

100

06

100

00

600

100

02

100

03

100

00

700

100

01

100

02

100

00

800

100

02

100

02

100

00

900

100

01

100

04

100

00

1000

1

0001

1

0003

1

0000

Min

1

0139

1

0096

1

0010

Sm

all

pro

ble

ms

Max

1

0282

1

0246

1

0072

Avg

1

0238

1

0192

1

0047

Min

1

0001

1

0002

1

0000

Lar

ge

pro

ble

ms

Max

1

0243

1

0178

1

0033

Avg

1

0050

1

0042

1

0005

Min

1

0001

1

0002

1

0000

r

Ov

eral

l p

rob

lem

s M

ax

102

82

102

46

100

72

0 -3A

vg

101

15

100

95

100

20

p Z

(Tab

le 3

Con

td)

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

lgtT

able

3 (

Con

td)

Z

--------

_shy

SCG

PS

EQ

CG

PS

SCD

S SC

GP

S E

QC

GP

S SN

EH

SN

EH

EQ

IjE

H

SCD

S --

~ Jo

b C

DS

CDS

CG

PS

NEH

N

EH

CG

PS

CD

S CD

S N

EH

en

en

3 0

91

9

0

83

17

12

88

0

0 gtzj

4 2

8

7

11

2

70

28

21

76

3

gt-l

[1j

5 2

82

16

4

58

38

28

66

6

0 0 1

j6

3

77

20

1

51

48

40

56

4

en

7 5

75

20

5

43

52

45

50

5

~ 0 0

8 6

70

24

8

35

57

44

47

9

~

gt-l

9 5

6

7

28

2

40

58

46

46

8

10

7

68

25

5

40

55

42

50

8

15

7

70

23

2

45

53

46

50

4

20

8

65

27

4

46

50

37

58

5

30

8

74

18

0

57

43

35

63

2

40

7

72

21

3

53

44

29

62

9

50

13

62

25

4

49

47

31

59

10

10

0

15

6

0

25

1

52

47

27

71

2

20

0

17

64

19

2

55

43

26

68

6

30

0

12

74

14

7

63

30

17

74

9

w

(T

able

3 C

ontd

)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

Job

S

co

Ps

CD

S E

QC

GP

SC

DS

SCD

S C

GPS

SC

GP

S N

EH

E

QC

GP

SN

EH

S

NE

H

CG

PS

NE

H

SCD

S E

Q

EH

CD

S SC

DS

NE

Il

N

400

14

63

23

5

58

37

14

81

5

500

13

62

25

1

57

42

20

78

2

60

0

9

61

30

4

54

42

12

82

6

700

11

66

23

8

56

36

13

79

8

80

0

10

63

27

4

57

39

14

82

4

900

16

63

21

2

60

38

17

81

2

1000

11

61

28

4

57

39

12

82

6

Sm

all

pro

ble

ms

Min

Max

Avg

0

67

9

7

91

28

375

00

77

125

0

191

250

0

8

337

50

35

17

83

58

525

000

44

1250

12

46

347

500

46

88

598

750

0

9

537

50

Lar

ge

pro

ble

ms

Min

Max

7

17

60

74

14

30

0

8

45

63

30

53

12

46

50

82

2

10

114

00

65

3333

2

326

67

3

4000

546

000

42

0000

233

333

71

333

3

533

33

Ov

eral

l p

rob

lem

s

Min

Max

Avg

0

60

9

17

91

30

873

91

69

434

8 2

182

61

0

8

339

13

35

17

83

58

538

696

42

739

1

12

46

273

043

~~~--~--

46

0

88

10

673

478

5

3478

c 0 ~ gtshy L

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014




5 CONCLUSION


Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

344 H C TANG


REFERENCES




















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N3 =v+ 1 n





V It












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2014

326 HCTANG












Dow

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2014







Finally since






(8)


k=l k=y



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2014

328 H C TANG






(C1) 11 =v












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P [(C1)Tl 100 (11)


(12)


T




i _[ (C2) + (C4) +(C6) + (C8) ] E - (C2)+(C3)+(C4)+(C5)+(C6)+(C7)+(C8) 100

for i == 3 7 9 (14)


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330 HCTANG





Ii _ [ (C3) + (C4) ] - (C3) +(C4) +(C5) +(C6) +(C7) +(C8) 100

for i 3 7 9 (16)



A _[ (A) ] (17)SB - (A) +(AB) + (B) 100





Dow

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Dow

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2014

332 H C TANG



Job P Popt ~1t1

3 59 100 10139 4 53 100 10185 10148 5 40 100 10309 10264 6 40 100 10317 10282 7 33 100 10318 10262 8 26 100 10355 10270 9 36 100 10355 10282 10 35 100 10337 10255 15 44 84 10299 10243 20 42 82 10300 10183 30 53 90 10157 10106 40 51 94 10132 10085 50 48 95 10128 10065 100 51 93 10083 10032 200 56 97 10040 10017 300 69 99 10021 10007 400 62 98 10022 10004 500 57 96 10018 10002 600 57 99 10017 10002 700 64 96 10013 10001 800 60 99 10012 10002

(Table 1 Contd)

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lOOO 60 97 10001

Small problems Max

Avg 59

402500 lOO lOO

10355 10289

10139 10282 10238

Large problems

Min Max

42 82 10011 10300

10001 10243 10050


503478 100

922609 10355 10156

10001 10282 10115




Dow

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ltgtl

ltgtl

Tab

le 2

C

om

para

tiv

e r

esu

lts

for

co

nd

itio

ns

(3)

(7)

an

d (

9)

--------------shy

Job

C

ondi

tion

s E

i R

i Ii

C

1 C

2 C

3 C

4 C

5 C

6 C

7 C

8 -----shy

(3)

59

39

0 0

2 0

0 0

951

220

0

0000

000

00

3 (7

) 59

41

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 59

41

0

0 0

0 0

0 10

000

00

0

0000

NA

-shy

(3)

53

39

4 0

0 0

4 0

829

787

0

3633

500

000

4 (7

) 53

47

0

0 0

0 0

0 10

000

00

0

0000

NA

53

47

0

0 0

0 0

0 10

000

00

0

0000

NA

---shy

-----------shy

(3)

40

44

9 0

1 0

6 0

733

333

0

4365

562

500

5 (7

) 40

60

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 40

eo

0

0 0

0 0

0 10

000

00

0

0000

NA

(3

) 40

4

7

5 0

0 0

8 0

783

333

0

3392

384

600

6 (7

) 40

6

0

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

40

60

0

0 0

0 0

0 10

000

00

0

000

0

NA

-----------shy

(3)

33

37

10

0

0 0

20

0 55

223

9

054

27

33

330

0

7 (7

) 33

6

7

0 0

0 0

0 0

100

0000

000

00

N

A

p (9

) 33

6

7

0 0

0 0

0 0

100

0000

000

00

N

A

0 ------~

(Tab

le 2

Con

td)

gtshy Z

C

)

Dow

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Con

diti

ons

~ z

Job

E

i R

i Ii

gt

C

l C

2 C

3 C

4 C

5 C

6 C

7 C

8 S CD

26

40

16

0 1

0 17

0

540

541

0

8209

470

600

CD

0 gt1j

8 (7

) 26

74

0

0 0

0 0

0 10

000

00

0

0000

NA

gt-3 r

(9)

26

74

0 0

0 0

0 0

100

0000

000

00

N

A

ttl

()

36

29

12

0 1

0 22

0

453

125

0

7050

342

900

0 0

9

(7)

36

64

0 0

0 0

0 0

100

0000

000

00

N

A

CD

t

(9)

36

64

0 0

0 0

0 0

100

0000

000

00

N

A

0 ~

0 0(3

) 35

29

19

0

0 0

17

0 44

615

4

079

33

52

780

0

gt-3 r10

(7

) 35

65

0

0 0

0 0

0 10

000

00

0

0000

NA

s

(9

) 35

65

0

0 0

0 0

0 10

000

00

0

0000

NA

(3

) 44

12

20

0

0 0

24

0 21

428

6

054

37

45

450

0

15

(7)

44

56

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

44

56

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

42

9 27

0

0 0

22

0 15

517

2

113

59

55

100

0

20

(7)

42

58

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

42

58

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

53

6 19

0

0 0

22

0 12

766

0

050

21

46

340

0

30

(7)

53

47

0 0

0 0

0 0

100

0000

000

00

N

A

53

47

0 ()

0 0

0 0

100

0000

000

00

N

A

CJ

) C

J)

Of

Dow

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2014

w

Job

--~~

~~-

~--

Ri

Ii

w

CIl

Cl

C2

C

3 C

4

C5

C6

C7

C

8 -----------shy

(3)

51

3 21

0

1 0

24

0

61

22

4

0

46

39

456

500

40

(7

) 51

4

9

0 0

0 0

0 0

10

00

00

0

0

00

00

NA

(9

) 51

4

9

0 -----_

_

-shy

0 0

0 --shy-----~~~~

0 0

-----------shy

10

00

00

0

0

00

00

---------shy

NA

(3

) 4

8

4 33

0

0 0

15

0

769

23

0

62

20

68

75

00

50

(7

) 4

8

52

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

48

5

2

0 0

0 0

0 0

100

0000

00

00

0

N

A

51

4 3

7

0 0

0 8

0 8

16

33

05

05

8

8

22

20

0

10

0

(7)

51

49

0

0 0

0 0

0 10

000

00

0

00

00

NA

(9

) 51

4

9

0 0

0 0

0 0

100

0000

00

00

0

N

A

----------shy

(3)

56

0

35

0 0

0 9

0 0

00

00

02

29

1

79

550

0

20

0

(7)

56

4

4

0 0

0 0

0 0

100

0000

00

00

0

N

A

(9)

56

4

4

0 0

0 0

0 0

100

0000

00

00

0

N

A

69

2

24

0

0 0

5 0

64

51

6

0

13

97

82

76

00

30

0

(7)

69

31

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

(9)

69

31

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

(3)

62

1

35

0

0 0

2 0

26

31

6

0

17

96

94

59

00

~

40

0

(7)

62

3

8

0 0

0 0

0 0

10

00

00

0

0

00

00

NA

0

(9)

62

3

8

0 0

0 0

0 0

100

0000

00

00

0

N

A

fja

tJte

2-C

onat

)

gt-3

)shy z Cl

Dow

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Uni

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t 22

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2014

0gtshy

Con

diti

ons

Job

E

i R

i Ii

C

l C

2 C

3 C

4 C

5 C

6 C

7 C

8 ~ rt

J gt-

lt57

0

38

0 0

0 5

0 0

0000

015

97

88

370

0

rtJ

j

500

(7)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

0 3

(9)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

tr1

tlj

0(3

) 57

1

39

0 0

0 3

0 2

3256

014

97

92

860

0

0 rtJ

60

0

(7)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

~ 57

43

0

0 0

0 0

0 10

000

00

0

0000

NA

0 0

1 34

0

gt-lt

(3)

64

0 0

1 0

277

78

0

1198

971

400

tO

3

700

(7)

64

36

0 0

0 0

0 0

100

0000

000

00

N

A

tr1 ~

(9)

64

36

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

60

2 38

0

0 0

0 0

500

00

0

0999

100

0000

800

(7)

60

40

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

60

40

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

62

0 38

0

0 0

0 0

000

00

0

0999

100

0000

900

(7)

62

38

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

62

38

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

60

0 39

0

0 0

1 0

000

0

010

99

97

500

0

1000

(7

) 60

40

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 60

40

0

0 0

0 0

0 10

000

00

0

0000

NA

w

w

(T

able

2 C

ontd

)

-l

Dow

nloa

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by [

Uni

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ity o

f T

enne

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Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

------

CIJ

Con

diti

ons

CIJ

Job

E

i R

i Ii

O

J

C1

C2

C3

C4

C

5 C

6 C

7

C8

Min

44

615

4

000

00

0

0000

Sm

all

(3

) M

ax

951

220

0

8209

562

500

pro

ble

ms

Avg

66

121

6

050

01

39

021

3

_

Min

0

0000

009

99

45

450

0

Lar

ge

(3

) M

ax

214

286

1

1359

100

0000

p

rob

lem

s A

vg

605

84

0

3374

784

187

--

-_

__

---

Min

0

0000

000

00

0

0000

Ov

eral

l

(3)

Max

95

122

0

113

59

10

000

00

pro

ble

ms

Avg

26

950

0

039

40

64

715

2

tr1

()

gt-3 ~ Q

Dow

nloa

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by [

Uni

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ity o

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Kno

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e] a

t 22

24 2

1 D

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2014

gtshyT

able

3

z C

om

par

ativ

e re

sult

s fo

r th

e C

GP

S

CD

S

an

d N

EH

alg

ori

thm

s ~

Job 3

4

5

6

7

8

9

10

15

20

30

40

50

100

200

101

39

101

48

102

64

102

82

102

62

102

7

102

82

102

55

102

43

101

83

101

06

100

85

100

65

100

32

100

17

~CDS

100

96

101

28

102

14

102

32

102

46

102

15

102

04

102

04

101

78

101

53

100

99

100

63

100

55

100

35

100

17

~~--------------

~NElI

100

1

100

39

100

53

100

54

100

48

100

72

100

50

100

47

100

25

100

33

100

08

100

05

100

06

100

02

100

01

(Tab

le 3

Con

td)

lfl

gt-

lfl

0 tJ r t=J

0 0 i


w

w

to

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

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Kno

xvill

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t 22

24 2

1 D

ecem

ber

2014

-----

---

co

jgt

~CGPS

~CDS

~NE

H 0

300

100

07

100

11

100

00

400

100

04

100

06

100

00

500

100

02

100

06

100

00

600

100

02

100

03

100

00

700

100

01

100

02

100

00

800

100

02

100

02

100

00

900

100

01

100

04

100

00

1000

1

0001

1

0003

1

0000

Min

1

0139

1

0096

1

0010

Sm

all

pro

ble

ms

Max

1

0282

1

0246

1

0072

Avg

1

0238

1

0192

1

0047

Min

1

0001

1

0002

1

0000

Lar

ge

pro

ble

ms

Max

1

0243

1

0178

1

0033

Avg

1

0050

1

0042

1

0005

Min

1

0001

1

0002

1

0000

r

Ov

eral

l p

rob

lem

s M

ax

102

82

102

46

100

72

0 -3A

vg

101

15

100

95

100

20

p Z

(Tab

le 3

Con

td)

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

lgtT

able

3 (

Con

td)

Z

--------

_shy

SCG

PS

EQ

CG

PS

SCD

S SC

GP

S E

QC

GP

S SN

EH

SN

EH

EQ

IjE

H

SCD

S --

~ Jo

b C

DS

CDS

CG

PS

NEH

N

EH

CG

PS

CD

S CD

S N

EH

en

en

3 0

91

9

0

83

17

12

88

0

0 gtzj

4 2

8

7

11

2

70

28

21

76

3

gt-l

[1j

5 2

82

16

4

58

38

28

66

6

0 0 1

j6

3

77

20

1

51

48

40

56

4

en

7 5

75

20

5

43

52

45

50

5

~ 0 0

8 6

70

24

8

35

57

44

47

9

~

gt-l

9 5

6

7

28

2

40

58

46

46

8

10

7

68

25

5

40

55

42

50

8

15

7

70

23

2

45

53

46

50

4

20

8

65

27

4

46

50

37

58

5

30

8

74

18

0

57

43

35

63

2

40

7

72

21

3

53

44

29

62

9

50

13

62

25

4

49

47

31

59

10

10

0

15

6

0

25

1

52

47

27

71

2

20

0

17

64

19

2

55

43

26

68

6

30

0

12

74

14

7

63

30

17

74

9

w

(T

able

3 C

ontd

)

Dow

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ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

Job

S

co

Ps

CD

S E

QC

GP

SC

DS

SCD

S C

GPS

SC

GP

S N

EH

E

QC

GP

SN

EH

S

NE

H

CG

PS

NE

H

SCD

S E

Q

EH

CD

S SC

DS

NE

Il

N

400

14

63

23

5

58

37

14

81

5

500

13

62

25

1

57

42

20

78

2

60

0

9

61

30

4

54

42

12

82

6

700

11

66

23

8

56

36

13

79

8

80

0

10

63

27

4

57

39

14

82

4

900

16

63

21

2

60

38

17

81

2

1000

11

61

28

4

57

39

12

82

6

Sm

all

pro

ble

ms

Min

Max

Avg

0

67

9

7

91

28

375

00

77

125

0

191

250

0

8

337

50

35

17

83

58

525

000

44

1250

12

46

347

500

46

88

598

750

0

9

537

50

Lar

ge

pro

ble

ms

Min

Max

7

17

60

74

14

30

0

8

45

63

30

53

12

46

50

82

2

10

114

00

65

3333

2

326

67

3

4000

546

000

42

0000

233

333

71

333

3

533

33

Ov

eral

l p

rob

lem

s

Min

Max

Avg

0

60

9

17

91

30

873

91

69

434

8 2

182

61

0

8

339

13

35

17

83

58

538

696

42

739

1

12

46

273

043

~~~--~--

46

0

88

10

673

478

5

3478

c 0 ~ gtshy L

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014




5 CONCLUSION


Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

344 H C TANG


REFERENCES




















Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

326 HCTANG












Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014







Finally since






(8)


k=l k=y



Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

328 H C TANG






(C1) 11 =v












Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014



P [(C1)Tl 100 (11)


(12)


T




i _[ (C2) + (C4) +(C6) + (C8) ] E - (C2)+(C3)+(C4)+(C5)+(C6)+(C7)+(C8) 100

for i == 3 7 9 (14)


Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

330 HCTANG





Ii _ [ (C3) + (C4) ] - (C3) +(C4) +(C5) +(C6) +(C7) +(C8) 100

for i 3 7 9 (16)



A _[ (A) ] (17)SB - (A) +(AB) + (B) 100





Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014









Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

332 H C TANG



Job P Popt ~1t1

3 59 100 10139 4 53 100 10185 10148 5 40 100 10309 10264 6 40 100 10317 10282 7 33 100 10318 10262 8 26 100 10355 10270 9 36 100 10355 10282 10 35 100 10337 10255 15 44 84 10299 10243 20 42 82 10300 10183 30 53 90 10157 10106 40 51 94 10132 10085 50 48 95 10128 10065 100 51 93 10083 10032 200 56 97 10040 10017 300 69 99 10021 10007 400 62 98 10022 10004 500 57 96 10018 10002 600 57 99 10017 10002 700 64 96 10013 10001 800 60 99 10012 10002

(Table 1 Contd)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014


lOOO 60 97 10001

Small problems Max

Avg 59

402500 lOO lOO

10355 10289

10139 10282 10238

Large problems

Min Max

42 82 10011 10300

10001 10243 10050


503478 100

922609 10355 10156

10001 10282 10115




Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

ltgtl

ltgtl

Tab

le 2

C

om

para

tiv

e r

esu

lts

for

co

nd

itio

ns

(3)

(7)

an

d (

9)

--------------shy

Job

C

ondi

tion

s E

i R

i Ii

C

1 C

2 C

3 C

4 C

5 C

6 C

7 C

8 -----shy

(3)

59

39

0 0

2 0

0 0

951

220

0

0000

000

00

3 (7

) 59

41

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 59

41

0

0 0

0 0

0 10

000

00

0

0000

NA

-shy

(3)

53

39

4 0

0 0

4 0

829

787

0

3633

500

000

4 (7

) 53

47

0

0 0

0 0

0 10

000

00

0

0000

NA

53

47

0

0 0

0 0

0 10

000

00

0

0000

NA

---shy

-----------shy

(3)

40

44

9 0

1 0

6 0

733

333

0

4365

562

500

5 (7

) 40

60

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 40

eo

0

0 0

0 0

0 10

000

00

0

0000

NA

(3

) 40

4

7

5 0

0 0

8 0

783

333

0

3392

384

600

6 (7

) 40

6

0

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

40

60

0

0 0

0 0

0 10

000

00

0

000

0

NA

-----------shy

(3)

33

37

10

0

0 0

20

0 55

223

9

054

27

33

330

0

7 (7

) 33

6

7

0 0

0 0

0 0

100

0000

000

00

N

A

p (9

) 33

6

7

0 0

0 0

0 0

100

0000

000

00

N

A

0 ------~

(Tab

le 2

Con

td)

gtshy Z

C

)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

Con

diti

ons

~ z

Job

E

i R

i Ii

gt

C

l C

2 C

3 C

4 C

5 C

6 C

7 C

8 S CD

26

40

16

0 1

0 17

0

540

541

0

8209

470

600

CD

0 gt1j

8 (7

) 26

74

0

0 0

0 0

0 10

000

00

0

0000

NA

gt-3 r

(9)

26

74

0 0

0 0

0 0

100

0000

000

00

N

A

ttl

()

36

29

12

0 1

0 22

0

453

125

0

7050

342

900

0 0

9

(7)

36

64

0 0

0 0

0 0

100

0000

000

00

N

A

CD

t

(9)

36

64

0 0

0 0

0 0

100

0000

000

00

N

A

0 ~

0 0(3

) 35

29

19

0

0 0

17

0 44

615

4

079

33

52

780

0

gt-3 r10

(7

) 35

65

0

0 0

0 0

0 10

000

00

0

0000

NA

s

(9

) 35

65

0

0 0

0 0

0 10

000

00

0

0000

NA

(3

) 44

12

20

0

0 0

24

0 21

428

6

054

37

45

450

0

15

(7)

44

56

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

44

56

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

42

9 27

0

0 0

22

0 15

517

2

113

59

55

100

0

20

(7)

42

58

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

42

58

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

53

6 19

0

0 0

22

0 12

766

0

050

21

46

340

0

30

(7)

53

47

0 0

0 0

0 0

100

0000

000

00

N

A

53

47

0 ()

0 0

0 0

100

0000

000

00

N

A

CJ

) C

J)

Of

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

w

Job

--~~

~~-

~--

Ri

Ii

w

CIl

Cl

C2

C

3 C

4

C5

C6

C7

C

8 -----------shy

(3)

51

3 21

0

1 0

24

0

61

22

4

0

46

39

456

500

40

(7

) 51

4

9

0 0

0 0

0 0

10

00

00

0

0

00

00

NA

(9

) 51

4

9

0 -----_

_

-shy

0 0

0 --shy-----~~~~

0 0

-----------shy

10

00

00

0

0

00

00

---------shy

NA

(3

) 4

8

4 33

0

0 0

15

0

769

23

0

62

20

68

75

00

50

(7

) 4

8

52

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

48

5

2

0 0

0 0

0 0

100

0000

00

00

0

N

A

51

4 3

7

0 0

0 8

0 8

16

33

05

05

8

8

22

20

0

10

0

(7)

51

49

0

0 0

0 0

0 10

000

00

0

00

00

NA

(9

) 51

4

9

0 0

0 0

0 0

100

0000

00

00

0

N

A

----------shy

(3)

56

0

35

0 0

0 9

0 0

00

00

02

29

1

79

550

0

20

0

(7)

56

4

4

0 0

0 0

0 0

100

0000

00

00

0

N

A

(9)

56

4

4

0 0

0 0

0 0

100

0000

00

00

0

N

A

69

2

24

0

0 0

5 0

64

51

6

0

13

97

82

76

00

30

0

(7)

69

31

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

(9)

69

31

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

(3)

62

1

35

0

0 0

2 0

26

31

6

0

17

96

94

59

00

~

40

0

(7)

62

3

8

0 0

0 0

0 0

10

00

00

0

0

00

00

NA

0

(9)

62

3

8

0 0

0 0

0 0

100

0000

00

00

0

N

A

fja

tJte

2-C

onat

)

gt-3

)shy z Cl

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

0gtshy

Con

diti

ons

Job

E

i R

i Ii

C

l C

2 C

3 C

4 C

5 C

6 C

7 C

8 ~ rt

J gt-

lt57

0

38

0 0

0 5

0 0

0000

015

97

88

370

0

rtJ

j

500

(7)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

0 3

(9)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

tr1

tlj

0(3

) 57

1

39

0 0

0 3

0 2

3256

014

97

92

860

0

0 rtJ

60

0

(7)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

~ 57

43

0

0 0

0 0

0 10

000

00

0

0000

NA

0 0

1 34

0

gt-lt

(3)

64

0 0

1 0

277

78

0

1198

971

400

tO

3

700

(7)

64

36

0 0

0 0

0 0

100

0000

000

00

N

A

tr1 ~

(9)

64

36

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

60

2 38

0

0 0

0 0

500

00

0

0999

100

0000

800

(7)

60

40

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

60

40

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

62

0 38

0

0 0

0 0

000

00

0

0999

100

0000

900

(7)

62

38

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

62

38

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

60

0 39

0

0 0

1 0

000

0

010

99

97

500

0

1000

(7

) 60

40

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 60

40

0

0 0

0 0

0 10

000

00

0

0000

NA

w

w

(T

able

2 C

ontd

)

-l

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

------

CIJ

Con

diti

ons

CIJ

Job

E

i R

i Ii

O

J

C1

C2

C3

C4

C

5 C

6 C

7

C8

Min

44

615

4

000

00

0

0000

Sm

all

(3

) M

ax

951

220

0

8209

562

500

pro

ble

ms

Avg

66

121

6

050

01

39

021

3

_

Min

0

0000

009

99

45

450

0

Lar

ge

(3

) M

ax

214

286

1

1359

100

0000

p

rob

lem

s A

vg

605

84

0

3374

784

187

--

-_

__

---

Min

0

0000

000

00

0

0000

Ov

eral

l

(3)

Max

95

122

0

113

59

10

000

00

pro

ble

ms

Avg

26

950

0

039

40

64

715

2

tr1

()

gt-3 ~ Q

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

gtshyT

able

3

z C

om

par

ativ

e re

sult

s fo

r th

e C

GP

S

CD

S

an

d N

EH

alg

ori

thm

s ~

Job 3

4

5

6

7

8

9

10

15

20

30

40

50

100

200

101

39

101

48

102

64

102

82

102

62

102

7

102

82

102

55

102

43

101

83

101

06

100

85

100

65

100

32

100

17

~CDS

100

96

101

28

102

14

102

32

102

46

102

15

102

04

102

04

101

78

101

53

100

99

100

63

100

55

100

35

100

17

~~--------------

~NElI

100

1

100

39

100

53

100

54

100

48

100

72

100

50

100

47

100

25

100

33

100

08

100

05

100

06

100

02

100

01

(Tab

le 3

Con

td)

lfl

gt-

lfl

0 tJ r t=J

0 0 i


w

w

to

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

-----

---

co

jgt

~CGPS

~CDS

~NE

H 0

300

100

07

100

11

100

00

400

100

04

100

06

100

00

500

100

02

100

06

100

00

600

100

02

100

03

100

00

700

100

01

100

02

100

00

800

100

02

100

02

100

00

900

100

01

100

04

100

00

1000

1

0001

1

0003

1

0000

Min

1

0139

1

0096

1

0010

Sm

all

pro

ble

ms

Max

1

0282

1

0246

1

0072

Avg

1

0238

1

0192

1

0047

Min

1

0001

1

0002

1

0000

Lar

ge

pro

ble

ms

Max

1

0243

1

0178

1

0033

Avg

1

0050

1

0042

1

0005

Min

1

0001

1

0002

1

0000

r

Ov

eral

l p

rob

lem

s M

ax

102

82

102

46

100

72

0 -3A

vg

101

15

100

95

100

20

p Z

(Tab

le 3

Con

td)

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

lgtT

able

3 (

Con

td)

Z

--------

_shy

SCG

PS

EQ

CG

PS

SCD

S SC

GP

S E

QC

GP

S SN

EH

SN

EH

EQ

IjE

H

SCD

S --

~ Jo

b C

DS

CDS

CG

PS

NEH

N

EH

CG

PS

CD

S CD

S N

EH

en

en

3 0

91

9

0

83

17

12

88

0

0 gtzj

4 2

8

7

11

2

70

28

21

76

3

gt-l

[1j

5 2

82

16

4

58

38

28

66

6

0 0 1

j6

3

77

20

1

51

48

40

56

4

en

7 5

75

20

5

43

52

45

50

5

~ 0 0

8 6

70

24

8

35

57

44

47

9

~

gt-l

9 5

6

7

28

2

40

58

46

46

8

10

7

68

25

5

40

55

42

50

8

15

7

70

23

2

45

53

46

50

4

20

8

65

27

4

46

50

37

58

5

30

8

74

18

0

57

43

35

63

2

40

7

72

21

3

53

44

29

62

9

50

13

62

25

4

49

47

31

59

10

10

0

15

6

0

25

1

52

47

27

71

2

20

0

17

64

19

2

55

43

26

68

6

30

0

12

74

14

7

63

30

17

74

9

w

(T

able

3 C

ontd

)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

Job

S

co

Ps

CD

S E

QC

GP

SC

DS

SCD

S C

GPS

SC

GP

S N

EH

E

QC

GP

SN

EH

S

NE

H

CG

PS

NE

H

SCD

S E

Q

EH

CD

S SC

DS

NE

Il

N

400

14

63

23

5

58

37

14

81

5

500

13

62

25

1

57

42

20

78

2

60

0

9

61

30

4

54

42

12

82

6

700

11

66

23

8

56

36

13

79

8

80

0

10

63

27

4

57

39

14

82

4

900

16

63

21

2

60

38

17

81

2

1000

11

61

28

4

57

39

12

82

6

Sm

all

pro

ble

ms

Min

Max

Avg

0

67

9

7

91

28

375

00

77

125

0

191

250

0

8

337

50

35

17

83

58

525

000

44

1250

12

46

347

500

46

88

598

750

0

9

537

50

Lar

ge

pro

ble

ms

Min

Max

7

17

60

74

14

30

0

8

45

63

30

53

12

46

50

82

2

10

114

00

65

3333

2

326

67

3

4000

546

000

42

0000

233

333

71

333

3

533

33

Ov

eral

l p

rob

lem

s

Min

Max

Avg

0

60

9

17

91

30

873

91

69

434

8 2

182

61

0

8

339

13

35

17

83

58

538

696

42

739

1

12

46

273

043

~~~--~--

46

0

88

10

673

478

5

3478

c 0 ~ gtshy L

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014




5 CONCLUSION


Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

344 H C TANG


REFERENCES




















Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014







Finally since






(8)


k=l k=y



Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

328 H C TANG






(C1) 11 =v












Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014



P [(C1)Tl 100 (11)


(12)


T




i _[ (C2) + (C4) +(C6) + (C8) ] E - (C2)+(C3)+(C4)+(C5)+(C6)+(C7)+(C8) 100

for i == 3 7 9 (14)


Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

330 HCTANG





Ii _ [ (C3) + (C4) ] - (C3) +(C4) +(C5) +(C6) +(C7) +(C8) 100

for i 3 7 9 (16)



A _[ (A) ] (17)SB - (A) +(AB) + (B) 100





Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014









Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

332 H C TANG



Job P Popt ~1t1

3 59 100 10139 4 53 100 10185 10148 5 40 100 10309 10264 6 40 100 10317 10282 7 33 100 10318 10262 8 26 100 10355 10270 9 36 100 10355 10282 10 35 100 10337 10255 15 44 84 10299 10243 20 42 82 10300 10183 30 53 90 10157 10106 40 51 94 10132 10085 50 48 95 10128 10065 100 51 93 10083 10032 200 56 97 10040 10017 300 69 99 10021 10007 400 62 98 10022 10004 500 57 96 10018 10002 600 57 99 10017 10002 700 64 96 10013 10001 800 60 99 10012 10002

(Table 1 Contd)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014


lOOO 60 97 10001

Small problems Max

Avg 59

402500 lOO lOO

10355 10289

10139 10282 10238

Large problems

Min Max

42 82 10011 10300

10001 10243 10050


503478 100

922609 10355 10156

10001 10282 10115




Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

ltgtl

ltgtl

Tab

le 2

C

om

para

tiv

e r

esu

lts

for

co

nd

itio

ns

(3)

(7)

an

d (

9)

--------------shy

Job

C

ondi

tion

s E

i R

i Ii

C

1 C

2 C

3 C

4 C

5 C

6 C

7 C

8 -----shy

(3)

59

39

0 0

2 0

0 0

951

220

0

0000

000

00

3 (7

) 59

41

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 59

41

0

0 0

0 0

0 10

000

00

0

0000

NA

-shy

(3)

53

39

4 0

0 0

4 0

829

787

0

3633

500

000

4 (7

) 53

47

0

0 0

0 0

0 10

000

00

0

0000

NA

53

47

0

0 0

0 0

0 10

000

00

0

0000

NA

---shy

-----------shy

(3)

40

44

9 0

1 0

6 0

733

333

0

4365

562

500

5 (7

) 40

60

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 40

eo

0

0 0

0 0

0 10

000

00

0

0000

NA

(3

) 40

4

7

5 0

0 0

8 0

783

333

0

3392

384

600

6 (7

) 40

6

0

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

40

60

0

0 0

0 0

0 10

000

00

0

000

0

NA

-----------shy

(3)

33

37

10

0

0 0

20

0 55

223

9

054

27

33

330

0

7 (7

) 33

6

7

0 0

0 0

0 0

100

0000

000

00

N

A

p (9

) 33

6

7

0 0

0 0

0 0

100

0000

000

00

N

A

0 ------~

(Tab

le 2

Con

td)

gtshy Z

C

)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

Con

diti

ons

~ z

Job

E

i R

i Ii

gt

C

l C

2 C

3 C

4 C

5 C

6 C

7 C

8 S CD

26

40

16

0 1

0 17

0

540

541

0

8209

470

600

CD

0 gt1j

8 (7

) 26

74

0

0 0

0 0

0 10

000

00

0

0000

NA

gt-3 r

(9)

26

74

0 0

0 0

0 0

100

0000

000

00

N

A

ttl

()

36

29

12

0 1

0 22

0

453

125

0

7050

342

900

0 0

9

(7)

36

64

0 0

0 0

0 0

100

0000

000

00

N

A

CD

t

(9)

36

64

0 0

0 0

0 0

100

0000

000

00

N

A

0 ~

0 0(3

) 35

29

19

0

0 0

17

0 44

615

4

079

33

52

780

0

gt-3 r10

(7

) 35

65

0

0 0

0 0

0 10

000

00

0

0000

NA

s

(9

) 35

65

0

0 0

0 0

0 10

000

00

0

0000

NA

(3

) 44

12

20

0

0 0

24

0 21

428

6

054

37

45

450

0

15

(7)

44

56

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

44

56

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

42

9 27

0

0 0

22

0 15

517

2

113

59

55

100

0

20

(7)

42

58

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

42

58

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

53

6 19

0

0 0

22

0 12

766

0

050

21

46

340

0

30

(7)

53

47

0 0

0 0

0 0

100

0000

000

00

N

A

53

47

0 ()

0 0

0 0

100

0000

000

00

N

A

CJ

) C

J)

Of

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

w

Job

--~~

~~-

~--

Ri

Ii

w

CIl

Cl

C2

C

3 C

4

C5

C6

C7

C

8 -----------shy

(3)

51

3 21

0

1 0

24

0

61

22

4

0

46

39

456

500

40

(7

) 51

4

9

0 0

0 0

0 0

10

00

00

0

0

00

00

NA

(9

) 51

4

9

0 -----_

_

-shy

0 0

0 --shy-----~~~~

0 0

-----------shy

10

00

00

0

0

00

00

---------shy

NA

(3

) 4

8

4 33

0

0 0

15

0

769

23

0

62

20

68

75

00

50

(7

) 4

8

52

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

48

5

2

0 0

0 0

0 0

100

0000

00

00

0

N

A

51

4 3

7

0 0

0 8

0 8

16

33

05

05

8

8

22

20

0

10

0

(7)

51

49

0

0 0

0 0

0 10

000

00

0

00

00

NA

(9

) 51

4

9

0 0

0 0

0 0

100

0000

00

00

0

N

A

----------shy

(3)

56

0

35

0 0

0 9

0 0

00

00

02

29

1

79

550

0

20

0

(7)

56

4

4

0 0

0 0

0 0

100

0000

00

00

0

N

A

(9)

56

4

4

0 0

0 0

0 0

100

0000

00

00

0

N

A

69

2

24

0

0 0

5 0

64

51

6

0

13

97

82

76

00

30

0

(7)

69

31

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

(9)

69

31

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

(3)

62

1

35

0

0 0

2 0

26

31

6

0

17

96

94

59

00

~

40

0

(7)

62

3

8

0 0

0 0

0 0

10

00

00

0

0

00

00

NA

0

(9)

62

3

8

0 0

0 0

0 0

100

0000

00

00

0

N

A

fja

tJte

2-C

onat

)

gt-3

)shy z Cl

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

0gtshy

Con

diti

ons

Job

E

i R

i Ii

C

l C

2 C

3 C

4 C

5 C

6 C

7 C

8 ~ rt

J gt-

lt57

0

38

0 0

0 5

0 0

0000

015

97

88

370

0

rtJ

j

500

(7)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

0 3

(9)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

tr1

tlj

0(3

) 57

1

39

0 0

0 3

0 2

3256

014

97

92

860

0

0 rtJ

60

0

(7)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

~ 57

43

0

0 0

0 0

0 10

000

00

0

0000

NA

0 0

1 34

0

gt-lt

(3)

64

0 0

1 0

277

78

0

1198

971

400

tO

3

700

(7)

64

36

0 0

0 0

0 0

100

0000

000

00

N

A

tr1 ~

(9)

64

36

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

60

2 38

0

0 0

0 0

500

00

0

0999

100

0000

800

(7)

60

40

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

60

40

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

62

0 38

0

0 0

0 0

000

00

0

0999

100

0000

900

(7)

62

38

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

62

38

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

60

0 39

0

0 0

1 0

000

0

010

99

97

500

0

1000

(7

) 60

40

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 60

40

0

0 0

0 0

0 10

000

00

0

0000

NA

w

w

(T

able

2 C

ontd

)

-l

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

------

CIJ

Con

diti

ons

CIJ

Job

E

i R

i Ii

O

J

C1

C2

C3

C4

C

5 C

6 C

7

C8

Min

44

615

4

000

00

0

0000

Sm

all

(3

) M

ax

951

220

0

8209

562

500

pro

ble

ms

Avg

66

121

6

050

01

39

021

3

_

Min

0

0000

009

99

45

450

0

Lar

ge

(3

) M

ax

214

286

1

1359

100

0000

p

rob

lem

s A

vg

605

84

0

3374

784

187

--

-_

__

---

Min

0

0000

000

00

0

0000

Ov

eral

l

(3)

Max

95

122

0

113

59

10

000

00

pro

ble

ms

Avg

26

950

0

039

40

64

715

2

tr1

()

gt-3 ~ Q

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

gtshyT

able

3

z C

om

par

ativ

e re

sult

s fo

r th

e C

GP

S

CD

S

an

d N

EH

alg

ori

thm

s ~

Job 3

4

5

6

7

8

9

10

15

20

30

40

50

100

200

101

39

101

48

102

64

102

82

102

62

102

7

102

82

102

55

102

43

101

83

101

06

100

85

100

65

100

32

100

17

~CDS

100

96

101

28

102

14

102

32

102

46

102

15

102

04

102

04

101

78

101

53

100

99

100

63

100

55

100

35

100

17

~~--------------

~NElI

100

1

100

39

100

53

100

54

100

48

100

72

100

50

100

47

100

25

100

33

100

08

100

05

100

06

100

02

100

01

(Tab

le 3

Con

td)

lfl

gt-

lfl

0 tJ r t=J

0 0 i


w

w

to

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

-----

---

co

jgt

~CGPS

~CDS

~NE

H 0

300

100

07

100

11

100

00

400

100

04

100

06

100

00

500

100

02

100

06

100

00

600

100

02

100

03

100

00

700

100

01

100

02

100

00

800

100

02

100

02

100

00

900

100

01

100

04

100

00

1000

1

0001

1

0003

1

0000

Min

1

0139

1

0096

1

0010

Sm

all

pro

ble

ms

Max

1

0282

1

0246

1

0072

Avg

1

0238

1

0192

1

0047

Min

1

0001

1

0002

1

0000

Lar

ge

pro

ble

ms

Max

1

0243

1

0178

1

0033

Avg

1

0050

1

0042

1

0005

Min

1

0001

1

0002

1

0000

r

Ov

eral

l p

rob

lem

s M

ax

102

82

102

46

100

72

0 -3A

vg

101

15

100

95

100

20

p Z

(Tab

le 3

Con

td)

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

lgtT

able

3 (

Con

td)

Z

--------

_shy

SCG

PS

EQ

CG

PS

SCD

S SC

GP

S E

QC

GP

S SN

EH

SN

EH

EQ

IjE

H

SCD

S --

~ Jo

b C

DS

CDS

CG

PS

NEH

N

EH

CG

PS

CD

S CD

S N

EH

en

en

3 0

91

9

0

83

17

12

88

0

0 gtzj

4 2

8

7

11

2

70

28

21

76

3

gt-l

[1j

5 2

82

16

4

58

38

28

66

6

0 0 1

j6

3

77

20

1

51

48

40

56

4

en

7 5

75

20

5

43

52

45

50

5

~ 0 0

8 6

70

24

8

35

57

44

47

9

~

gt-l

9 5

6

7

28

2

40

58

46

46

8

10

7

68

25

5

40

55

42

50

8

15

7

70

23

2

45

53

46

50

4

20

8

65

27

4

46

50

37

58

5

30

8

74

18

0

57

43

35

63

2

40

7

72

21

3

53

44

29

62

9

50

13

62

25

4

49

47

31

59

10

10

0

15

6

0

25

1

52

47

27

71

2

20

0

17

64

19

2

55

43

26

68

6

30

0

12

74

14

7

63

30

17

74

9

w

(T

able

3 C

ontd

)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

Job

S

co

Ps

CD

S E

QC

GP

SC

DS

SCD

S C

GPS

SC

GP

S N

EH

E

QC

GP

SN

EH

S

NE

H

CG

PS

NE

H

SCD

S E

Q

EH

CD

S SC

DS

NE

Il

N

400

14

63

23

5

58

37

14

81

5

500

13

62

25

1

57

42

20

78

2

60

0

9

61

30

4

54

42

12

82

6

700

11

66

23

8

56

36

13

79

8

80

0

10

63

27

4

57

39

14

82

4

900

16

63

21

2

60

38

17

81

2

1000

11

61

28

4

57

39

12

82

6

Sm

all

pro

ble

ms

Min

Max

Avg

0

67

9

7

91

28

375

00

77

125

0

191

250

0

8

337

50

35

17

83

58

525

000

44

1250

12

46

347

500

46

88

598

750

0

9

537

50

Lar

ge

pro

ble

ms

Min

Max

7

17

60

74

14

30

0

8

45

63

30

53

12

46

50

82

2

10

114

00

65

3333

2

326

67

3

4000

546

000

42

0000

233

333

71

333

3

533

33

Ov

eral

l p

rob

lem

s

Min

Max

Avg

0

60

9

17

91

30

873

91

69

434

8 2

182

61

0

8

339

13

35

17

83

58

538

696

42

739

1

12

46

273

043

~~~--~--

46

0

88

10

673

478

5

3478

c 0 ~ gtshy L

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014




5 CONCLUSION


Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

344 H C TANG


REFERENCES




















Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

328 H C TANG






(C1) 11 =v












Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014



P [(C1)Tl 100 (11)


(12)


T




i _[ (C2) + (C4) +(C6) + (C8) ] E - (C2)+(C3)+(C4)+(C5)+(C6)+(C7)+(C8) 100

for i == 3 7 9 (14)


Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

330 HCTANG





Ii _ [ (C3) + (C4) ] - (C3) +(C4) +(C5) +(C6) +(C7) +(C8) 100

for i 3 7 9 (16)



A _[ (A) ] (17)SB - (A) +(AB) + (B) 100





Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014









Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

332 H C TANG



Job P Popt ~1t1

3 59 100 10139 4 53 100 10185 10148 5 40 100 10309 10264 6 40 100 10317 10282 7 33 100 10318 10262 8 26 100 10355 10270 9 36 100 10355 10282 10 35 100 10337 10255 15 44 84 10299 10243 20 42 82 10300 10183 30 53 90 10157 10106 40 51 94 10132 10085 50 48 95 10128 10065 100 51 93 10083 10032 200 56 97 10040 10017 300 69 99 10021 10007 400 62 98 10022 10004 500 57 96 10018 10002 600 57 99 10017 10002 700 64 96 10013 10001 800 60 99 10012 10002

(Table 1 Contd)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014


lOOO 60 97 10001

Small problems Max

Avg 59

402500 lOO lOO

10355 10289

10139 10282 10238

Large problems

Min Max

42 82 10011 10300

10001 10243 10050


503478 100

922609 10355 10156

10001 10282 10115




Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

ltgtl

ltgtl

Tab

le 2

C

om

para

tiv

e r

esu

lts

for

co

nd

itio

ns

(3)

(7)

an

d (

9)

--------------shy

Job

C

ondi

tion

s E

i R

i Ii

C

1 C

2 C

3 C

4 C

5 C

6 C

7 C

8 -----shy

(3)

59

39

0 0

2 0

0 0

951

220

0

0000

000

00

3 (7

) 59

41

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 59

41

0

0 0

0 0

0 10

000

00

0

0000

NA

-shy

(3)

53

39

4 0

0 0

4 0

829

787

0

3633

500

000

4 (7

) 53

47

0

0 0

0 0

0 10

000

00

0

0000

NA

53

47

0

0 0

0 0

0 10

000

00

0

0000

NA

---shy

-----------shy

(3)

40

44

9 0

1 0

6 0

733

333

0

4365

562

500

5 (7

) 40

60

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 40

eo

0

0 0

0 0

0 10

000

00

0

0000

NA

(3

) 40

4

7

5 0

0 0

8 0

783

333

0

3392

384

600

6 (7

) 40

6

0

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

40

60

0

0 0

0 0

0 10

000

00

0

000

0

NA

-----------shy

(3)

33

37

10

0

0 0

20

0 55

223

9

054

27

33

330

0

7 (7

) 33

6

7

0 0

0 0

0 0

100

0000

000

00

N

A

p (9

) 33

6

7

0 0

0 0

0 0

100

0000

000

00

N

A

0 ------~

(Tab

le 2

Con

td)

gtshy Z

C

)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

Con

diti

ons

~ z

Job

E

i R

i Ii

gt

C

l C

2 C

3 C

4 C

5 C

6 C

7 C

8 S CD

26

40

16

0 1

0 17

0

540

541

0

8209

470

600

CD

0 gt1j

8 (7

) 26

74

0

0 0

0 0

0 10

000

00

0

0000

NA

gt-3 r

(9)

26

74

0 0

0 0

0 0

100

0000

000

00

N

A

ttl

()

36

29

12

0 1

0 22

0

453

125

0

7050

342

900

0 0

9

(7)

36

64

0 0

0 0

0 0

100

0000

000

00

N

A

CD

t

(9)

36

64

0 0

0 0

0 0

100

0000

000

00

N

A

0 ~

0 0(3

) 35

29

19

0

0 0

17

0 44

615

4

079

33

52

780

0

gt-3 r10

(7

) 35

65

0

0 0

0 0

0 10

000

00

0

0000

NA

s

(9

) 35

65

0

0 0

0 0

0 10

000

00

0

0000

NA

(3

) 44

12

20

0

0 0

24

0 21

428

6

054

37

45

450

0

15

(7)

44

56

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

44

56

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

42

9 27

0

0 0

22

0 15

517

2

113

59

55

100

0

20

(7)

42

58

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

42

58

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

53

6 19

0

0 0

22

0 12

766

0

050

21

46

340

0

30

(7)

53

47

0 0

0 0

0 0

100

0000

000

00

N

A

53

47

0 ()

0 0

0 0

100

0000

000

00

N

A

CJ

) C

J)

Of

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

w

Job

--~~

~~-

~--

Ri

Ii

w

CIl

Cl

C2

C

3 C

4

C5

C6

C7

C

8 -----------shy

(3)

51

3 21

0

1 0

24

0

61

22

4

0

46

39

456

500

40

(7

) 51

4

9

0 0

0 0

0 0

10

00

00

0

0

00

00

NA

(9

) 51

4

9

0 -----_

_

-shy

0 0

0 --shy-----~~~~

0 0

-----------shy

10

00

00

0

0

00

00

---------shy

NA

(3

) 4

8

4 33

0

0 0

15

0

769

23

0

62

20

68

75

00

50

(7

) 4

8

52

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

48

5

2

0 0

0 0

0 0

100

0000

00

00

0

N

A

51

4 3

7

0 0

0 8

0 8

16

33

05

05

8

8

22

20

0

10

0

(7)

51

49

0

0 0

0 0

0 10

000

00

0

00

00

NA

(9

) 51

4

9

0 0

0 0

0 0

100

0000

00

00

0

N

A

----------shy

(3)

56

0

35

0 0

0 9

0 0

00

00

02

29

1

79

550

0

20

0

(7)

56

4

4

0 0

0 0

0 0

100

0000

00

00

0

N

A

(9)

56

4

4

0 0

0 0

0 0

100

0000

00

00

0

N

A

69

2

24

0

0 0

5 0

64

51

6

0

13

97

82

76

00

30

0

(7)

69

31

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

(9)

69

31

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

(3)

62

1

35

0

0 0

2 0

26

31

6

0

17

96

94

59

00

~

40

0

(7)

62

3

8

0 0

0 0

0 0

10

00

00

0

0

00

00

NA

0

(9)

62

3

8

0 0

0 0

0 0

100

0000

00

00

0

N

A

fja

tJte

2-C

onat

)

gt-3

)shy z Cl

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

0gtshy

Con

diti

ons

Job

E

i R

i Ii

C

l C

2 C

3 C

4 C

5 C

6 C

7 C

8 ~ rt

J gt-

lt57

0

38

0 0

0 5

0 0

0000

015

97

88

370

0

rtJ

j

500

(7)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

0 3

(9)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

tr1

tlj

0(3

) 57

1

39

0 0

0 3

0 2

3256

014

97

92

860

0

0 rtJ

60

0

(7)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

~ 57

43

0

0 0

0 0

0 10

000

00

0

0000

NA

0 0

1 34

0

gt-lt

(3)

64

0 0

1 0

277

78

0

1198

971

400

tO

3

700

(7)

64

36

0 0

0 0

0 0

100

0000

000

00

N

A

tr1 ~

(9)

64

36

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

60

2 38

0

0 0

0 0

500

00

0

0999

100

0000

800

(7)

60

40

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

60

40

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

62

0 38

0

0 0

0 0

000

00

0

0999

100

0000

900

(7)

62

38

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

62

38

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

60

0 39

0

0 0

1 0

000

0

010

99

97

500

0

1000

(7

) 60

40

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 60

40

0

0 0

0 0

0 10

000

00

0

0000

NA

w

w

(T

able

2 C

ontd

)

-l

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

------

CIJ

Con

diti

ons

CIJ

Job

E

i R

i Ii

O

J

C1

C2

C3

C4

C

5 C

6 C

7

C8

Min

44

615

4

000

00

0

0000

Sm

all

(3

) M

ax

951

220

0

8209

562

500

pro

ble

ms

Avg

66

121

6

050

01

39

021

3

_

Min

0

0000

009

99

45

450

0

Lar

ge

(3

) M

ax

214

286

1

1359

100

0000

p

rob

lem

s A

vg

605

84

0

3374

784

187

--

-_

__

---

Min

0

0000

000

00

0

0000

Ov

eral

l

(3)

Max

95

122

0

113

59

10

000

00

pro

ble

ms

Avg

26

950

0

039

40

64

715

2

tr1

()

gt-3 ~ Q

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

gtshyT

able

3

z C

om

par

ativ

e re

sult

s fo

r th

e C

GP

S

CD

S

an

d N

EH

alg

ori

thm

s ~

Job 3

4

5

6

7

8

9

10

15

20

30

40

50

100

200

101

39

101

48

102

64

102

82

102

62

102

7

102

82

102

55

102

43

101

83

101

06

100

85

100

65

100

32

100

17

~CDS

100

96

101

28

102

14

102

32

102

46

102

15

102

04

102

04

101

78

101

53

100

99

100

63

100

55

100

35

100

17

~~--------------

~NElI

100

1

100

39

100

53

100

54

100

48

100

72

100

50

100

47

100

25

100

33

100

08

100

05

100

06

100

02

100

01

(Tab

le 3

Con

td)

lfl

gt-

lfl

0 tJ r t=J

0 0 i


w

w

to

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

-----

---

co

jgt

~CGPS

~CDS

~NE

H 0

300

100

07

100

11

100

00

400

100

04

100

06

100

00

500

100

02

100

06

100

00

600

100

02

100

03

100

00

700

100

01

100

02

100

00

800

100

02

100

02

100

00

900

100

01

100

04

100

00

1000

1

0001

1

0003

1

0000

Min

1

0139

1

0096

1

0010

Sm

all

pro

ble

ms

Max

1

0282

1

0246

1

0072

Avg

1

0238

1

0192

1

0047

Min

1

0001

1

0002

1

0000

Lar

ge

pro

ble

ms

Max

1

0243

1

0178

1

0033

Avg

1

0050

1

0042

1

0005

Min

1

0001

1

0002

1

0000

r

Ov

eral

l p

rob

lem

s M

ax

102

82

102

46

100

72

0 -3A

vg

101

15

100

95

100

20

p Z

(Tab

le 3

Con

td)

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

lgtT

able

3 (

Con

td)

Z

--------

_shy

SCG

PS

EQ

CG

PS

SCD

S SC

GP

S E

QC

GP

S SN

EH

SN

EH

EQ

IjE

H

SCD

S --

~ Jo

b C

DS

CDS

CG

PS

NEH

N

EH

CG

PS

CD

S CD

S N

EH

en

en

3 0

91

9

0

83

17

12

88

0

0 gtzj

4 2

8

7

11

2

70

28

21

76

3

gt-l

[1j

5 2

82

16

4

58

38

28

66

6

0 0 1

j6

3

77

20

1

51

48

40

56

4

en

7 5

75

20

5

43

52

45

50

5

~ 0 0

8 6

70

24

8

35

57

44

47

9

~

gt-l

9 5

6

7

28

2

40

58

46

46

8

10

7

68

25

5

40

55

42

50

8

15

7

70

23

2

45

53

46

50

4

20

8

65

27

4

46

50

37

58

5

30

8

74

18

0

57

43

35

63

2

40

7

72

21

3

53

44

29

62

9

50

13

62

25

4

49

47

31

59

10

10

0

15

6

0

25

1

52

47

27

71

2

20

0

17

64

19

2

55

43

26

68

6

30

0

12

74

14

7

63

30

17

74

9

w

(T

able

3 C

ontd

)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

Job

S

co

Ps

CD

S E

QC

GP

SC

DS

SCD

S C

GPS

SC

GP

S N

EH

E

QC

GP

SN

EH

S

NE

H

CG

PS

NE

H

SCD

S E

Q

EH

CD

S SC

DS

NE

Il

N

400

14

63

23

5

58

37

14

81

5

500

13

62

25

1

57

42

20

78

2

60

0

9

61

30

4

54

42

12

82

6

700

11

66

23

8

56

36

13

79

8

80

0

10

63

27

4

57

39

14

82

4

900

16

63

21

2

60

38

17

81

2

1000

11

61

28

4

57

39

12

82

6

Sm

all

pro

ble

ms

Min

Max

Avg

0

67

9

7

91

28

375

00

77

125

0

191

250

0

8

337

50

35

17

83

58

525

000

44

1250

12

46

347

500

46

88

598

750

0

9

537

50

Lar

ge

pro

ble

ms

Min

Max

7

17

60

74

14

30

0

8

45

63

30

53

12

46

50

82

2

10

114

00

65

3333

2

326

67

3

4000

546

000

42

0000

233

333

71

333

3

533

33

Ov

eral

l p

rob

lem

s

Min

Max

Avg

0

60

9

17

91

30

873

91

69

434

8 2

182

61

0

8

339

13

35

17

83

58

538

696

42

739

1

12

46

273

043

~~~--~--

46

0

88

10

673

478

5

3478

c 0 ~ gtshy L

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014




5 CONCLUSION


Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

344 H C TANG


REFERENCES




















Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014



P [(C1)Tl 100 (11)


(12)


T




i _[ (C2) + (C4) +(C6) + (C8) ] E - (C2)+(C3)+(C4)+(C5)+(C6)+(C7)+(C8) 100

for i == 3 7 9 (14)


Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

330 HCTANG





Ii _ [ (C3) + (C4) ] - (C3) +(C4) +(C5) +(C6) +(C7) +(C8) 100

for i 3 7 9 (16)



A _[ (A) ] (17)SB - (A) +(AB) + (B) 100





Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014









Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

332 H C TANG



Job P Popt ~1t1

3 59 100 10139 4 53 100 10185 10148 5 40 100 10309 10264 6 40 100 10317 10282 7 33 100 10318 10262 8 26 100 10355 10270 9 36 100 10355 10282 10 35 100 10337 10255 15 44 84 10299 10243 20 42 82 10300 10183 30 53 90 10157 10106 40 51 94 10132 10085 50 48 95 10128 10065 100 51 93 10083 10032 200 56 97 10040 10017 300 69 99 10021 10007 400 62 98 10022 10004 500 57 96 10018 10002 600 57 99 10017 10002 700 64 96 10013 10001 800 60 99 10012 10002

(Table 1 Contd)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014


lOOO 60 97 10001

Small problems Max

Avg 59

402500 lOO lOO

10355 10289

10139 10282 10238

Large problems

Min Max

42 82 10011 10300

10001 10243 10050


503478 100

922609 10355 10156

10001 10282 10115




Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

ltgtl

ltgtl

Tab

le 2

C

om

para

tiv

e r

esu

lts

for

co

nd

itio

ns

(3)

(7)

an

d (

9)

--------------shy

Job

C

ondi

tion

s E

i R

i Ii

C

1 C

2 C

3 C

4 C

5 C

6 C

7 C

8 -----shy

(3)

59

39

0 0

2 0

0 0

951

220

0

0000

000

00

3 (7

) 59

41

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 59

41

0

0 0

0 0

0 10

000

00

0

0000

NA

-shy

(3)

53

39

4 0

0 0

4 0

829

787

0

3633

500

000

4 (7

) 53

47

0

0 0

0 0

0 10

000

00

0

0000

NA

53

47

0

0 0

0 0

0 10

000

00

0

0000

NA

---shy

-----------shy

(3)

40

44

9 0

1 0

6 0

733

333

0

4365

562

500

5 (7

) 40

60

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 40

eo

0

0 0

0 0

0 10

000

00

0

0000

NA

(3

) 40

4

7

5 0

0 0

8 0

783

333

0

3392

384

600

6 (7

) 40

6

0

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

40

60

0

0 0

0 0

0 10

000

00

0

000

0

NA

-----------shy

(3)

33

37

10

0

0 0

20

0 55

223

9

054

27

33

330

0

7 (7

) 33

6

7

0 0

0 0

0 0

100

0000

000

00

N

A

p (9

) 33

6

7

0 0

0 0

0 0

100

0000

000

00

N

A

0 ------~

(Tab

le 2

Con

td)

gtshy Z

C

)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

Con

diti

ons

~ z

Job

E

i R

i Ii

gt

C

l C

2 C

3 C

4 C

5 C

6 C

7 C

8 S CD

26

40

16

0 1

0 17

0

540

541

0

8209

470

600

CD

0 gt1j

8 (7

) 26

74

0

0 0

0 0

0 10

000

00

0

0000

NA

gt-3 r

(9)

26

74

0 0

0 0

0 0

100

0000

000

00

N

A

ttl

()

36

29

12

0 1

0 22

0

453

125

0

7050

342

900

0 0

9

(7)

36

64

0 0

0 0

0 0

100

0000

000

00

N

A

CD

t

(9)

36

64

0 0

0 0

0 0

100

0000

000

00

N

A

0 ~

0 0(3

) 35

29

19

0

0 0

17

0 44

615

4

079

33

52

780

0

gt-3 r10

(7

) 35

65

0

0 0

0 0

0 10

000

00

0

0000

NA

s

(9

) 35

65

0

0 0

0 0

0 10

000

00

0

0000

NA

(3

) 44

12

20

0

0 0

24

0 21

428

6

054

37

45

450

0

15

(7)

44

56

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

44

56

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

42

9 27

0

0 0

22

0 15

517

2

113

59

55

100

0

20

(7)

42

58

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

42

58

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

53

6 19

0

0 0

22

0 12

766

0

050

21

46

340

0

30

(7)

53

47

0 0

0 0

0 0

100

0000

000

00

N

A

53

47

0 ()

0 0

0 0

100

0000

000

00

N

A

CJ

) C

J)

Of

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

w

Job

--~~

~~-

~--

Ri

Ii

w

CIl

Cl

C2

C

3 C

4

C5

C6

C7

C

8 -----------shy

(3)

51

3 21

0

1 0

24

0

61

22

4

0

46

39

456

500

40

(7

) 51

4

9

0 0

0 0

0 0

10

00

00

0

0

00

00

NA

(9

) 51

4

9

0 -----_

_

-shy

0 0

0 --shy-----~~~~

0 0

-----------shy

10

00

00

0

0

00

00

---------shy

NA

(3

) 4

8

4 33

0

0 0

15

0

769

23

0

62

20

68

75

00

50

(7

) 4

8

52

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

48

5

2

0 0

0 0

0 0

100

0000

00

00

0

N

A

51

4 3

7

0 0

0 8

0 8

16

33

05

05

8

8

22

20

0

10

0

(7)

51

49

0

0 0

0 0

0 10

000

00

0

00

00

NA

(9

) 51

4

9

0 0

0 0

0 0

100

0000

00

00

0

N

A

----------shy

(3)

56

0

35

0 0

0 9

0 0

00

00

02

29

1

79

550

0

20

0

(7)

56

4

4

0 0

0 0

0 0

100

0000

00

00

0

N

A

(9)

56

4

4

0 0

0 0

0 0

100

0000

00

00

0

N

A

69

2

24

0

0 0

5 0

64

51

6

0

13

97

82

76

00

30

0

(7)

69

31

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

(9)

69

31

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

(3)

62

1

35

0

0 0

2 0

26

31

6

0

17

96

94

59

00

~

40

0

(7)

62

3

8

0 0

0 0

0 0

10

00

00

0

0

00

00

NA

0

(9)

62

3

8

0 0

0 0

0 0

100

0000

00

00

0

N

A

fja

tJte

2-C

onat

)

gt-3

)shy z Cl

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

0gtshy

Con

diti

ons

Job

E

i R

i Ii

C

l C

2 C

3 C

4 C

5 C

6 C

7 C

8 ~ rt

J gt-

lt57

0

38

0 0

0 5

0 0

0000

015

97

88

370

0

rtJ

j

500

(7)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

0 3

(9)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

tr1

tlj

0(3

) 57

1

39

0 0

0 3

0 2

3256

014

97

92

860

0

0 rtJ

60

0

(7)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

~ 57

43

0

0 0

0 0

0 10

000

00

0

0000

NA

0 0

1 34

0

gt-lt

(3)

64

0 0

1 0

277

78

0

1198

971

400

tO

3

700

(7)

64

36

0 0

0 0

0 0

100

0000

000

00

N

A

tr1 ~

(9)

64

36

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

60

2 38

0

0 0

0 0

500

00

0

0999

100

0000

800

(7)

60

40

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

60

40

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

62

0 38

0

0 0

0 0

000

00

0

0999

100

0000

900

(7)

62

38

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

62

38

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

60

0 39

0

0 0

1 0

000

0

010

99

97

500

0

1000

(7

) 60

40

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 60

40

0

0 0

0 0

0 10

000

00

0

0000

NA

w

w

(T

able

2 C

ontd

)

-l

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

------

CIJ

Con

diti

ons

CIJ

Job

E

i R

i Ii

O

J

C1

C2

C3

C4

C

5 C

6 C

7

C8

Min

44

615

4

000

00

0

0000

Sm

all

(3

) M

ax

951

220

0

8209

562

500

pro

ble

ms

Avg

66

121

6

050

01

39

021

3

_

Min

0

0000

009

99

45

450

0

Lar

ge

(3

) M

ax

214

286

1

1359

100

0000

p

rob

lem

s A

vg

605

84

0

3374

784

187

--

-_

__

---

Min

0

0000

000

00

0

0000

Ov

eral

l

(3)

Max

95

122

0

113

59

10

000

00

pro

ble

ms

Avg

26

950

0

039

40

64

715

2

tr1

()

gt-3 ~ Q

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

gtshyT

able

3

z C

om

par

ativ

e re

sult

s fo

r th

e C

GP

S

CD

S

an

d N

EH

alg

ori

thm

s ~

Job 3

4

5

6

7

8

9

10

15

20

30

40

50

100

200

101

39

101

48

102

64

102

82

102

62

102

7

102

82

102

55

102

43

101

83

101

06

100

85

100

65

100

32

100

17

~CDS

100

96

101

28

102

14

102

32

102

46

102

15

102

04

102

04

101

78

101

53

100

99

100

63

100

55

100

35

100

17

~~--------------

~NElI

100

1

100

39

100

53

100

54

100

48

100

72

100

50

100

47

100

25

100

33

100

08

100

05

100

06

100

02

100

01

(Tab

le 3

Con

td)

lfl

gt-

lfl

0 tJ r t=J

0 0 i


w

w

to

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

-----

---

co

jgt

~CGPS

~CDS

~NE

H 0

300

100

07

100

11

100

00

400

100

04

100

06

100

00

500

100

02

100

06

100

00

600

100

02

100

03

100

00

700

100

01

100

02

100

00

800

100

02

100

02

100

00

900

100

01

100

04

100

00

1000

1

0001

1

0003

1

0000

Min

1

0139

1

0096

1

0010

Sm

all

pro

ble

ms

Max

1

0282

1

0246

1

0072

Avg

1

0238

1

0192

1

0047

Min

1

0001

1

0002

1

0000

Lar

ge

pro

ble

ms

Max

1

0243

1

0178

1

0033

Avg

1

0050

1

0042

1

0005

Min

1

0001

1

0002

1

0000

r

Ov

eral

l p

rob

lem

s M

ax

102

82

102

46

100

72

0 -3A

vg

101

15

100

95

100

20

p Z

(Tab

le 3

Con

td)

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

lgtT

able

3 (

Con

td)

Z

--------

_shy

SCG

PS

EQ

CG

PS

SCD

S SC

GP

S E

QC

GP

S SN

EH

SN

EH

EQ

IjE

H

SCD

S --

~ Jo

b C

DS

CDS

CG

PS

NEH

N

EH

CG

PS

CD

S CD

S N

EH

en

en

3 0

91

9

0

83

17

12

88

0

0 gtzj

4 2

8

7

11

2

70

28

21

76

3

gt-l

[1j

5 2

82

16

4

58

38

28

66

6

0 0 1

j6

3

77

20

1

51

48

40

56

4

en

7 5

75

20

5

43

52

45

50

5

~ 0 0

8 6

70

24

8

35

57

44

47

9

~

gt-l

9 5

6

7

28

2

40

58

46

46

8

10

7

68

25

5

40

55

42

50

8

15

7

70

23

2

45

53

46

50

4

20

8

65

27

4

46

50

37

58

5

30

8

74

18

0

57

43

35

63

2

40

7

72

21

3

53

44

29

62

9

50

13

62

25

4

49

47

31

59

10

10

0

15

6

0

25

1

52

47

27

71

2

20

0

17

64

19

2

55

43

26

68

6

30

0

12

74

14

7

63

30

17

74

9

w

(T

able

3 C

ontd

)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

Job

S

co

Ps

CD

S E

QC

GP

SC

DS

SCD

S C

GPS

SC

GP

S N

EH

E

QC

GP

SN

EH

S

NE

H

CG

PS

NE

H

SCD

S E

Q

EH

CD

S SC

DS

NE

Il

N

400

14

63

23

5

58

37

14

81

5

500

13

62

25

1

57

42

20

78

2

60

0

9

61

30

4

54

42

12

82

6

700

11

66

23

8

56

36

13

79

8

80

0

10

63

27

4

57

39

14

82

4

900

16

63

21

2

60

38

17

81

2

1000

11

61

28

4

57

39

12

82

6

Sm

all

pro

ble

ms

Min

Max

Avg

0

67

9

7

91

28

375

00

77

125

0

191

250

0

8

337

50

35

17

83

58

525

000

44

1250

12

46

347

500

46

88

598

750

0

9

537

50

Lar

ge

pro

ble

ms

Min

Max

7

17

60

74

14

30

0

8

45

63

30

53

12

46

50

82

2

10

114

00

65

3333

2

326

67

3

4000

546

000

42

0000

233

333

71

333

3

533

33

Ov

eral

l p

rob

lem

s

Min

Max

Avg

0

60

9

17

91

30

873

91

69

434

8 2

182

61

0

8

339

13

35

17

83

58

538

696

42

739

1

12

46

273

043

~~~--~--

46

0

88

10

673

478

5

3478

c 0 ~ gtshy L

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014




5 CONCLUSION


Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

344 H C TANG


REFERENCES




















Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

330 HCTANG





Ii _ [ (C3) + (C4) ] - (C3) +(C4) +(C5) +(C6) +(C7) +(C8) 100

for i 3 7 9 (16)



A _[ (A) ] (17)SB - (A) +(AB) + (B) 100





Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014









Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

332 H C TANG



Job P Popt ~1t1

3 59 100 10139 4 53 100 10185 10148 5 40 100 10309 10264 6 40 100 10317 10282 7 33 100 10318 10262 8 26 100 10355 10270 9 36 100 10355 10282 10 35 100 10337 10255 15 44 84 10299 10243 20 42 82 10300 10183 30 53 90 10157 10106 40 51 94 10132 10085 50 48 95 10128 10065 100 51 93 10083 10032 200 56 97 10040 10017 300 69 99 10021 10007 400 62 98 10022 10004 500 57 96 10018 10002 600 57 99 10017 10002 700 64 96 10013 10001 800 60 99 10012 10002

(Table 1 Contd)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014


lOOO 60 97 10001

Small problems Max

Avg 59

402500 lOO lOO

10355 10289

10139 10282 10238

Large problems

Min Max

42 82 10011 10300

10001 10243 10050


503478 100

922609 10355 10156

10001 10282 10115




Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

ltgtl

ltgtl

Tab

le 2

C

om

para

tiv

e r

esu

lts

for

co

nd

itio

ns

(3)

(7)

an

d (

9)

--------------shy

Job

C

ondi

tion

s E

i R

i Ii

C

1 C

2 C

3 C

4 C

5 C

6 C

7 C

8 -----shy

(3)

59

39

0 0

2 0

0 0

951

220

0

0000

000

00

3 (7

) 59

41

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 59

41

0

0 0

0 0

0 10

000

00

0

0000

NA

-shy

(3)

53

39

4 0

0 0

4 0

829

787

0

3633

500

000

4 (7

) 53

47

0

0 0

0 0

0 10

000

00

0

0000

NA

53

47

0

0 0

0 0

0 10

000

00

0

0000

NA

---shy

-----------shy

(3)

40

44

9 0

1 0

6 0

733

333

0

4365

562

500

5 (7

) 40

60

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 40

eo

0

0 0

0 0

0 10

000

00

0

0000

NA

(3

) 40

4

7

5 0

0 0

8 0

783

333

0

3392

384

600

6 (7

) 40

6

0

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

40

60

0

0 0

0 0

0 10

000

00

0

000

0

NA

-----------shy

(3)

33

37

10

0

0 0

20

0 55

223

9

054

27

33

330

0

7 (7

) 33

6

7

0 0

0 0

0 0

100

0000

000

00

N

A

p (9

) 33

6

7

0 0

0 0

0 0

100

0000

000

00

N

A

0 ------~

(Tab

le 2

Con

td)

gtshy Z

C

)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

Con

diti

ons

~ z

Job

E

i R

i Ii

gt

C

l C

2 C

3 C

4 C

5 C

6 C

7 C

8 S CD

26

40

16

0 1

0 17

0

540

541

0

8209

470

600

CD

0 gt1j

8 (7

) 26

74

0

0 0

0 0

0 10

000

00

0

0000

NA

gt-3 r

(9)

26

74

0 0

0 0

0 0

100

0000

000

00

N

A

ttl

()

36

29

12

0 1

0 22

0

453

125

0

7050

342

900

0 0

9

(7)

36

64

0 0

0 0

0 0

100

0000

000

00

N

A

CD

t

(9)

36

64

0 0

0 0

0 0

100

0000

000

00

N

A

0 ~

0 0(3

) 35

29

19

0

0 0

17

0 44

615

4

079

33

52

780

0

gt-3 r10

(7

) 35

65

0

0 0

0 0

0 10

000

00

0

0000

NA

s

(9

) 35

65

0

0 0

0 0

0 10

000

00

0

0000

NA

(3

) 44

12

20

0

0 0

24

0 21

428

6

054

37

45

450

0

15

(7)

44

56

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

44

56

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

42

9 27

0

0 0

22

0 15

517

2

113

59

55

100

0

20

(7)

42

58

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

42

58

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

53

6 19

0

0 0

22

0 12

766

0

050

21

46

340

0

30

(7)

53

47

0 0

0 0

0 0

100

0000

000

00

N

A

53

47

0 ()

0 0

0 0

100

0000

000

00

N

A

CJ

) C

J)

Of

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

w

Job

--~~

~~-

~--

Ri

Ii

w

CIl

Cl

C2

C

3 C

4

C5

C6

C7

C

8 -----------shy

(3)

51

3 21

0

1 0

24

0

61

22

4

0

46

39

456

500

40

(7

) 51

4

9

0 0

0 0

0 0

10

00

00

0

0

00

00

NA

(9

) 51

4

9

0 -----_

_

-shy

0 0

0 --shy-----~~~~

0 0

-----------shy

10

00

00

0

0

00

00

---------shy

NA

(3

) 4

8

4 33

0

0 0

15

0

769

23

0

62

20

68

75

00

50

(7

) 4

8

52

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

48

5

2

0 0

0 0

0 0

100

0000

00

00

0

N

A

51

4 3

7

0 0

0 8

0 8

16

33

05

05

8

8

22

20

0

10

0

(7)

51

49

0

0 0

0 0

0 10

000

00

0

00

00

NA

(9

) 51

4

9

0 0

0 0

0 0

100

0000

00

00

0

N

A

----------shy

(3)

56

0

35

0 0

0 9

0 0

00

00

02

29

1

79

550

0

20

0

(7)

56

4

4

0 0

0 0

0 0

100

0000

00

00

0

N

A

(9)

56

4

4

0 0

0 0

0 0

100

0000

00

00

0

N

A

69

2

24

0

0 0

5 0

64

51

6

0

13

97

82

76

00

30

0

(7)

69

31

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

(9)

69

31

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

(3)

62

1

35

0

0 0

2 0

26

31

6

0

17

96

94

59

00

~

40

0

(7)

62

3

8

0 0

0 0

0 0

10

00

00

0

0

00

00

NA

0

(9)

62

3

8

0 0

0 0

0 0

100

0000

00

00

0

N

A

fja

tJte

2-C

onat

)

gt-3

)shy z Cl

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

0gtshy

Con

diti

ons

Job

E

i R

i Ii

C

l C

2 C

3 C

4 C

5 C

6 C

7 C

8 ~ rt

J gt-

lt57

0

38

0 0

0 5

0 0

0000

015

97

88

370

0

rtJ

j

500

(7)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

0 3

(9)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

tr1

tlj

0(3

) 57

1

39

0 0

0 3

0 2

3256

014

97

92

860

0

0 rtJ

60

0

(7)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

~ 57

43

0

0 0

0 0

0 10

000

00

0

0000

NA

0 0

1 34

0

gt-lt

(3)

64

0 0

1 0

277

78

0

1198

971

400

tO

3

700

(7)

64

36

0 0

0 0

0 0

100

0000

000

00

N

A

tr1 ~

(9)

64

36

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

60

2 38

0

0 0

0 0

500

00

0

0999

100

0000

800

(7)

60

40

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

60

40

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

62

0 38

0

0 0

0 0

000

00

0

0999

100

0000

900

(7)

62

38

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

62

38

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

60

0 39

0

0 0

1 0

000

0

010

99

97

500

0

1000

(7

) 60

40

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 60

40

0

0 0

0 0

0 10

000

00

0

0000

NA

w

w

(T

able

2 C

ontd

)

-l

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

------

CIJ

Con

diti

ons

CIJ

Job

E

i R

i Ii

O

J

C1

C2

C3

C4

C

5 C

6 C

7

C8

Min

44

615

4

000

00

0

0000

Sm

all

(3

) M

ax

951

220

0

8209

562

500

pro

ble

ms

Avg

66

121

6

050

01

39

021

3

_

Min

0

0000

009

99

45

450

0

Lar

ge

(3

) M

ax

214

286

1

1359

100

0000

p

rob

lem

s A

vg

605

84

0

3374

784

187

--

-_

__

---

Min

0

0000

000

00

0

0000

Ov

eral

l

(3)

Max

95

122

0

113

59

10

000

00

pro

ble

ms

Avg

26

950

0

039

40

64

715

2

tr1

()

gt-3 ~ Q

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

gtshyT

able

3

z C

om

par

ativ

e re

sult

s fo

r th

e C

GP

S

CD

S

an

d N

EH

alg

ori

thm

s ~

Job 3

4

5

6

7

8

9

10

15

20

30

40

50

100

200

101

39

101

48

102

64

102

82

102

62

102

7

102

82

102

55

102

43

101

83

101

06

100

85

100

65

100

32

100

17

~CDS

100

96

101

28

102

14

102

32

102

46

102

15

102

04

102

04

101

78

101

53

100

99

100

63

100

55

100

35

100

17

~~--------------

~NElI

100

1

100

39

100

53

100

54

100

48

100

72

100

50

100

47

100

25

100

33

100

08

100

05

100

06

100

02

100

01

(Tab

le 3

Con

td)

lfl

gt-

lfl

0 tJ r t=J

0 0 i


w

w

to

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

-----

---

co

jgt

~CGPS

~CDS

~NE

H 0

300

100

07

100

11

100

00

400

100

04

100

06

100

00

500

100

02

100

06

100

00

600

100

02

100

03

100

00

700

100

01

100

02

100

00

800

100

02

100

02

100

00

900

100

01

100

04

100

00

1000

1

0001

1

0003

1

0000

Min

1

0139

1

0096

1

0010

Sm

all

pro

ble

ms

Max

1

0282

1

0246

1

0072

Avg

1

0238

1

0192

1

0047

Min

1

0001

1

0002

1

0000

Lar

ge

pro

ble

ms

Max

1

0243

1

0178

1

0033

Avg

1

0050

1

0042

1

0005

Min

1

0001

1

0002

1

0000

r

Ov

eral

l p

rob

lem

s M

ax

102

82

102

46

100

72

0 -3A

vg

101

15

100

95

100

20

p Z

(Tab

le 3

Con

td)

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

lgtT

able

3 (

Con

td)

Z

--------

_shy

SCG

PS

EQ

CG

PS

SCD

S SC

GP

S E

QC

GP

S SN

EH

SN

EH

EQ

IjE

H

SCD

S --

~ Jo

b C

DS

CDS

CG

PS

NEH

N

EH

CG

PS

CD

S CD

S N

EH

en

en

3 0

91

9

0

83

17

12

88

0

0 gtzj

4 2

8

7

11

2

70

28

21

76

3

gt-l

[1j

5 2

82

16

4

58

38

28

66

6

0 0 1

j6

3

77

20

1

51

48

40

56

4

en

7 5

75

20

5

43

52

45

50

5

~ 0 0

8 6

70

24

8

35

57

44

47

9

~

gt-l

9 5

6

7

28

2

40

58

46

46

8

10

7

68

25

5

40

55

42

50

8

15

7

70

23

2

45

53

46

50

4

20

8

65

27

4

46

50

37

58

5

30

8

74

18

0

57

43

35

63

2

40

7

72

21

3

53

44

29

62

9

50

13

62

25

4

49

47

31

59

10

10

0

15

6

0

25

1

52

47

27

71

2

20

0

17

64

19

2

55

43

26

68

6

30

0

12

74

14

7

63

30

17

74

9

w

(T

able

3 C

ontd

)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

Job

S

co

Ps

CD

S E

QC

GP

SC

DS

SCD

S C

GPS

SC

GP

S N

EH

E

QC

GP

SN

EH

S

NE

H

CG

PS

NE

H

SCD

S E

Q

EH

CD

S SC

DS

NE

Il

N

400

14

63

23

5

58

37

14

81

5

500

13

62

25

1

57

42

20

78

2

60

0

9

61

30

4

54

42

12

82

6

700

11

66

23

8

56

36

13

79

8

80

0

10

63

27

4

57

39

14

82

4

900

16

63

21

2

60

38

17

81

2

1000

11

61

28

4

57

39

12

82

6

Sm

all

pro

ble

ms

Min

Max

Avg

0

67

9

7

91

28

375

00

77

125

0

191

250

0

8

337

50

35

17

83

58

525

000

44

1250

12

46

347

500

46

88

598

750

0

9

537

50

Lar

ge

pro

ble

ms

Min

Max

7

17

60

74

14

30

0

8

45

63

30

53

12

46

50

82

2

10

114

00

65

3333

2

326

67

3

4000

546

000

42

0000

233

333

71

333

3

533

33

Ov

eral

l p

rob

lem

s

Min

Max

Avg

0

60

9

17

91

30

873

91

69

434

8 2

182

61

0

8

339

13

35

17

83

58

538

696

42

739

1

12

46

273

043

~~~--~--

46

0

88

10

673

478

5

3478

c 0 ~ gtshy L

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014




5 CONCLUSION


Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

344 H C TANG


REFERENCES




















Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014









Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

332 H C TANG



Job P Popt ~1t1

3 59 100 10139 4 53 100 10185 10148 5 40 100 10309 10264 6 40 100 10317 10282 7 33 100 10318 10262 8 26 100 10355 10270 9 36 100 10355 10282 10 35 100 10337 10255 15 44 84 10299 10243 20 42 82 10300 10183 30 53 90 10157 10106 40 51 94 10132 10085 50 48 95 10128 10065 100 51 93 10083 10032 200 56 97 10040 10017 300 69 99 10021 10007 400 62 98 10022 10004 500 57 96 10018 10002 600 57 99 10017 10002 700 64 96 10013 10001 800 60 99 10012 10002

(Table 1 Contd)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014


lOOO 60 97 10001

Small problems Max

Avg 59

402500 lOO lOO

10355 10289

10139 10282 10238

Large problems

Min Max

42 82 10011 10300

10001 10243 10050


503478 100

922609 10355 10156

10001 10282 10115




Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

ltgtl

ltgtl

Tab

le 2

C

om

para

tiv

e r

esu

lts

for

co

nd

itio

ns

(3)

(7)

an

d (

9)

--------------shy

Job

C

ondi

tion

s E

i R

i Ii

C

1 C

2 C

3 C

4 C

5 C

6 C

7 C

8 -----shy

(3)

59

39

0 0

2 0

0 0

951

220

0

0000

000

00

3 (7

) 59

41

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 59

41

0

0 0

0 0

0 10

000

00

0

0000

NA

-shy

(3)

53

39

4 0

0 0

4 0

829

787

0

3633

500

000

4 (7

) 53

47

0

0 0

0 0

0 10

000

00

0

0000

NA

53

47

0

0 0

0 0

0 10

000

00

0

0000

NA

---shy

-----------shy

(3)

40

44

9 0

1 0

6 0

733

333

0

4365

562

500

5 (7

) 40

60

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 40

eo

0

0 0

0 0

0 10

000

00

0

0000

NA

(3

) 40

4

7

5 0

0 0

8 0

783

333

0

3392

384

600

6 (7

) 40

6

0

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

40

60

0

0 0

0 0

0 10

000

00

0

000

0

NA

-----------shy

(3)

33

37

10

0

0 0

20

0 55

223

9

054

27

33

330

0

7 (7

) 33

6

7

0 0

0 0

0 0

100

0000

000

00

N

A

p (9

) 33

6

7

0 0

0 0

0 0

100

0000

000

00

N

A

0 ------~

(Tab

le 2

Con

td)

gtshy Z

C

)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

Con

diti

ons

~ z

Job

E

i R

i Ii

gt

C

l C

2 C

3 C

4 C

5 C

6 C

7 C

8 S CD

26

40

16

0 1

0 17

0

540

541

0

8209

470

600

CD

0 gt1j

8 (7

) 26

74

0

0 0

0 0

0 10

000

00

0

0000

NA

gt-3 r

(9)

26

74

0 0

0 0

0 0

100

0000

000

00

N

A

ttl

()

36

29

12

0 1

0 22

0

453

125

0

7050

342

900

0 0

9

(7)

36

64

0 0

0 0

0 0

100

0000

000

00

N

A

CD

t

(9)

36

64

0 0

0 0

0 0

100

0000

000

00

N

A

0 ~

0 0(3

) 35

29

19

0

0 0

17

0 44

615

4

079

33

52

780

0

gt-3 r10

(7

) 35

65

0

0 0

0 0

0 10

000

00

0

0000

NA

s

(9

) 35

65

0

0 0

0 0

0 10

000

00

0

0000

NA

(3

) 44

12

20

0

0 0

24

0 21

428

6

054

37

45

450

0

15

(7)

44

56

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

44

56

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

42

9 27

0

0 0

22

0 15

517

2

113

59

55

100

0

20

(7)

42

58

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

42

58

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

53

6 19

0

0 0

22

0 12

766

0

050

21

46

340

0

30

(7)

53

47

0 0

0 0

0 0

100

0000

000

00

N

A

53

47

0 ()

0 0

0 0

100

0000

000

00

N

A

CJ

) C

J)

Of

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

w

Job

--~~

~~-

~--

Ri

Ii

w

CIl

Cl

C2

C

3 C

4

C5

C6

C7

C

8 -----------shy

(3)

51

3 21

0

1 0

24

0

61

22

4

0

46

39

456

500

40

(7

) 51

4

9

0 0

0 0

0 0

10

00

00

0

0

00

00

NA

(9

) 51

4

9

0 -----_

_

-shy

0 0

0 --shy-----~~~~

0 0

-----------shy

10

00

00

0

0

00

00

---------shy

NA

(3

) 4

8

4 33

0

0 0

15

0

769

23

0

62

20

68

75

00

50

(7

) 4

8

52

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

48

5

2

0 0

0 0

0 0

100

0000

00

00

0

N

A

51

4 3

7

0 0

0 8

0 8

16

33

05

05

8

8

22

20

0

10

0

(7)

51

49

0

0 0

0 0

0 10

000

00

0

00

00

NA

(9

) 51

4

9

0 0

0 0

0 0

100

0000

00

00

0

N

A

----------shy

(3)

56

0

35

0 0

0 9

0 0

00

00

02

29

1

79

550

0

20

0

(7)

56

4

4

0 0

0 0

0 0

100

0000

00

00

0

N

A

(9)

56

4

4

0 0

0 0

0 0

100

0000

00

00

0

N

A

69

2

24

0

0 0

5 0

64

51

6

0

13

97

82

76

00

30

0

(7)

69

31

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

(9)

69

31

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

(3)

62

1

35

0

0 0

2 0

26

31

6

0

17

96

94

59

00

~

40

0

(7)

62

3

8

0 0

0 0

0 0

10

00

00

0

0

00

00

NA

0

(9)

62

3

8

0 0

0 0

0 0

100

0000

00

00

0

N

A

fja

tJte

2-C

onat

)

gt-3

)shy z Cl

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

0gtshy

Con

diti

ons

Job

E

i R

i Ii

C

l C

2 C

3 C

4 C

5 C

6 C

7 C

8 ~ rt

J gt-

lt57

0

38

0 0

0 5

0 0

0000

015

97

88

370

0

rtJ

j

500

(7)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

0 3

(9)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

tr1

tlj

0(3

) 57

1

39

0 0

0 3

0 2

3256

014

97

92

860

0

0 rtJ

60

0

(7)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

~ 57

43

0

0 0

0 0

0 10

000

00

0

0000

NA

0 0

1 34

0

gt-lt

(3)

64

0 0

1 0

277

78

0

1198

971

400

tO

3

700

(7)

64

36

0 0

0 0

0 0

100

0000

000

00

N

A

tr1 ~

(9)

64

36

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

60

2 38

0

0 0

0 0

500

00

0

0999

100

0000

800

(7)

60

40

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

60

40

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

62

0 38

0

0 0

0 0

000

00

0

0999

100

0000

900

(7)

62

38

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

62

38

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

60

0 39

0

0 0

1 0

000

0

010

99

97

500

0

1000

(7

) 60

40

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 60

40

0

0 0

0 0

0 10

000

00

0

0000

NA

w

w

(T

able

2 C

ontd

)

-l

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

------

CIJ

Con

diti

ons

CIJ

Job

E

i R

i Ii

O

J

C1

C2

C3

C4

C

5 C

6 C

7

C8

Min

44

615

4

000

00

0

0000

Sm

all

(3

) M

ax

951

220

0

8209

562

500

pro

ble

ms

Avg

66

121

6

050

01

39

021

3

_

Min

0

0000

009

99

45

450

0

Lar

ge

(3

) M

ax

214

286

1

1359

100

0000

p

rob

lem

s A

vg

605

84

0

3374

784

187

--

-_

__

---

Min

0

0000

000

00

0

0000

Ov

eral

l

(3)

Max

95

122

0

113

59

10

000

00

pro

ble

ms

Avg

26

950

0

039

40

64

715

2

tr1

()

gt-3 ~ Q

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

gtshyT

able

3

z C

om

par

ativ

e re

sult

s fo

r th

e C

GP

S

CD

S

an

d N

EH

alg

ori

thm

s ~

Job 3

4

5

6

7

8

9

10

15

20

30

40

50

100

200

101

39

101

48

102

64

102

82

102

62

102

7

102

82

102

55

102

43

101

83

101

06

100

85

100

65

100

32

100

17

~CDS

100

96

101

28

102

14

102

32

102

46

102

15

102

04

102

04

101

78

101

53

100

99

100

63

100

55

100

35

100

17

~~--------------

~NElI

100

1

100

39

100

53

100

54

100

48

100

72

100

50

100

47

100

25

100

33

100

08

100

05

100

06

100

02

100

01

(Tab

le 3

Con

td)

lfl

gt-

lfl

0 tJ r t=J

0 0 i


w

w

to

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

-----

---

co

jgt

~CGPS

~CDS

~NE

H 0

300

100

07

100

11

100

00

400

100

04

100

06

100

00

500

100

02

100

06

100

00

600

100

02

100

03

100

00

700

100

01

100

02

100

00

800

100

02

100

02

100

00

900

100

01

100

04

100

00

1000

1

0001

1

0003

1

0000

Min

1

0139

1

0096

1

0010

Sm

all

pro

ble

ms

Max

1

0282

1

0246

1

0072

Avg

1

0238

1

0192

1

0047

Min

1

0001

1

0002

1

0000

Lar

ge

pro

ble

ms

Max

1

0243

1

0178

1

0033

Avg

1

0050

1

0042

1

0005

Min

1

0001

1

0002

1

0000

r

Ov

eral

l p

rob

lem

s M

ax

102

82

102

46

100

72

0 -3A

vg

101

15

100

95

100

20

p Z

(Tab

le 3

Con

td)

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

lgtT

able

3 (

Con

td)

Z

--------

_shy

SCG

PS

EQ

CG

PS

SCD

S SC

GP

S E

QC

GP

S SN

EH

SN

EH

EQ

IjE

H

SCD

S --

~ Jo

b C

DS

CDS

CG

PS

NEH

N

EH

CG

PS

CD

S CD

S N

EH

en

en

3 0

91

9

0

83

17

12

88

0

0 gtzj

4 2

8

7

11

2

70

28

21

76

3

gt-l

[1j

5 2

82

16

4

58

38

28

66

6

0 0 1

j6

3

77

20

1

51

48

40

56

4

en

7 5

75

20

5

43

52

45

50

5

~ 0 0

8 6

70

24

8

35

57

44

47

9

~

gt-l

9 5

6

7

28

2

40

58

46

46

8

10

7

68

25

5

40

55

42

50

8

15

7

70

23

2

45

53

46

50

4

20

8

65

27

4

46

50

37

58

5

30

8

74

18

0

57

43

35

63

2

40

7

72

21

3

53

44

29

62

9

50

13

62

25

4

49

47

31

59

10

10

0

15

6

0

25

1

52

47

27

71

2

20

0

17

64

19

2

55

43

26

68

6

30

0

12

74

14

7

63

30

17

74

9

w

(T

able

3 C

ontd

)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

Job

S

co

Ps

CD

S E

QC

GP

SC

DS

SCD

S C

GPS

SC

GP

S N

EH

E

QC

GP

SN

EH

S

NE

H

CG

PS

NE

H

SCD

S E

Q

EH

CD

S SC

DS

NE

Il

N

400

14

63

23

5

58

37

14

81

5

500

13

62

25

1

57

42

20

78

2

60

0

9

61

30

4

54

42

12

82

6

700

11

66

23

8

56

36

13

79

8

80

0

10

63

27

4

57

39

14

82

4

900

16

63

21

2

60

38

17

81

2

1000

11

61

28

4

57

39

12

82

6

Sm

all

pro

ble

ms

Min

Max

Avg

0

67

9

7

91

28

375

00

77

125

0

191

250

0

8

337

50

35

17

83

58

525

000

44

1250

12

46

347

500

46

88

598

750

0

9

537

50

Lar

ge

pro

ble

ms

Min

Max

7

17

60

74

14

30

0

8

45

63

30

53

12

46

50

82

2

10

114

00

65

3333

2

326

67

3

4000

546

000

42

0000

233

333

71

333

3

533

33

Ov

eral

l p

rob

lem

s

Min

Max

Avg

0

60

9

17

91

30

873

91

69

434

8 2

182

61

0

8

339

13

35

17

83

58

538

696

42

739

1

12

46

273

043

~~~--~--

46

0

88

10

673

478

5

3478

c 0 ~ gtshy L

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014




5 CONCLUSION


Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

344 H C TANG


REFERENCES




















Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

332 H C TANG



Job P Popt ~1t1

3 59 100 10139 4 53 100 10185 10148 5 40 100 10309 10264 6 40 100 10317 10282 7 33 100 10318 10262 8 26 100 10355 10270 9 36 100 10355 10282 10 35 100 10337 10255 15 44 84 10299 10243 20 42 82 10300 10183 30 53 90 10157 10106 40 51 94 10132 10085 50 48 95 10128 10065 100 51 93 10083 10032 200 56 97 10040 10017 300 69 99 10021 10007 400 62 98 10022 10004 500 57 96 10018 10002 600 57 99 10017 10002 700 64 96 10013 10001 800 60 99 10012 10002

(Table 1 Contd)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014


lOOO 60 97 10001

Small problems Max

Avg 59

402500 lOO lOO

10355 10289

10139 10282 10238

Large problems

Min Max

42 82 10011 10300

10001 10243 10050


503478 100

922609 10355 10156

10001 10282 10115




Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

ltgtl

ltgtl

Tab

le 2

C

om

para

tiv

e r

esu

lts

for

co

nd

itio

ns

(3)

(7)

an

d (

9)

--------------shy

Job

C

ondi

tion

s E

i R

i Ii

C

1 C

2 C

3 C

4 C

5 C

6 C

7 C

8 -----shy

(3)

59

39

0 0

2 0

0 0

951

220

0

0000

000

00

3 (7

) 59

41

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 59

41

0

0 0

0 0

0 10

000

00

0

0000

NA

-shy

(3)

53

39

4 0

0 0

4 0

829

787

0

3633

500

000

4 (7

) 53

47

0

0 0

0 0

0 10

000

00

0

0000

NA

53

47

0

0 0

0 0

0 10

000

00

0

0000

NA

---shy

-----------shy

(3)

40

44

9 0

1 0

6 0

733

333

0

4365

562

500

5 (7

) 40

60

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 40

eo

0

0 0

0 0

0 10

000

00

0

0000

NA

(3

) 40

4

7

5 0

0 0

8 0

783

333

0

3392

384

600

6 (7

) 40

6

0

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

40

60

0

0 0

0 0

0 10

000

00

0

000

0

NA

-----------shy

(3)

33

37

10

0

0 0

20

0 55

223

9

054

27

33

330

0

7 (7

) 33

6

7

0 0

0 0

0 0

100

0000

000

00

N

A

p (9

) 33

6

7

0 0

0 0

0 0

100

0000

000

00

N

A

0 ------~

(Tab

le 2

Con

td)

gtshy Z

C

)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

Con

diti

ons

~ z

Job

E

i R

i Ii

gt

C

l C

2 C

3 C

4 C

5 C

6 C

7 C

8 S CD

26

40

16

0 1

0 17

0

540

541

0

8209

470

600

CD

0 gt1j

8 (7

) 26

74

0

0 0

0 0

0 10

000

00

0

0000

NA

gt-3 r

(9)

26

74

0 0

0 0

0 0

100

0000

000

00

N

A

ttl

()

36

29

12

0 1

0 22

0

453

125

0

7050

342

900

0 0

9

(7)

36

64

0 0

0 0

0 0

100

0000

000

00

N

A

CD

t

(9)

36

64

0 0

0 0

0 0

100

0000

000

00

N

A

0 ~

0 0(3

) 35

29

19

0

0 0

17

0 44

615

4

079

33

52

780

0

gt-3 r10

(7

) 35

65

0

0 0

0 0

0 10

000

00

0

0000

NA

s

(9

) 35

65

0

0 0

0 0

0 10

000

00

0

0000

NA

(3

) 44

12

20

0

0 0

24

0 21

428

6

054

37

45

450

0

15

(7)

44

56

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

44

56

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

42

9 27

0

0 0

22

0 15

517

2

113

59

55

100

0

20

(7)

42

58

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

42

58

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

53

6 19

0

0 0

22

0 12

766

0

050

21

46

340

0

30

(7)

53

47

0 0

0 0

0 0

100

0000

000

00

N

A

53

47

0 ()

0 0

0 0

100

0000

000

00

N

A

CJ

) C

J)

Of

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

w

Job

--~~

~~-

~--

Ri

Ii

w

CIl

Cl

C2

C

3 C

4

C5

C6

C7

C

8 -----------shy

(3)

51

3 21

0

1 0

24

0

61

22

4

0

46

39

456

500

40

(7

) 51

4

9

0 0

0 0

0 0

10

00

00

0

0

00

00

NA

(9

) 51

4

9

0 -----_

_

-shy

0 0

0 --shy-----~~~~

0 0

-----------shy

10

00

00

0

0

00

00

---------shy

NA

(3

) 4

8

4 33

0

0 0

15

0

769

23

0

62

20

68

75

00

50

(7

) 4

8

52

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

48

5

2

0 0

0 0

0 0

100

0000

00

00

0

N

A

51

4 3

7

0 0

0 8

0 8

16

33

05

05

8

8

22

20

0

10

0

(7)

51

49

0

0 0

0 0

0 10

000

00

0

00

00

NA

(9

) 51

4

9

0 0

0 0

0 0

100

0000

00

00

0

N

A

----------shy

(3)

56

0

35

0 0

0 9

0 0

00

00

02

29

1

79

550

0

20

0

(7)

56

4

4

0 0

0 0

0 0

100

0000

00

00

0

N

A

(9)

56

4

4

0 0

0 0

0 0

100

0000

00

00

0

N

A

69

2

24

0

0 0

5 0

64

51

6

0

13

97

82

76

00

30

0

(7)

69

31

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

(9)

69

31

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

(3)

62

1

35

0

0 0

2 0

26

31

6

0

17

96

94

59

00

~

40

0

(7)

62

3

8

0 0

0 0

0 0

10

00

00

0

0

00

00

NA

0

(9)

62

3

8

0 0

0 0

0 0

100

0000

00

00

0

N

A

fja

tJte

2-C

onat

)

gt-3

)shy z Cl

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

0gtshy

Con

diti

ons

Job

E

i R

i Ii

C

l C

2 C

3 C

4 C

5 C

6 C

7 C

8 ~ rt

J gt-

lt57

0

38

0 0

0 5

0 0

0000

015

97

88

370

0

rtJ

j

500

(7)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

0 3

(9)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

tr1

tlj

0(3

) 57

1

39

0 0

0 3

0 2

3256

014

97

92

860

0

0 rtJ

60

0

(7)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

~ 57

43

0

0 0

0 0

0 10

000

00

0

0000

NA

0 0

1 34

0

gt-lt

(3)

64

0 0

1 0

277

78

0

1198

971

400

tO

3

700

(7)

64

36

0 0

0 0

0 0

100

0000

000

00

N

A

tr1 ~

(9)

64

36

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

60

2 38

0

0 0

0 0

500

00

0

0999

100

0000

800

(7)

60

40

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

60

40

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

62

0 38

0

0 0

0 0

000

00

0

0999

100

0000

900

(7)

62

38

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

62

38

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

60

0 39

0

0 0

1 0

000

0

010

99

97

500

0

1000

(7

) 60

40

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 60

40

0

0 0

0 0

0 10

000

00

0

0000

NA

w

w

(T

able

2 C

ontd

)

-l

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

------

CIJ

Con

diti

ons

CIJ

Job

E

i R

i Ii

O

J

C1

C2

C3

C4

C

5 C

6 C

7

C8

Min

44

615

4

000

00

0

0000

Sm

all

(3

) M

ax

951

220

0

8209

562

500

pro

ble

ms

Avg

66

121

6

050

01

39

021

3

_

Min

0

0000

009

99

45

450

0

Lar

ge

(3

) M

ax

214

286

1

1359

100

0000

p

rob

lem

s A

vg

605

84

0

3374

784

187

--

-_

__

---

Min

0

0000

000

00

0

0000

Ov

eral

l

(3)

Max

95

122

0

113

59

10

000

00

pro

ble

ms

Avg

26

950

0

039

40

64

715

2

tr1

()

gt-3 ~ Q

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

gtshyT

able

3

z C

om

par

ativ

e re

sult

s fo

r th

e C

GP

S

CD

S

an

d N

EH

alg

ori

thm

s ~

Job 3

4

5

6

7

8

9

10

15

20

30

40

50

100

200

101

39

101

48

102

64

102

82

102

62

102

7

102

82

102

55

102

43

101

83

101

06

100

85

100

65

100

32

100

17

~CDS

100

96

101

28

102

14

102

32

102

46

102

15

102

04

102

04

101

78

101

53

100

99

100

63

100

55

100

35

100

17

~~--------------

~NElI

100

1

100

39

100

53

100

54

100

48

100

72

100

50

100

47

100

25

100

33

100

08

100

05

100

06

100

02

100

01

(Tab

le 3

Con

td)

lfl

gt-

lfl

0 tJ r t=J

0 0 i


w

w

to

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

-----

---

co

jgt

~CGPS

~CDS

~NE

H 0

300

100

07

100

11

100

00

400

100

04

100

06

100

00

500

100

02

100

06

100

00

600

100

02

100

03

100

00

700

100

01

100

02

100

00

800

100

02

100

02

100

00

900

100

01

100

04

100

00

1000

1

0001

1

0003

1

0000

Min

1

0139

1

0096

1

0010

Sm

all

pro

ble

ms

Max

1

0282

1

0246

1

0072

Avg

1

0238

1

0192

1

0047

Min

1

0001

1

0002

1

0000

Lar

ge

pro

ble

ms

Max

1

0243

1

0178

1

0033

Avg

1

0050

1

0042

1

0005

Min

1

0001

1

0002

1

0000

r

Ov

eral

l p

rob

lem

s M

ax

102

82

102

46

100

72

0 -3A

vg

101

15

100

95

100

20

p Z

(Tab

le 3

Con

td)

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

lgtT

able

3 (

Con

td)

Z

--------

_shy

SCG

PS

EQ

CG

PS

SCD

S SC

GP

S E

QC

GP

S SN

EH

SN

EH

EQ

IjE

H

SCD

S --

~ Jo

b C

DS

CDS

CG

PS

NEH

N

EH

CG

PS

CD

S CD

S N

EH

en

en

3 0

91

9

0

83

17

12

88

0

0 gtzj

4 2

8

7

11

2

70

28

21

76

3

gt-l

[1j

5 2

82

16

4

58

38

28

66

6

0 0 1

j6

3

77

20

1

51

48

40

56

4

en

7 5

75

20

5

43

52

45

50

5

~ 0 0

8 6

70

24

8

35

57

44

47

9

~

gt-l

9 5

6

7

28

2

40

58

46

46

8

10

7

68

25

5

40

55

42

50

8

15

7

70

23

2

45

53

46

50

4

20

8

65

27

4

46

50

37

58

5

30

8

74

18

0

57

43

35

63

2

40

7

72

21

3

53

44

29

62

9

50

13

62

25

4

49

47

31

59

10

10

0

15

6

0

25

1

52

47

27

71

2

20

0

17

64

19

2

55

43

26

68

6

30

0

12

74

14

7

63

30

17

74

9

w

(T

able

3 C

ontd

)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

Job

S

co

Ps

CD

S E

QC

GP

SC

DS

SCD

S C

GPS

SC

GP

S N

EH

E

QC

GP

SN

EH

S

NE

H

CG

PS

NE

H

SCD

S E

Q

EH

CD

S SC

DS

NE

Il

N

400

14

63

23

5

58

37

14

81

5

500

13

62

25

1

57

42

20

78

2

60

0

9

61

30

4

54

42

12

82

6

700

11

66

23

8

56

36

13

79

8

80

0

10

63

27

4

57

39

14

82

4

900

16

63

21

2

60

38

17

81

2

1000

11

61

28

4

57

39

12

82

6

Sm

all

pro

ble

ms

Min

Max

Avg

0

67

9

7

91

28

375

00

77

125

0

191

250

0

8

337

50

35

17

83

58

525

000

44

1250

12

46

347

500

46

88

598

750

0

9

537

50

Lar

ge

pro

ble

ms

Min

Max

7

17

60

74

14

30

0

8

45

63

30

53

12

46

50

82

2

10

114

00

65

3333

2

326

67

3

4000

546

000

42

0000

233

333

71

333

3

533

33

Ov

eral

l p

rob

lem

s

Min

Max

Avg

0

60

9

17

91

30

873

91

69

434

8 2

182

61

0

8

339

13

35

17

83

58

538

696

42

739

1

12

46

273

043

~~~--~--

46

0

88

10

673

478

5

3478

c 0 ~ gtshy L

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014




5 CONCLUSION


Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

344 H C TANG


REFERENCES




















Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014


lOOO 60 97 10001

Small problems Max

Avg 59

402500 lOO lOO

10355 10289

10139 10282 10238

Large problems

Min Max

42 82 10011 10300

10001 10243 10050


503478 100

922609 10355 10156

10001 10282 10115




Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

ltgtl

ltgtl

Tab

le 2

C

om

para

tiv

e r

esu

lts

for

co

nd

itio

ns

(3)

(7)

an

d (

9)

--------------shy

Job

C

ondi

tion

s E

i R

i Ii

C

1 C

2 C

3 C

4 C

5 C

6 C

7 C

8 -----shy

(3)

59

39

0 0

2 0

0 0

951

220

0

0000

000

00

3 (7

) 59

41

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 59

41

0

0 0

0 0

0 10

000

00

0

0000

NA

-shy

(3)

53

39

4 0

0 0

4 0

829

787

0

3633

500

000

4 (7

) 53

47

0

0 0

0 0

0 10

000

00

0

0000

NA

53

47

0

0 0

0 0

0 10

000

00

0

0000

NA

---shy

-----------shy

(3)

40

44

9 0

1 0

6 0

733

333

0

4365

562

500

5 (7

) 40

60

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 40

eo

0

0 0

0 0

0 10

000

00

0

0000

NA

(3

) 40

4

7

5 0

0 0

8 0

783

333

0

3392

384

600

6 (7

) 40

6

0

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

40

60

0

0 0

0 0

0 10

000

00

0

000

0

NA

-----------shy

(3)

33

37

10

0

0 0

20

0 55

223

9

054

27

33

330

0

7 (7

) 33

6

7

0 0

0 0

0 0

100

0000

000

00

N

A

p (9

) 33

6

7

0 0

0 0

0 0

100

0000

000

00

N

A

0 ------~

(Tab

le 2

Con

td)

gtshy Z

C

)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

Con

diti

ons

~ z

Job

E

i R

i Ii

gt

C

l C

2 C

3 C

4 C

5 C

6 C

7 C

8 S CD

26

40

16

0 1

0 17

0

540

541

0

8209

470

600

CD

0 gt1j

8 (7

) 26

74

0

0 0

0 0

0 10

000

00

0

0000

NA

gt-3 r

(9)

26

74

0 0

0 0

0 0

100

0000

000

00

N

A

ttl

()

36

29

12

0 1

0 22

0

453

125

0

7050

342

900

0 0

9

(7)

36

64

0 0

0 0

0 0

100

0000

000

00

N

A

CD

t

(9)

36

64

0 0

0 0

0 0

100

0000

000

00

N

A

0 ~

0 0(3

) 35

29

19

0

0 0

17

0 44

615

4

079

33

52

780

0

gt-3 r10

(7

) 35

65

0

0 0

0 0

0 10

000

00

0

0000

NA

s

(9

) 35

65

0

0 0

0 0

0 10

000

00

0

0000

NA

(3

) 44

12

20

0

0 0

24

0 21

428

6

054

37

45

450

0

15

(7)

44

56

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

44

56

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

42

9 27

0

0 0

22

0 15

517

2

113

59

55

100

0

20

(7)

42

58

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

42

58

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

53

6 19

0

0 0

22

0 12

766

0

050

21

46

340

0

30

(7)

53

47

0 0

0 0

0 0

100

0000

000

00

N

A

53

47

0 ()

0 0

0 0

100

0000

000

00

N

A

CJ

) C

J)

Of

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

w

Job

--~~

~~-

~--

Ri

Ii

w

CIl

Cl

C2

C

3 C

4

C5

C6

C7

C

8 -----------shy

(3)

51

3 21

0

1 0

24

0

61

22

4

0

46

39

456

500

40

(7

) 51

4

9

0 0

0 0

0 0

10

00

00

0

0

00

00

NA

(9

) 51

4

9

0 -----_

_

-shy

0 0

0 --shy-----~~~~

0 0

-----------shy

10

00

00

0

0

00

00

---------shy

NA

(3

) 4

8

4 33

0

0 0

15

0

769

23

0

62

20

68

75

00

50

(7

) 4

8

52

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

48

5

2

0 0

0 0

0 0

100

0000

00

00

0

N

A

51

4 3

7

0 0

0 8

0 8

16

33

05

05

8

8

22

20

0

10

0

(7)

51

49

0

0 0

0 0

0 10

000

00

0

00

00

NA

(9

) 51

4

9

0 0

0 0

0 0

100

0000

00

00

0

N

A

----------shy

(3)

56

0

35

0 0

0 9

0 0

00

00

02

29

1

79

550

0

20

0

(7)

56

4

4

0 0

0 0

0 0

100

0000

00

00

0

N

A

(9)

56

4

4

0 0

0 0

0 0

100

0000

00

00

0

N

A

69

2

24

0

0 0

5 0

64

51

6

0

13

97

82

76

00

30

0

(7)

69

31

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

(9)

69

31

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

(3)

62

1

35

0

0 0

2 0

26

31

6

0

17

96

94

59

00

~

40

0

(7)

62

3

8

0 0

0 0

0 0

10

00

00

0

0

00

00

NA

0

(9)

62

3

8

0 0

0 0

0 0

100

0000

00

00

0

N

A

fja

tJte

2-C

onat

)

gt-3

)shy z Cl

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

0gtshy

Con

diti

ons

Job

E

i R

i Ii

C

l C

2 C

3 C

4 C

5 C

6 C

7 C

8 ~ rt

J gt-

lt57

0

38

0 0

0 5

0 0

0000

015

97

88

370

0

rtJ

j

500

(7)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

0 3

(9)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

tr1

tlj

0(3

) 57

1

39

0 0

0 3

0 2

3256

014

97

92

860

0

0 rtJ

60

0

(7)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

~ 57

43

0

0 0

0 0

0 10

000

00

0

0000

NA

0 0

1 34

0

gt-lt

(3)

64

0 0

1 0

277

78

0

1198

971

400

tO

3

700

(7)

64

36

0 0

0 0

0 0

100

0000

000

00

N

A

tr1 ~

(9)

64

36

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

60

2 38

0

0 0

0 0

500

00

0

0999

100

0000

800

(7)

60

40

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

60

40

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

62

0 38

0

0 0

0 0

000

00

0

0999

100

0000

900

(7)

62

38

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

62

38

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

60

0 39

0

0 0

1 0

000

0

010

99

97

500

0

1000

(7

) 60

40

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 60

40

0

0 0

0 0

0 10

000

00

0

0000

NA

w

w

(T

able

2 C

ontd

)

-l

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

------

CIJ

Con

diti

ons

CIJ

Job

E

i R

i Ii

O

J

C1

C2

C3

C4

C

5 C

6 C

7

C8

Min

44

615

4

000

00

0

0000

Sm

all

(3

) M

ax

951

220

0

8209

562

500

pro

ble

ms

Avg

66

121

6

050

01

39

021

3

_

Min

0

0000

009

99

45

450

0

Lar

ge

(3

) M

ax

214

286

1

1359

100

0000

p

rob

lem

s A

vg

605

84

0

3374

784

187

--

-_

__

---

Min

0

0000

000

00

0

0000

Ov

eral

l

(3)

Max

95

122

0

113

59

10

000

00

pro

ble

ms

Avg

26

950

0

039

40

64

715

2

tr1

()

gt-3 ~ Q

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

gtshyT

able

3

z C

om

par

ativ

e re

sult

s fo

r th

e C

GP

S

CD

S

an

d N

EH

alg

ori

thm

s ~

Job 3

4

5

6

7

8

9

10

15

20

30

40

50

100

200

101

39

101

48

102

64

102

82

102

62

102

7

102

82

102

55

102

43

101

83

101

06

100

85

100

65

100

32

100

17

~CDS

100

96

101

28

102

14

102

32

102

46

102

15

102

04

102

04

101

78

101

53

100

99

100

63

100

55

100

35

100

17

~~--------------

~NElI

100

1

100

39

100

53

100

54

100

48

100

72

100

50

100

47

100

25

100

33

100

08

100

05

100

06

100

02

100

01

(Tab

le 3

Con

td)

lfl

gt-

lfl

0 tJ r t=J

0 0 i


w

w

to

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

-----

---

co

jgt

~CGPS

~CDS

~NE

H 0

300

100

07

100

11

100

00

400

100

04

100

06

100

00

500

100

02

100

06

100

00

600

100

02

100

03

100

00

700

100

01

100

02

100

00

800

100

02

100

02

100

00

900

100

01

100

04

100

00

1000

1

0001

1

0003

1

0000

Min

1

0139

1

0096

1

0010

Sm

all

pro

ble

ms

Max

1

0282

1

0246

1

0072

Avg

1

0238

1

0192

1

0047

Min

1

0001

1

0002

1

0000

Lar

ge

pro

ble

ms

Max

1

0243

1

0178

1

0033

Avg

1

0050

1

0042

1

0005

Min

1

0001

1

0002

1

0000

r

Ov

eral

l p

rob

lem

s M

ax

102

82

102

46

100

72

0 -3A

vg

101

15

100

95

100

20

p Z

(Tab

le 3

Con

td)

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

lgtT

able

3 (

Con

td)

Z

--------

_shy

SCG

PS

EQ

CG

PS

SCD

S SC

GP

S E

QC

GP

S SN

EH

SN

EH

EQ

IjE

H

SCD

S --

~ Jo

b C

DS

CDS

CG

PS

NEH

N

EH

CG

PS

CD

S CD

S N

EH

en

en

3 0

91

9

0

83

17

12

88

0

0 gtzj

4 2

8

7

11

2

70

28

21

76

3

gt-l

[1j

5 2

82

16

4

58

38

28

66

6

0 0 1

j6

3

77

20

1

51

48

40

56

4

en

7 5

75

20

5

43

52

45

50

5

~ 0 0

8 6

70

24

8

35

57

44

47

9

~

gt-l

9 5

6

7

28

2

40

58

46

46

8

10

7

68

25

5

40

55

42

50

8

15

7

70

23

2

45

53

46

50

4

20

8

65

27

4

46

50

37

58

5

30

8

74

18

0

57

43

35

63

2

40

7

72

21

3

53

44

29

62

9

50

13

62

25

4

49

47

31

59

10

10

0

15

6

0

25

1

52

47

27

71

2

20

0

17

64

19

2

55

43

26

68

6

30

0

12

74

14

7

63

30

17

74

9

w

(T

able

3 C

ontd

)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

Job

S

co

Ps

CD

S E

QC

GP

SC

DS

SCD

S C

GPS

SC

GP

S N

EH

E

QC

GP

SN

EH

S

NE

H

CG

PS

NE

H

SCD

S E

Q

EH

CD

S SC

DS

NE

Il

N

400

14

63

23

5

58

37

14

81

5

500

13

62

25

1

57

42

20

78

2

60

0

9

61

30

4

54

42

12

82

6

700

11

66

23

8

56

36

13

79

8

80

0

10

63

27

4

57

39

14

82

4

900

16

63

21

2

60

38

17

81

2

1000

11

61

28

4

57

39

12

82

6

Sm

all

pro

ble

ms

Min

Max

Avg

0

67

9

7

91

28

375

00

77

125

0

191

250

0

8

337

50

35

17

83

58

525

000

44

1250

12

46

347

500

46

88

598

750

0

9

537

50

Lar

ge

pro

ble

ms

Min

Max

7

17

60

74

14

30

0

8

45

63

30

53

12

46

50

82

2

10

114

00

65

3333

2

326

67

3

4000

546

000

42

0000

233

333

71

333

3

533

33

Ov

eral

l p

rob

lem

s

Min

Max

Avg

0

60

9

17

91

30

873

91

69

434

8 2

182

61

0

8

339

13

35

17

83

58

538

696

42

739

1

12

46

273

043

~~~--~--

46

0

88

10

673

478

5

3478

c 0 ~ gtshy L

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014




5 CONCLUSION


Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

344 H C TANG


REFERENCES




















Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

ltgtl

ltgtl

Tab

le 2

C

om

para

tiv

e r

esu

lts

for

co

nd

itio

ns

(3)

(7)

an

d (

9)

--------------shy

Job

C

ondi

tion

s E

i R

i Ii

C

1 C

2 C

3 C

4 C

5 C

6 C

7 C

8 -----shy

(3)

59

39

0 0

2 0

0 0

951

220

0

0000

000

00

3 (7

) 59

41

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 59

41

0

0 0

0 0

0 10

000

00

0

0000

NA

-shy

(3)

53

39

4 0

0 0

4 0

829

787

0

3633

500

000

4 (7

) 53

47

0

0 0

0 0

0 10

000

00

0

0000

NA

53

47

0

0 0

0 0

0 10

000

00

0

0000

NA

---shy

-----------shy

(3)

40

44

9 0

1 0

6 0

733

333

0

4365

562

500

5 (7

) 40

60

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 40

eo

0

0 0

0 0

0 10

000

00

0

0000

NA

(3

) 40

4

7

5 0

0 0

8 0

783

333

0

3392

384

600

6 (7

) 40

6

0

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

40

60

0

0 0

0 0

0 10

000

00

0

000

0

NA

-----------shy

(3)

33

37

10

0

0 0

20

0 55

223

9

054

27

33

330

0

7 (7

) 33

6

7

0 0

0 0

0 0

100

0000

000

00

N

A

p (9

) 33

6

7

0 0

0 0

0 0

100

0000

000

00

N

A

0 ------~

(Tab

le 2

Con

td)

gtshy Z

C

)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

Con

diti

ons

~ z

Job

E

i R

i Ii

gt

C

l C

2 C

3 C

4 C

5 C

6 C

7 C

8 S CD

26

40

16

0 1

0 17

0

540

541

0

8209

470

600

CD

0 gt1j

8 (7

) 26

74

0

0 0

0 0

0 10

000

00

0

0000

NA

gt-3 r

(9)

26

74

0 0

0 0

0 0

100

0000

000

00

N

A

ttl

()

36

29

12

0 1

0 22

0

453

125

0

7050

342

900

0 0

9

(7)

36

64

0 0

0 0

0 0

100

0000

000

00

N

A

CD

t

(9)

36

64

0 0

0 0

0 0

100

0000

000

00

N

A

0 ~

0 0(3

) 35

29

19

0

0 0

17

0 44

615

4

079

33

52

780

0

gt-3 r10

(7

) 35

65

0

0 0

0 0

0 10

000

00

0

0000

NA

s

(9

) 35

65

0

0 0

0 0

0 10

000

00

0

0000

NA

(3

) 44

12

20

0

0 0

24

0 21

428

6

054

37

45

450

0

15

(7)

44

56

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

44

56

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

42

9 27

0

0 0

22

0 15

517

2

113

59

55

100

0

20

(7)

42

58

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

42

58

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

53

6 19

0

0 0

22

0 12

766

0

050

21

46

340

0

30

(7)

53

47

0 0

0 0

0 0

100

0000

000

00

N

A

53

47

0 ()

0 0

0 0

100

0000

000

00

N

A

CJ

) C

J)

Of

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

w

Job

--~~

~~-

~--

Ri

Ii

w

CIl

Cl

C2

C

3 C

4

C5

C6

C7

C

8 -----------shy

(3)

51

3 21

0

1 0

24

0

61

22

4

0

46

39

456

500

40

(7

) 51

4

9

0 0

0 0

0 0

10

00

00

0

0

00

00

NA

(9

) 51

4

9

0 -----_

_

-shy

0 0

0 --shy-----~~~~

0 0

-----------shy

10

00

00

0

0

00

00

---------shy

NA

(3

) 4

8

4 33

0

0 0

15

0

769

23

0

62

20

68

75

00

50

(7

) 4

8

52

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

48

5

2

0 0

0 0

0 0

100

0000

00

00

0

N

A

51

4 3

7

0 0

0 8

0 8

16

33

05

05

8

8

22

20

0

10

0

(7)

51

49

0

0 0

0 0

0 10

000

00

0

00

00

NA

(9

) 51

4

9

0 0

0 0

0 0

100

0000

00

00

0

N

A

----------shy

(3)

56

0

35

0 0

0 9

0 0

00

00

02

29

1

79

550

0

20

0

(7)

56

4

4

0 0

0 0

0 0

100

0000

00

00

0

N

A

(9)

56

4

4

0 0

0 0

0 0

100

0000

00

00

0

N

A

69

2

24

0

0 0

5 0

64

51

6

0

13

97

82

76

00

30

0

(7)

69

31

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

(9)

69

31

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

(3)

62

1

35

0

0 0

2 0

26

31

6

0

17

96

94

59

00

~

40

0

(7)

62

3

8

0 0

0 0

0 0

10

00

00

0

0

00

00

NA

0

(9)

62

3

8

0 0

0 0

0 0

100

0000

00

00

0

N

A

fja

tJte

2-C

onat

)

gt-3

)shy z Cl

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

0gtshy

Con

diti

ons

Job

E

i R

i Ii

C

l C

2 C

3 C

4 C

5 C

6 C

7 C

8 ~ rt

J gt-

lt57

0

38

0 0

0 5

0 0

0000

015

97

88

370

0

rtJ

j

500

(7)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

0 3

(9)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

tr1

tlj

0(3

) 57

1

39

0 0

0 3

0 2

3256

014

97

92

860

0

0 rtJ

60

0

(7)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

~ 57

43

0

0 0

0 0

0 10

000

00

0

0000

NA

0 0

1 34

0

gt-lt

(3)

64

0 0

1 0

277

78

0

1198

971

400

tO

3

700

(7)

64

36

0 0

0 0

0 0

100

0000

000

00

N

A

tr1 ~

(9)

64

36

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

60

2 38

0

0 0

0 0

500

00

0

0999

100

0000

800

(7)

60

40

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

60

40

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

62

0 38

0

0 0

0 0

000

00

0

0999

100

0000

900

(7)

62

38

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

62

38

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

60

0 39

0

0 0

1 0

000

0

010

99

97

500

0

1000

(7

) 60

40

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 60

40

0

0 0

0 0

0 10

000

00

0

0000

NA

w

w

(T

able

2 C

ontd

)

-l

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

------

CIJ

Con

diti

ons

CIJ

Job

E

i R

i Ii

O

J

C1

C2

C3

C4

C

5 C

6 C

7

C8

Min

44

615

4

000

00

0

0000

Sm

all

(3

) M

ax

951

220

0

8209

562

500

pro

ble

ms

Avg

66

121

6

050

01

39

021

3

_

Min

0

0000

009

99

45

450

0

Lar

ge

(3

) M

ax

214

286

1

1359

100

0000

p

rob

lem

s A

vg

605

84

0

3374

784

187

--

-_

__

---

Min

0

0000

000

00

0

0000

Ov

eral

l

(3)

Max

95

122

0

113

59

10

000

00

pro

ble

ms

Avg

26

950

0

039

40

64

715

2

tr1

()

gt-3 ~ Q

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

gtshyT

able

3

z C

om

par

ativ

e re

sult

s fo

r th

e C

GP

S

CD

S

an

d N

EH

alg

ori

thm

s ~

Job 3

4

5

6

7

8

9

10

15

20

30

40

50

100

200

101

39

101

48

102

64

102

82

102

62

102

7

102

82

102

55

102

43

101

83

101

06

100

85

100

65

100

32

100

17

~CDS

100

96

101

28

102

14

102

32

102

46

102

15

102

04

102

04

101

78

101

53

100

99

100

63

100

55

100

35

100

17

~~--------------

~NElI

100

1

100

39

100

53

100

54

100

48

100

72

100

50

100

47

100

25

100

33

100

08

100

05

100

06

100

02

100

01

(Tab

le 3

Con

td)

lfl

gt-

lfl

0 tJ r t=J

0 0 i


w

w

to

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

-----

---

co

jgt

~CGPS

~CDS

~NE

H 0

300

100

07

100

11

100

00

400

100

04

100

06

100

00

500

100

02

100

06

100

00

600

100

02

100

03

100

00

700

100

01

100

02

100

00

800

100

02

100

02

100

00

900

100

01

100

04

100

00

1000

1

0001

1

0003

1

0000

Min

1

0139

1

0096

1

0010

Sm

all

pro

ble

ms

Max

1

0282

1

0246

1

0072

Avg

1

0238

1

0192

1

0047

Min

1

0001

1

0002

1

0000

Lar

ge

pro

ble

ms

Max

1

0243

1

0178

1

0033

Avg

1

0050

1

0042

1

0005

Min

1

0001

1

0002

1

0000

r

Ov

eral

l p

rob

lem

s M

ax

102

82

102

46

100

72

0 -3A

vg

101

15

100

95

100

20

p Z

(Tab

le 3

Con

td)

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

lgtT

able

3 (

Con

td)

Z

--------

_shy

SCG

PS

EQ

CG

PS

SCD

S SC

GP

S E

QC

GP

S SN

EH

SN

EH

EQ

IjE

H

SCD

S --

~ Jo

b C

DS

CDS

CG

PS

NEH

N

EH

CG

PS

CD

S CD

S N

EH

en

en

3 0

91

9

0

83

17

12

88

0

0 gtzj

4 2

8

7

11

2

70

28

21

76

3

gt-l

[1j

5 2

82

16

4

58

38

28

66

6

0 0 1

j6

3

77

20

1

51

48

40

56

4

en

7 5

75

20

5

43

52

45

50

5

~ 0 0

8 6

70

24

8

35

57

44

47

9

~

gt-l

9 5

6

7

28

2

40

58

46

46

8

10

7

68

25

5

40

55

42

50

8

15

7

70

23

2

45

53

46

50

4

20

8

65

27

4

46

50

37

58

5

30

8

74

18

0

57

43

35

63

2

40

7

72

21

3

53

44

29

62

9

50

13

62

25

4

49

47

31

59

10

10

0

15

6

0

25

1

52

47

27

71

2

20

0

17

64

19

2

55

43

26

68

6

30

0

12

74

14

7

63

30

17

74

9

w

(T

able

3 C

ontd

)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

Job

S

co

Ps

CD

S E

QC

GP

SC

DS

SCD

S C

GPS

SC

GP

S N

EH

E

QC

GP

SN

EH

S

NE

H

CG

PS

NE

H

SCD

S E

Q

EH

CD

S SC

DS

NE

Il

N

400

14

63

23

5

58

37

14

81

5

500

13

62

25

1

57

42

20

78

2

60

0

9

61

30

4

54

42

12

82

6

700

11

66

23

8

56

36

13

79

8

80

0

10

63

27

4

57

39

14

82

4

900

16

63

21

2

60

38

17

81

2

1000

11

61

28

4

57

39

12

82

6

Sm

all

pro

ble

ms

Min

Max

Avg

0

67

9

7

91

28

375

00

77

125

0

191

250

0

8

337

50

35

17

83

58

525

000

44

1250

12

46

347

500

46

88

598

750

0

9

537

50

Lar

ge

pro

ble

ms

Min

Max

7

17

60

74

14

30

0

8

45

63

30

53

12

46

50

82

2

10

114

00

65

3333

2

326

67

3

4000

546

000

42

0000

233

333

71

333

3

533

33

Ov

eral

l p

rob

lem

s

Min

Max

Avg

0

60

9

17

91

30

873

91

69

434

8 2

182

61

0

8

339

13

35

17

83

58

538

696

42

739

1

12

46

273

043

~~~--~--

46

0

88

10

673

478

5

3478

c 0 ~ gtshy L

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014




5 CONCLUSION


Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

344 H C TANG


REFERENCES




















Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

Con

diti

ons

~ z

Job

E

i R

i Ii

gt

C

l C

2 C

3 C

4 C

5 C

6 C

7 C

8 S CD

26

40

16

0 1

0 17

0

540

541

0

8209

470

600

CD

0 gt1j

8 (7

) 26

74

0

0 0

0 0

0 10

000

00

0

0000

NA

gt-3 r

(9)

26

74

0 0

0 0

0 0

100

0000

000

00

N

A

ttl

()

36

29

12

0 1

0 22

0

453

125

0

7050

342

900

0 0

9

(7)

36

64

0 0

0 0

0 0

100

0000

000

00

N

A

CD

t

(9)

36

64

0 0

0 0

0 0

100

0000

000

00

N

A

0 ~

0 0(3

) 35

29

19

0

0 0

17

0 44

615

4

079

33

52

780

0

gt-3 r10

(7

) 35

65

0

0 0

0 0

0 10

000

00

0

0000

NA

s

(9

) 35

65

0

0 0

0 0

0 10

000

00

0

0000

NA

(3

) 44

12

20

0

0 0

24

0 21

428

6

054

37

45

450

0

15

(7)

44

56

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

44

56

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

42

9 27

0

0 0

22

0 15

517

2

113

59

55

100

0

20

(7)

42

58

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

42

58

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

53

6 19

0

0 0

22

0 12

766

0

050

21

46

340

0

30

(7)

53

47

0 0

0 0

0 0

100

0000

000

00

N

A

53

47

0 ()

0 0

0 0

100

0000

000

00

N

A

CJ

) C

J)

Of

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

w

Job

--~~

~~-

~--

Ri

Ii

w

CIl

Cl

C2

C

3 C

4

C5

C6

C7

C

8 -----------shy

(3)

51

3 21

0

1 0

24

0

61

22

4

0

46

39

456

500

40

(7

) 51

4

9

0 0

0 0

0 0

10

00

00

0

0

00

00

NA

(9

) 51

4

9

0 -----_

_

-shy

0 0

0 --shy-----~~~~

0 0

-----------shy

10

00

00

0

0

00

00

---------shy

NA

(3

) 4

8

4 33

0

0 0

15

0

769

23

0

62

20

68

75

00

50

(7

) 4

8

52

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

48

5

2

0 0

0 0

0 0

100

0000

00

00

0

N

A

51

4 3

7

0 0

0 8

0 8

16

33

05

05

8

8

22

20

0

10

0

(7)

51

49

0

0 0

0 0

0 10

000

00

0

00

00

NA

(9

) 51

4

9

0 0

0 0

0 0

100

0000

00

00

0

N

A

----------shy

(3)

56

0

35

0 0

0 9

0 0

00

00

02

29

1

79

550

0

20

0

(7)

56

4

4

0 0

0 0

0 0

100

0000

00

00

0

N

A

(9)

56

4

4

0 0

0 0

0 0

100

0000

00

00

0

N

A

69

2

24

0

0 0

5 0

64

51

6

0

13

97

82

76

00

30

0

(7)

69

31

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

(9)

69

31

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

(3)

62

1

35

0

0 0

2 0

26

31

6

0

17

96

94

59

00

~

40

0

(7)

62

3

8

0 0

0 0

0 0

10

00

00

0

0

00

00

NA

0

(9)

62

3

8

0 0

0 0

0 0

100

0000

00

00

0

N

A

fja

tJte

2-C

onat

)

gt-3

)shy z Cl

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

0gtshy

Con

diti

ons

Job

E

i R

i Ii

C

l C

2 C

3 C

4 C

5 C

6 C

7 C

8 ~ rt

J gt-

lt57

0

38

0 0

0 5

0 0

0000

015

97

88

370

0

rtJ

j

500

(7)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

0 3

(9)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

tr1

tlj

0(3

) 57

1

39

0 0

0 3

0 2

3256

014

97

92

860

0

0 rtJ

60

0

(7)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

~ 57

43

0

0 0

0 0

0 10

000

00

0

0000

NA

0 0

1 34

0

gt-lt

(3)

64

0 0

1 0

277

78

0

1198

971

400

tO

3

700

(7)

64

36

0 0

0 0

0 0

100

0000

000

00

N

A

tr1 ~

(9)

64

36

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

60

2 38

0

0 0

0 0

500

00

0

0999

100

0000

800

(7)

60

40

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

60

40

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

62

0 38

0

0 0

0 0

000

00

0

0999

100

0000

900

(7)

62

38

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

62

38

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

60

0 39

0

0 0

1 0

000

0

010

99

97

500

0

1000

(7

) 60

40

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 60

40

0

0 0

0 0

0 10

000

00

0

0000

NA

w

w

(T

able

2 C

ontd

)

-l

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

------

CIJ

Con

diti

ons

CIJ

Job

E

i R

i Ii

O

J

C1

C2

C3

C4

C

5 C

6 C

7

C8

Min

44

615

4

000

00

0

0000

Sm

all

(3

) M

ax

951

220

0

8209

562

500

pro

ble

ms

Avg

66

121

6

050

01

39

021

3

_

Min

0

0000

009

99

45

450

0

Lar

ge

(3

) M

ax

214

286

1

1359

100

0000

p

rob

lem

s A

vg

605

84

0

3374

784

187

--

-_

__

---

Min

0

0000

000

00

0

0000

Ov

eral

l

(3)

Max

95

122

0

113

59

10

000

00

pro

ble

ms

Avg

26

950

0

039

40

64

715

2

tr1

()

gt-3 ~ Q

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

gtshyT

able

3

z C

om

par

ativ

e re

sult

s fo

r th

e C

GP

S

CD

S

an

d N

EH

alg

ori

thm

s ~

Job 3

4

5

6

7

8

9

10

15

20

30

40

50

100

200

101

39

101

48

102

64

102

82

102

62

102

7

102

82

102

55

102

43

101

83

101

06

100

85

100

65

100

32

100

17

~CDS

100

96

101

28

102

14

102

32

102

46

102

15

102

04

102

04

101

78

101

53

100

99

100

63

100

55

100

35

100

17

~~--------------

~NElI

100

1

100

39

100

53

100

54

100

48

100

72

100

50

100

47

100

25

100

33

100

08

100

05

100

06

100

02

100

01

(Tab

le 3

Con

td)

lfl

gt-

lfl

0 tJ r t=J

0 0 i


w

w

to

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

-----

---

co

jgt

~CGPS

~CDS

~NE

H 0

300

100

07

100

11

100

00

400

100

04

100

06

100

00

500

100

02

100

06

100

00

600

100

02

100

03

100

00

700

100

01

100

02

100

00

800

100

02

100

02

100

00

900

100

01

100

04

100

00

1000

1

0001

1

0003

1

0000

Min

1

0139

1

0096

1

0010

Sm

all

pro

ble

ms

Max

1

0282

1

0246

1

0072

Avg

1

0238

1

0192

1

0047

Min

1

0001

1

0002

1

0000

Lar

ge

pro

ble

ms

Max

1

0243

1

0178

1

0033

Avg

1

0050

1

0042

1

0005

Min

1

0001

1

0002

1

0000

r

Ov

eral

l p

rob

lem

s M

ax

102

82

102

46

100

72

0 -3A

vg

101

15

100

95

100

20

p Z

(Tab

le 3

Con

td)

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

lgtT

able

3 (

Con

td)

Z

--------

_shy

SCG

PS

EQ

CG

PS

SCD

S SC

GP

S E

QC

GP

S SN

EH

SN

EH

EQ

IjE

H

SCD

S --

~ Jo

b C

DS

CDS

CG

PS

NEH

N

EH

CG

PS

CD

S CD

S N

EH

en

en

3 0

91

9

0

83

17

12

88

0

0 gtzj

4 2

8

7

11

2

70

28

21

76

3

gt-l

[1j

5 2

82

16

4

58

38

28

66

6

0 0 1

j6

3

77

20

1

51

48

40

56

4

en

7 5

75

20

5

43

52

45

50

5

~ 0 0

8 6

70

24

8

35

57

44

47

9

~

gt-l

9 5

6

7

28

2

40

58

46

46

8

10

7

68

25

5

40

55

42

50

8

15

7

70

23

2

45

53

46

50

4

20

8

65

27

4

46

50

37

58

5

30

8

74

18

0

57

43

35

63

2

40

7

72

21

3

53

44

29

62

9

50

13

62

25

4

49

47

31

59

10

10

0

15

6

0

25

1

52

47

27

71

2

20

0

17

64

19

2

55

43

26

68

6

30

0

12

74

14

7

63

30

17

74

9

w

(T

able

3 C

ontd

)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

Job

S

co

Ps

CD

S E

QC

GP

SC

DS

SCD

S C

GPS

SC

GP

S N

EH

E

QC

GP

SN

EH

S

NE

H

CG

PS

NE

H

SCD

S E

Q

EH

CD

S SC

DS

NE

Il

N

400

14

63

23

5

58

37

14

81

5

500

13

62

25

1

57

42

20

78

2

60

0

9

61

30

4

54

42

12

82

6

700

11

66

23

8

56

36

13

79

8

80

0

10

63

27

4

57

39

14

82

4

900

16

63

21

2

60

38

17

81

2

1000

11

61

28

4

57

39

12

82

6

Sm

all

pro

ble

ms

Min

Max

Avg

0

67

9

7

91

28

375

00

77

125

0

191

250

0

8

337

50

35

17

83

58

525

000

44

1250

12

46

347

500

46

88

598

750

0

9

537

50

Lar

ge

pro

ble

ms

Min

Max

7

17

60

74

14

30

0

8

45

63

30

53

12

46

50

82

2

10

114

00

65

3333

2

326

67

3

4000

546

000

42

0000

233

333

71

333

3

533

33

Ov

eral

l p

rob

lem

s

Min

Max

Avg

0

60

9

17

91

30

873

91

69

434

8 2

182

61

0

8

339

13

35

17

83

58

538

696

42

739

1

12

46

273

043

~~~--~--

46

0

88

10

673

478

5

3478

c 0 ~ gtshy L

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014




5 CONCLUSION


Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

344 H C TANG


REFERENCES




















Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

w

Job

--~~

~~-

~--

Ri

Ii

w

CIl

Cl

C2

C

3 C

4

C5

C6

C7

C

8 -----------shy

(3)

51

3 21

0

1 0

24

0

61

22

4

0

46

39

456

500

40

(7

) 51

4

9

0 0

0 0

0 0

10

00

00

0

0

00

00

NA

(9

) 51

4

9

0 -----_

_

-shy

0 0

0 --shy-----~~~~

0 0

-----------shy

10

00

00

0

0

00

00

---------shy

NA

(3

) 4

8

4 33

0

0 0

15

0

769

23

0

62

20

68

75

00

50

(7

) 4

8

52

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

48

5

2

0 0

0 0

0 0

100

0000

00

00

0

N

A

51

4 3

7

0 0

0 8

0 8

16

33

05

05

8

8

22

20

0

10

0

(7)

51

49

0

0 0

0 0

0 10

000

00

0

00

00

NA

(9

) 51

4

9

0 0

0 0

0 0

100

0000

00

00

0

N

A

----------shy

(3)

56

0

35

0 0

0 9

0 0

00

00

02

29

1

79

550

0

20

0

(7)

56

4

4

0 0

0 0

0 0

100

0000

00

00

0

N

A

(9)

56

4

4

0 0

0 0

0 0

100

0000

00

00

0

N

A

69

2

24

0

0 0

5 0

64

51

6

0

13

97

82

76

00

30

0

(7)

69

31

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

(9)

69

31

0

0 0

0 0

0 1

00

00

00

00

00

0

N

A

(3)

62

1

35

0

0 0

2 0

26

31

6

0

17

96

94

59

00

~

40

0

(7)

62

3

8

0 0

0 0

0 0

10

00

00

0

0

00

00

NA

0

(9)

62

3

8

0 0

0 0

0 0

100

0000

00

00

0

N

A

fja

tJte

2-C

onat

)

gt-3

)shy z Cl

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

0gtshy

Con

diti

ons

Job

E

i R

i Ii

C

l C

2 C

3 C

4 C

5 C

6 C

7 C

8 ~ rt

J gt-

lt57

0

38

0 0

0 5

0 0

0000

015

97

88

370

0

rtJ

j

500

(7)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

0 3

(9)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

tr1

tlj

0(3

) 57

1

39

0 0

0 3

0 2

3256

014

97

92

860

0

0 rtJ

60

0

(7)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

~ 57

43

0

0 0

0 0

0 10

000

00

0

0000

NA

0 0

1 34

0

gt-lt

(3)

64

0 0

1 0

277

78

0

1198

971

400

tO

3

700

(7)

64

36

0 0

0 0

0 0

100

0000

000

00

N

A

tr1 ~

(9)

64

36

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

60

2 38

0

0 0

0 0

500

00

0

0999

100

0000

800

(7)

60

40

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

60

40

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

62

0 38

0

0 0

0 0

000

00

0

0999

100

0000

900

(7)

62

38

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

62

38

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

60

0 39

0

0 0

1 0

000

0

010

99

97

500

0

1000

(7

) 60

40

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 60

40

0

0 0

0 0

0 10

000

00

0

0000

NA

w

w

(T

able

2 C

ontd

)

-l

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

------

CIJ

Con

diti

ons

CIJ

Job

E

i R

i Ii

O

J

C1

C2

C3

C4

C

5 C

6 C

7

C8

Min

44

615

4

000

00

0

0000

Sm

all

(3

) M

ax

951

220

0

8209

562

500

pro

ble

ms

Avg

66

121

6

050

01

39

021

3

_

Min

0

0000

009

99

45

450

0

Lar

ge

(3

) M

ax

214

286

1

1359

100

0000

p

rob

lem

s A

vg

605

84

0

3374

784

187

--

-_

__

---

Min

0

0000

000

00

0

0000

Ov

eral

l

(3)

Max

95

122

0

113

59

10

000

00

pro

ble

ms

Avg

26

950

0

039

40

64

715

2

tr1

()

gt-3 ~ Q

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

gtshyT

able

3

z C

om

par

ativ

e re

sult

s fo

r th

e C

GP

S

CD

S

an

d N

EH

alg

ori

thm

s ~

Job 3

4

5

6

7

8

9

10

15

20

30

40

50

100

200

101

39

101

48

102

64

102

82

102

62

102

7

102

82

102

55

102

43

101

83

101

06

100

85

100

65

100

32

100

17

~CDS

100

96

101

28

102

14

102

32

102

46

102

15

102

04

102

04

101

78

101

53

100

99

100

63

100

55

100

35

100

17

~~--------------

~NElI

100

1

100

39

100

53

100

54

100

48

100

72

100

50

100

47

100

25

100

33

100

08

100

05

100

06

100

02

100

01

(Tab

le 3

Con

td)

lfl

gt-

lfl

0 tJ r t=J

0 0 i


w

w

to

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

-----

---

co

jgt

~CGPS

~CDS

~NE

H 0

300

100

07

100

11

100

00

400

100

04

100

06

100

00

500

100

02

100

06

100

00

600

100

02

100

03

100

00

700

100

01

100

02

100

00

800

100

02

100

02

100

00

900

100

01

100

04

100

00

1000

1

0001

1

0003

1

0000

Min

1

0139

1

0096

1

0010

Sm

all

pro

ble

ms

Max

1

0282

1

0246

1

0072

Avg

1

0238

1

0192

1

0047

Min

1

0001

1

0002

1

0000

Lar

ge

pro

ble

ms

Max

1

0243

1

0178

1

0033

Avg

1

0050

1

0042

1

0005

Min

1

0001

1

0002

1

0000

r

Ov

eral

l p

rob

lem

s M

ax

102

82

102

46

100

72

0 -3A

vg

101

15

100

95

100

20

p Z

(Tab

le 3

Con

td)

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

lgtT

able

3 (

Con

td)

Z

--------

_shy

SCG

PS

EQ

CG

PS

SCD

S SC

GP

S E

QC

GP

S SN

EH

SN

EH

EQ

IjE

H

SCD

S --

~ Jo

b C

DS

CDS

CG

PS

NEH

N

EH

CG

PS

CD

S CD

S N

EH

en

en

3 0

91

9

0

83

17

12

88

0

0 gtzj

4 2

8

7

11

2

70

28

21

76

3

gt-l

[1j

5 2

82

16

4

58

38

28

66

6

0 0 1

j6

3

77

20

1

51

48

40

56

4

en

7 5

75

20

5

43

52

45

50

5

~ 0 0

8 6

70

24

8

35

57

44

47

9

~

gt-l

9 5

6

7

28

2

40

58

46

46

8

10

7

68

25

5

40

55

42

50

8

15

7

70

23

2

45

53

46

50

4

20

8

65

27

4

46

50

37

58

5

30

8

74

18

0

57

43

35

63

2

40

7

72

21

3

53

44

29

62

9

50

13

62

25

4

49

47

31

59

10

10

0

15

6

0

25

1

52

47

27

71

2

20

0

17

64

19

2

55

43

26

68

6

30

0

12

74

14

7

63

30

17

74

9

w

(T

able

3 C

ontd

)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

Job

S

co

Ps

CD

S E

QC

GP

SC

DS

SCD

S C

GPS

SC

GP

S N

EH

E

QC

GP

SN

EH

S

NE

H

CG

PS

NE

H

SCD

S E

Q

EH

CD

S SC

DS

NE

Il

N

400

14

63

23

5

58

37

14

81

5

500

13

62

25

1

57

42

20

78

2

60

0

9

61

30

4

54

42

12

82

6

700

11

66

23

8

56

36

13

79

8

80

0

10

63

27

4

57

39

14

82

4

900

16

63

21

2

60

38

17

81

2

1000

11

61

28

4

57

39

12

82

6

Sm

all

pro

ble

ms

Min

Max

Avg

0

67

9

7

91

28

375

00

77

125

0

191

250

0

8

337

50

35

17

83

58

525

000

44

1250

12

46

347

500

46

88

598

750

0

9

537

50

Lar

ge

pro

ble

ms

Min

Max

7

17

60

74

14

30

0

8

45

63

30

53

12

46

50

82

2

10

114

00

65

3333

2

326

67

3

4000

546

000

42

0000

233

333

71

333

3

533

33

Ov

eral

l p

rob

lem

s

Min

Max

Avg

0

60

9

17

91

30

873

91

69

434

8 2

182

61

0

8

339

13

35

17

83

58

538

696

42

739

1

12

46

273

043

~~~--~--

46

0

88

10

673

478

5

3478

c 0 ~ gtshy L

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014




5 CONCLUSION


Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

344 H C TANG


REFERENCES




















Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

0gtshy

Con

diti

ons

Job

E

i R

i Ii

C

l C

2 C

3 C

4 C

5 C

6 C

7 C

8 ~ rt

J gt-

lt57

0

38

0 0

0 5

0 0

0000

015

97

88

370

0

rtJ

j

500

(7)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

0 3

(9)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

tr1

tlj

0(3

) 57

1

39

0 0

0 3

0 2

3256

014

97

92

860

0

0 rtJ

60

0

(7)

57

43

0 0

0 0

0 0

100

0000

000

00

N

A

~ 57

43

0

0 0

0 0

0 10

000

00

0

0000

NA

0 0

1 34

0

gt-lt

(3)

64

0 0

1 0

277

78

0

1198

971

400

tO

3

700

(7)

64

36

0 0

0 0

0 0

100

0000

000

00

N

A

tr1 ~

(9)

64

36

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

60

2 38

0

0 0

0 0

500

00

0

0999

100

0000

800

(7)

60

40

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

60

40

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

62

0 38

0

0 0

0 0

000

00

0

0999

100

0000

900

(7)

62

38

0 0

0 0

0 0

100

0000

000

00

N

A

(9)

62

38

0 0

0 0

0 0

100

0000

000

00

N

A

(3)

60

0 39

0

0 0

1 0

000

0

010

99

97

500

0

1000

(7

) 60

40

0

0 0

0 0

0 10

000

00

0

0000

NA

(9

) 60

40

0

0 0

0 0

0 10

000

00

0

0000

NA

w

w

(T

able

2 C

ontd

)

-l

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

------

CIJ

Con

diti

ons

CIJ

Job

E

i R

i Ii

O

J

C1

C2

C3

C4

C

5 C

6 C

7

C8

Min

44

615

4

000

00

0

0000

Sm

all

(3

) M

ax

951

220

0

8209

562

500

pro

ble

ms

Avg

66

121

6

050

01

39

021

3

_

Min

0

0000

009

99

45

450

0

Lar

ge

(3

) M

ax

214

286

1

1359

100

0000

p

rob

lem

s A

vg

605

84

0

3374

784

187

--

-_

__

---

Min

0

0000

000

00

0

0000

Ov

eral

l

(3)

Max

95

122

0

113

59

10

000

00

pro

ble

ms

Avg

26

950

0

039

40

64

715

2

tr1

()

gt-3 ~ Q

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

gtshyT

able

3

z C

om

par

ativ

e re

sult

s fo

r th

e C

GP

S

CD

S

an

d N

EH

alg

ori

thm

s ~

Job 3

4

5

6

7

8

9

10

15

20

30

40

50

100

200

101

39

101

48

102

64

102

82

102

62

102

7

102

82

102

55

102

43

101

83

101

06

100

85

100

65

100

32

100

17

~CDS

100

96

101

28

102

14

102

32

102

46

102

15

102

04

102

04

101

78

101

53

100

99

100

63

100

55

100

35

100

17

~~--------------

~NElI

100

1

100

39

100

53

100

54

100

48

100

72

100

50

100

47

100

25

100

33

100

08

100

05

100

06

100

02

100

01

(Tab

le 3

Con

td)

lfl

gt-

lfl

0 tJ r t=J

0 0 i


w

w

to

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

-----

---

co

jgt

~CGPS

~CDS

~NE

H 0

300

100

07

100

11

100

00

400

100

04

100

06

100

00

500

100

02

100

06

100

00

600

100

02

100

03

100

00

700

100

01

100

02

100

00

800

100

02

100

02

100

00

900

100

01

100

04

100

00

1000

1

0001

1

0003

1

0000

Min

1

0139

1

0096

1

0010

Sm

all

pro

ble

ms

Max

1

0282

1

0246

1

0072

Avg

1

0238

1

0192

1

0047

Min

1

0001

1

0002

1

0000

Lar

ge

pro

ble

ms

Max

1

0243

1

0178

1

0033

Avg

1

0050

1

0042

1

0005

Min

1

0001

1

0002

1

0000

r

Ov

eral

l p

rob

lem

s M

ax

102

82

102

46

100

72

0 -3A

vg

101

15

100

95

100

20

p Z

(Tab

le 3

Con

td)

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

lgtT

able

3 (

Con

td)

Z

--------

_shy

SCG

PS

EQ

CG

PS

SCD

S SC

GP

S E

QC

GP

S SN

EH

SN

EH

EQ

IjE

H

SCD

S --

~ Jo

b C

DS

CDS

CG

PS

NEH

N

EH

CG

PS

CD

S CD

S N

EH

en

en

3 0

91

9

0

83

17

12

88

0

0 gtzj

4 2

8

7

11

2

70

28

21

76

3

gt-l

[1j

5 2

82

16

4

58

38

28

66

6

0 0 1

j6

3

77

20

1

51

48

40

56

4

en

7 5

75

20

5

43

52

45

50

5

~ 0 0

8 6

70

24

8

35

57

44

47

9

~

gt-l

9 5

6

7

28

2

40

58

46

46

8

10

7

68

25

5

40

55

42

50

8

15

7

70

23

2

45

53

46

50

4

20

8

65

27

4

46

50

37

58

5

30

8

74

18

0

57

43

35

63

2

40

7

72

21

3

53

44

29

62

9

50

13

62

25

4

49

47

31

59

10

10

0

15

6

0

25

1

52

47

27

71

2

20

0

17

64

19

2

55

43

26

68

6

30

0

12

74

14

7

63

30

17

74

9

w

(T

able

3 C

ontd

)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

Job

S

co

Ps

CD

S E

QC

GP

SC

DS

SCD

S C

GPS

SC

GP

S N

EH

E

QC

GP

SN

EH

S

NE

H

CG

PS

NE

H

SCD

S E

Q

EH

CD

S SC

DS

NE

Il

N

400

14

63

23

5

58

37

14

81

5

500

13

62

25

1

57

42

20

78

2

60

0

9

61

30

4

54

42

12

82

6

700

11

66

23

8

56

36

13

79

8

80

0

10

63

27

4

57

39

14

82

4

900

16

63

21

2

60

38

17

81

2

1000

11

61

28

4

57

39

12

82

6

Sm

all

pro

ble

ms

Min

Max

Avg

0

67

9

7

91

28

375

00

77

125

0

191

250

0

8

337

50

35

17

83

58

525

000

44

1250

12

46

347

500

46

88

598

750

0

9

537

50

Lar

ge

pro

ble

ms

Min

Max

7

17

60

74

14

30

0

8

45

63

30

53

12

46

50

82

2

10

114

00

65

3333

2

326

67

3

4000

546

000

42

0000

233

333

71

333

3

533

33

Ov

eral

l p

rob

lem

s

Min

Max

Avg

0

60

9

17

91

30

873

91

69

434

8 2

182

61

0

8

339

13

35

17

83

58

538

696

42

739

1

12

46

273

043

~~~--~--

46

0

88

10

673

478

5

3478

c 0 ~ gtshy L

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014




5 CONCLUSION


Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

344 H C TANG


REFERENCES




















Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

------

CIJ

Con

diti

ons

CIJ

Job

E

i R

i Ii

O

J

C1

C2

C3

C4

C

5 C

6 C

7

C8

Min

44

615

4

000

00

0

0000

Sm

all

(3

) M

ax

951

220

0

8209

562

500

pro

ble

ms

Avg

66

121

6

050

01

39

021

3

_

Min

0

0000

009

99

45

450

0

Lar

ge

(3

) M

ax

214

286

1

1359

100

0000

p

rob

lem

s A

vg

605

84

0

3374

784

187

--

-_

__

---

Min

0

0000

000

00

0

0000

Ov

eral

l

(3)

Max

95

122

0

113

59

10

000

00

pro

ble

ms

Avg

26

950

0

039

40

64

715

2

tr1

()

gt-3 ~ Q

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

gtshyT

able

3

z C

om

par

ativ

e re

sult

s fo

r th

e C

GP

S

CD

S

an

d N

EH

alg

ori

thm

s ~

Job 3

4

5

6

7

8

9

10

15

20

30

40

50

100

200

101

39

101

48

102

64

102

82

102

62

102

7

102

82

102

55

102

43

101

83

101

06

100

85

100

65

100

32

100

17

~CDS

100

96

101

28

102

14

102

32

102

46

102

15

102

04

102

04

101

78

101

53

100

99

100

63

100

55

100

35

100

17

~~--------------

~NElI

100

1

100

39

100

53

100

54

100

48

100

72

100

50

100

47

100

25

100

33

100

08

100

05

100

06

100

02

100

01

(Tab

le 3

Con

td)

lfl

gt-

lfl

0 tJ r t=J

0 0 i


w

w

to

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

-----

---

co

jgt

~CGPS

~CDS

~NE

H 0

300

100

07

100

11

100

00

400

100

04

100

06

100

00

500

100

02

100

06

100

00

600

100

02

100

03

100

00

700

100

01

100

02

100

00

800

100

02

100

02

100

00

900

100

01

100

04

100

00

1000

1

0001

1

0003

1

0000

Min

1

0139

1

0096

1

0010

Sm

all

pro

ble

ms

Max

1

0282

1

0246

1

0072

Avg

1

0238

1

0192

1

0047

Min

1

0001

1

0002

1

0000

Lar

ge

pro

ble

ms

Max

1

0243

1

0178

1

0033

Avg

1

0050

1

0042

1

0005

Min

1

0001

1

0002

1

0000

r

Ov

eral

l p

rob

lem

s M

ax

102

82

102

46

100

72

0 -3A

vg

101

15

100

95

100

20

p Z

(Tab

le 3

Con

td)

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

lgtT

able

3 (

Con

td)

Z

--------

_shy

SCG

PS

EQ

CG

PS

SCD

S SC

GP

S E

QC

GP

S SN

EH

SN

EH

EQ

IjE

H

SCD

S --

~ Jo

b C

DS

CDS

CG

PS

NEH

N

EH

CG

PS

CD

S CD

S N

EH

en

en

3 0

91

9

0

83

17

12

88

0

0 gtzj

4 2

8

7

11

2

70

28

21

76

3

gt-l

[1j

5 2

82

16

4

58

38

28

66

6

0 0 1

j6

3

77

20

1

51

48

40

56

4

en

7 5

75

20

5

43

52

45

50

5

~ 0 0

8 6

70

24

8

35

57

44

47

9

~

gt-l

9 5

6

7

28

2

40

58

46

46

8

10

7

68

25

5

40

55

42

50

8

15

7

70

23

2

45

53

46

50

4

20

8

65

27

4

46

50

37

58

5

30

8

74

18

0

57

43

35

63

2

40

7

72

21

3

53

44

29

62

9

50

13

62

25

4

49

47

31

59

10

10

0

15

6

0

25

1

52

47

27

71

2

20

0

17

64

19

2

55

43

26

68

6

30

0

12

74

14

7

63

30

17

74

9

w

(T

able

3 C

ontd

)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

Job

S

co

Ps

CD

S E

QC

GP

SC

DS

SCD

S C

GPS

SC

GP

S N

EH

E

QC

GP

SN

EH

S

NE

H

CG

PS

NE

H

SCD

S E

Q

EH

CD

S SC

DS

NE

Il

N

400

14

63

23

5

58

37

14

81

5

500

13

62

25

1

57

42

20

78

2

60

0

9

61

30

4

54

42

12

82

6

700

11

66

23

8

56

36

13

79

8

80

0

10

63

27

4

57

39

14

82

4

900

16

63

21

2

60

38

17

81

2

1000

11

61

28

4

57

39

12

82

6

Sm

all

pro

ble

ms

Min

Max

Avg

0

67

9

7

91

28

375

00

77

125

0

191

250

0

8

337

50

35

17

83

58

525

000

44

1250

12

46

347

500

46

88

598

750

0

9

537

50

Lar

ge

pro

ble

ms

Min

Max

7

17

60

74

14

30

0

8

45

63

30

53

12

46

50

82

2

10

114

00

65

3333

2

326

67

3

4000

546

000

42

0000

233

333

71

333

3

533

33

Ov

eral

l p

rob

lem

s

Min

Max

Avg

0

60

9

17

91

30

873

91

69

434

8 2

182

61

0

8

339

13

35

17

83

58

538

696

42

739

1

12

46

273

043

~~~--~--

46

0

88

10

673

478

5

3478

c 0 ~ gtshy L

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014




5 CONCLUSION


Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

344 H C TANG


REFERENCES




















Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

gtshyT

able

3

z C

om

par

ativ

e re

sult

s fo

r th

e C

GP

S

CD

S

an

d N

EH

alg

ori

thm

s ~

Job 3

4

5

6

7

8

9

10

15

20

30

40

50

100

200

101

39

101

48

102

64

102

82

102

62

102

7

102

82

102

55

102

43

101

83

101

06

100

85

100

65

100

32

100

17

~CDS

100

96

101

28

102

14

102

32

102

46

102

15

102

04

102

04

101

78

101

53

100

99

100

63

100

55

100

35

100

17

~~--------------

~NElI

100

1

100

39

100

53

100

54

100

48

100

72

100

50

100

47

100

25

100

33

100

08

100

05

100

06

100

02

100

01

(Tab

le 3

Con

td)

lfl

gt-

lfl

0 tJ r t=J

0 0 i


w

w

to

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

-----

---

co

jgt

~CGPS

~CDS

~NE

H 0

300

100

07

100

11

100

00

400

100

04

100

06

100

00

500

100

02

100

06

100

00

600

100

02

100

03

100

00

700

100

01

100

02

100

00

800

100

02

100

02

100

00

900

100

01

100

04

100

00

1000

1

0001

1

0003

1

0000

Min

1

0139

1

0096

1

0010

Sm

all

pro

ble

ms

Max

1

0282

1

0246

1

0072

Avg

1

0238

1

0192

1

0047

Min

1

0001

1

0002

1

0000

Lar

ge

pro

ble

ms

Max

1

0243

1

0178

1

0033

Avg

1

0050

1

0042

1

0005

Min

1

0001

1

0002

1

0000

r

Ov

eral

l p

rob

lem

s M

ax

102

82

102

46

100

72

0 -3A

vg

101

15

100

95

100

20

p Z

(Tab

le 3

Con

td)

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

lgtT

able

3 (

Con

td)

Z

--------

_shy

SCG

PS

EQ

CG

PS

SCD

S SC

GP

S E

QC

GP

S SN

EH

SN

EH

EQ

IjE

H

SCD

S --

~ Jo

b C

DS

CDS

CG

PS

NEH

N

EH

CG

PS

CD

S CD

S N

EH

en

en

3 0

91

9

0

83

17

12

88

0

0 gtzj

4 2

8

7

11

2

70

28

21

76

3

gt-l

[1j

5 2

82

16

4

58

38

28

66

6

0 0 1

j6

3

77

20

1

51

48

40

56

4

en

7 5

75

20

5

43

52

45

50

5

~ 0 0

8 6

70

24

8

35

57

44

47

9

~

gt-l

9 5

6

7

28

2

40

58

46

46

8

10

7

68

25

5

40

55

42

50

8

15

7

70

23

2

45

53

46

50

4

20

8

65

27

4

46

50

37

58

5

30

8

74

18

0

57

43

35

63

2

40

7

72

21

3

53

44

29

62

9

50

13

62

25

4

49

47

31

59

10

10

0

15

6

0

25

1

52

47

27

71

2

20

0

17

64

19

2

55

43

26

68

6

30

0

12

74

14

7

63

30

17

74

9

w

(T

able

3 C

ontd

)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

Job

S

co

Ps

CD

S E

QC

GP

SC

DS

SCD

S C

GPS

SC

GP

S N

EH

E

QC

GP

SN

EH

S

NE

H

CG

PS

NE

H

SCD

S E

Q

EH

CD

S SC

DS

NE

Il

N

400

14

63

23

5

58

37

14

81

5

500

13

62

25

1

57

42

20

78

2

60

0

9

61

30

4

54

42

12

82

6

700

11

66

23

8

56

36

13

79

8

80

0

10

63

27

4

57

39

14

82

4

900

16

63

21

2

60

38

17

81

2

1000

11

61

28

4

57

39

12

82

6

Sm

all

pro

ble

ms

Min

Max

Avg

0

67

9

7

91

28

375

00

77

125

0

191

250

0

8

337

50

35

17

83

58

525

000

44

1250

12

46

347

500

46

88

598

750

0

9

537

50

Lar

ge

pro

ble

ms

Min

Max

7

17

60

74

14

30

0

8

45

63

30

53

12

46

50

82

2

10

114

00

65

3333

2

326

67

3

4000

546

000

42

0000

233

333

71

333

3

533

33

Ov

eral

l p

rob

lem

s

Min

Max

Avg

0

60

9

17

91

30

873

91

69

434

8 2

182

61

0

8

339

13

35

17

83

58

538

696

42

739

1

12

46

273

043

~~~--~--

46

0

88

10

673

478

5

3478

c 0 ~ gtshy L

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014




5 CONCLUSION


Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

344 H C TANG


REFERENCES




















Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

-----

---

co

jgt

~CGPS

~CDS

~NE

H 0

300

100

07

100

11

100

00

400

100

04

100

06

100

00

500

100

02

100

06

100

00

600

100

02

100

03

100

00

700

100

01

100

02

100

00

800

100

02

100

02

100

00

900

100

01

100

04

100

00

1000

1

0001

1

0003

1

0000

Min

1

0139

1

0096

1

0010

Sm

all

pro

ble

ms

Max

1

0282

1

0246

1

0072

Avg

1

0238

1

0192

1

0047

Min

1

0001

1

0002

1

0000

Lar

ge

pro

ble

ms

Max

1

0243

1

0178

1

0033

Avg

1

0050

1

0042

1

0005

Min

1

0001

1

0002

1

0000

r

Ov

eral

l p

rob

lem

s M

ax

102

82

102

46

100

72

0 -3A

vg

101

15

100

95

100

20

p Z

(Tab

le 3

Con

td)

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

lgtT

able

3 (

Con

td)

Z

--------

_shy

SCG

PS

EQ

CG

PS

SCD

S SC

GP

S E

QC

GP

S SN

EH

SN

EH

EQ

IjE

H

SCD

S --

~ Jo

b C

DS

CDS

CG

PS

NEH

N

EH

CG

PS

CD

S CD

S N

EH

en

en

3 0

91

9

0

83

17

12

88

0

0 gtzj

4 2

8

7

11

2

70

28

21

76

3

gt-l

[1j

5 2

82

16

4

58

38

28

66

6

0 0 1

j6

3

77

20

1

51

48

40

56

4

en

7 5

75

20

5

43

52

45

50

5

~ 0 0

8 6

70

24

8

35

57

44

47

9

~

gt-l

9 5

6

7

28

2

40

58

46

46

8

10

7

68

25

5

40

55

42

50

8

15

7

70

23

2

45

53

46

50

4

20

8

65

27

4

46

50

37

58

5

30

8

74

18

0

57

43

35

63

2

40

7

72

21

3

53

44

29

62

9

50

13

62

25

4

49

47

31

59

10

10

0

15

6

0

25

1

52

47

27

71

2

20

0

17

64

19

2

55

43

26

68

6

30

0

12

74

14

7

63

30

17

74

9

w

(T

able

3 C

ontd

)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

Job

S

co

Ps

CD

S E

QC

GP

SC

DS

SCD

S C

GPS

SC

GP

S N

EH

E

QC

GP

SN

EH

S

NE

H

CG

PS

NE

H

SCD

S E

Q

EH

CD

S SC

DS

NE

Il

N

400

14

63

23

5

58

37

14

81

5

500

13

62

25

1

57

42

20

78

2

60

0

9

61

30

4

54

42

12

82

6

700

11

66

23

8

56

36

13

79

8

80

0

10

63

27

4

57

39

14

82

4

900

16

63

21

2

60

38

17

81

2

1000

11

61

28

4

57

39

12

82

6

Sm

all

pro

ble

ms

Min

Max

Avg

0

67

9

7

91

28

375

00

77

125

0

191

250

0

8

337

50

35

17

83

58

525

000

44

1250

12

46

347

500

46

88

598

750

0

9

537

50

Lar

ge

pro

ble

ms

Min

Max

7

17

60

74

14

30

0

8

45

63

30

53

12

46

50

82

2

10

114

00

65

3333

2

326

67

3

4000

546

000

42

0000

233

333

71

333

3

533

33

Ov

eral

l p

rob

lem

s

Min

Max

Avg

0

60

9

17

91

30

873

91

69

434

8 2

182

61

0

8

339

13

35

17

83

58

538

696

42

739

1

12

46

273

043

~~~--~--

46

0

88

10

673

478

5

3478

c 0 ~ gtshy L

0

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014




5 CONCLUSION


Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

344 H C TANG


REFERENCES




















Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

lgtT

able

3 (

Con

td)

Z

--------

_shy

SCG

PS

EQ

CG

PS

SCD

S SC

GP

S E

QC

GP

S SN

EH

SN

EH

EQ

IjE

H

SCD

S --

~ Jo

b C

DS

CDS

CG

PS

NEH

N

EH

CG

PS

CD

S CD

S N

EH

en

en

3 0

91

9

0

83

17

12

88

0

0 gtzj

4 2

8

7

11

2

70

28

21

76

3

gt-l

[1j

5 2

82

16

4

58

38

28

66

6

0 0 1

j6

3

77

20

1

51

48

40

56

4

en

7 5

75

20

5

43

52

45

50

5

~ 0 0

8 6

70

24

8

35

57

44

47

9

~

gt-l

9 5

6

7

28

2

40

58

46

46

8

10

7

68

25

5

40

55

42

50

8

15

7

70

23

2

45

53

46

50

4

20

8

65

27

4

46

50

37

58

5

30

8

74

18

0

57

43

35

63

2

40

7

72

21

3

53

44

29

62

9

50

13

62

25

4

49

47

31

59

10

10

0

15

6

0

25

1

52

47

27

71

2

20

0

17

64

19

2

55

43

26

68

6

30

0

12

74

14

7

63

30

17

74

9

w

(T

able

3 C

ontd

)

Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

Job

S

co

Ps

CD

S E

QC

GP

SC

DS

SCD

S C

GPS

SC

GP

S N

EH

E

QC

GP

SN

EH

S

NE

H

CG

PS

NE

H

SCD

S E

Q

EH

CD

S SC

DS

NE

Il

N

400

14

63

23

5

58

37

14

81

5

500

13

62

25

1

57

42

20

78

2

60

0

9

61

30

4

54

42

12

82

6

700

11

66

23

8

56

36

13

79

8

80

0

10

63

27

4

57

39

14

82

4

900

16

63

21

2

60

38

17

81

2

1000

11

61

28

4

57

39

12

82

6

Sm

all

pro

ble

ms

Min

Max

Avg

0

67

9

7

91

28

375

00

77

125

0

191

250

0

8

337

50

35

17

83

58

525

000

44

1250

12

46

347

500

46

88

598

750

0

9

537

50

Lar

ge

pro

ble

ms

Min

Max

7

17

60

74

14

30

0

8

45

63

30

53

12

46

50

82

2

10

114

00

65

3333

2

326

67

3

4000

546

000

42

0000

233

333

71

333

3

533

33

Ov

eral

l p

rob

lem

s

Min

Max

Avg

0

60

9

17

91

30

873

91

69

434

8 2

182

61

0

8

339

13

35

17

83

58

538

696

42

739

1

12

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043

~~~--~--

46

0

88

10

673

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5

3478

c 0 ~ gtshy L

0

Dow

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ded

by [

Uni

vers

ity o

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enne

ssee

Kno

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e] a

t 22

24 2

1 D

ecem

ber

2014




5 CONCLUSION


Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

344 H C TANG


REFERENCES




















Dow

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ded

by [

Uni

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f T

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ssee

Kno

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e] a

t 22

24 2

1 D

ecem

ber

2014

Job

S

co

Ps

CD

S E

QC

GP

SC

DS

SCD

S C

GPS

SC

GP

S N

EH

E

QC

GP

SN

EH

S

NE

H

CG

PS

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H

SCD

S E

Q

EH

CD

S SC

DS

NE

Il

N

400

14

63

23

5

58

37

14

81

5

500

13

62

25

1

57

42

20

78

2

60

0

9

61

30

4

54

42

12

82

6

700

11

66

23

8

56

36

13

79

8

80

0

10

63

27

4

57

39

14

82

4

900

16

63

21

2

60

38

17

81

2

1000

11

61

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57

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6

Sm

all

pro

ble

ms

Min

Max

Avg

0

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7

91

28

375

00

77

125

0

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250

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1250

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750

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Max

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Ov

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Min

Max

Avg

0

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91

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434

8 2

182

61

0

8

339

13

35

17

83

58

538

696

42

739

1

12

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273

043

~~~--~--

46

0

88

10

673

478

5

3478

c 0 ~ gtshy L

0

Dow

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by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014




5 CONCLUSION


Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

344 H C TANG


REFERENCES




















Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014




5 CONCLUSION


Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

344 H C TANG


REFERENCES




















Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

344 H C TANG


REFERENCES




















Dow

nloa

ded

by [

Uni

vers

ity o

f T

enne

ssee

Kno

xvill

e] a

t 22

24 2

1 D

ecem

ber

2014

Documents

An experimental analysis of the CGPS algorithm for the three-machine flow shop scheduling with minimum makespan criterion