Process Planning and Due-date Assignment with
ATC Dispatching where Earliness, Tardiness and
Due-dates are Punished
Halil Ibrahim Demir, Tarık Cakar, Mumtaz Ipek, Ozer Uygun, and Murat Sari Industrial Engineering Department, Sakarya University, Sakarya, Turkey
Email: {hidemir, tcakar, ipek, ouygun, muratsari}@sakarya.edu.tr
Abstract—Conventionally process planning, scheduling
and due-date assignment are performed independently. But
treating these three functions simultaneously improves
global performance. In literature there are numerous works
on process planning and scheduling and on scheduling with
due-date assignment. But integrating these three functions
are not treated much. In this study, process planning and
due-date assignment are simultaneously treated with ATC
dispatching using genetic algorithm (genetic search) and
random search. Three shop floors are tested in this study.
One is small shop floor with 50 jobs and the other is
medium shop floor with 100 jobs and the third one is the
largest shop floor with 200 jobs. In this study Earliness and
Tardiness symmetrically and quadratically penalized and
length of due-date is linearly punished. Results of Genetic
search and Random search are compared with each other
and with random solution and with unintegrated solution.
Results are summarized and compared with each other.
According to results Genetic search-integrated solution is
the best, Random search-integrated solution is the second,
Random-integrated solution is the third and Unintegrated-
random solution is the poorest.1
Index Terms—Due-date assignment, Process planning, Job
shop scheduling, Genetic Algorithm
I. INTRODUCTION
When we look at the literature we can see many works
on integrated process planning and scheduling and
numerous work on scheduling with due-date assignment.
Traditionally these three functions were being done
sequentially and separately. Unintegrated solutions
become poor inputs to the downstream functions and
global performance can be poor. For example if process
plans are made independently then process planner can
choose same desired machines repeatedly and they don’t
care about scheduling and due-date assignment
performance. Because they can select same machines
repeatedly some machines can become bottleneck and
some machines can be starving and this cause
unbalanced machine loading. When some unexpected
things occur such as machine breakdowns then it
becomes hard to react these occurrences. If we integrate
process plans with other functions then in case of need
Manuscript received July 1, 2014; revised November 1, 2014.
we can react to the unexpected situation and we can
improve shop floor balance. Good and flexible inputs for
scheduling and due-date assignment provide us to make
better scheduling and better due-date assignment.
The scheduling problems involving due dates are of
permanent interest. In a traditional production
environment, a job is expected to be completed before its
due date. In a just-in-time environment, a job is expected
to be completed exactly at its due date…The problems
with due-date determination have received considerable
attention in the last 15 years due to the introduction of
new methods of inventory management such as just-in-
time (JIT) concepts. In JIT systems jobs are to be
completed neither too early nor too late which leads to
the scheduling problems with both earliness and
tardiness costs and assigning due dates. T.C.E. Cheng,
who contributed a lot to the due date assignment and the
related scheduling approaches, remarks that “completing
a job early means to bear the costs of holding
unnecessary inventories, while finishing a job late results
in contractual penalty and loss of customer good-will”
Gordon et al. [1].
II. LITERATURE SURVEY
For integrated process planning and scheduling
problem, Tan and Khosnevis [2] presented a good
literature survey. For scheduling with common due-date
assignment problem, it will be useful to see Gordon et al.
[1] as a state-of-the-art survey about this topic.
Following study uses multiple process plans in contrast
to traditional way.
Chen and Khoshnevis [3] investigated the problem of
integrating the process planning and scheduling functions
as a scheduling problem with flexible process plans.
They developed a concurrent assignment algorithm based
on the added flexibilities introduced by the integration
Above study used multiple process plans and
following study, Jiang and Chen [4], investigated the
influence of alternate process planning on the scheduling
performance according to three criteria, which are mean
tardiness, mean work-in-process and mean machine
utilization.
Integration can be done with manual process plans or
computer aided process plans. Computer advantage is
very important to develop alternative process plans and
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integrating process plans with scheduling. Following
studies dealt with process plan or computer aided process
plan integration with the scheduling.
In their paper, Lim and Zhang [5] introduced a multi-
agent based framework in which process planning and
production scheduling are integrated, as a preliminary
step towards agile manufacturing. Kumar and Rajotia [6]
studied integration of scheduling with computer aided
process planning.
Since integrated process planning and scheduling
problems are NP-hard problems, proposed mathematical
solutions are only possible for small sized problems. We
used genetic algorithm in this study, because problem in
this study is more complex than sub integration problems.
Jiang and Hsiao [7] developed an analytic solution to
the problem but their 0-1 integer programming is only
applicable to small sized problems. Hutchison et al. [8]
developed two off-line and one real time scheduling
scheme. The first of the off-line schemes gives an overall
optimal solution to the problem but again it is only
applicable to the small sized problems in terms of
computational time requirements.
Since applying mathematical techniques is not
practical for large-scale problems artificial intelligent
techniques such as neural network, genetic algorithms,
multi-agents and evolutionary algorithms are used and
recommended for many problems.
The integration of process planning and scheduling is
important for an efficient utilization of manufacturing
resources. Kim et al. [9] presented a new method, an
artificial intelligent search technique, called symbiotic
evolutionary algorithm, was presented to handle the two
functions at the same time. Zhao and Wu [10] suggested
a genetic algorithm (GA) to solve the job-sequencing
problem for a production shop that is characterized by
flexible routing and flexible machines. Lee and Kim [11]
proposed a new approach to the integration of process
planning and scheduling using simulation based genetic
algorithms. In their paper, Ming and Mak [12]
formulated the problem of selecting exactly one
representative from a set of alternative process plans…
The techniques of Hopfield neural network and genetic
algorithm are introduced as possible approaches to solve
such a problem.
When we look at these types of problems, objective
functions are not always the same but generally,
objectives are minimizing the cost. Below studies are
given to show what kinds of objectives are used in the
literature.
Thomalla [13] investigated an optimization
methodology for scheduling jobs in a just-in-time
environment. He considered the non-preemptive case
where each job consists of a distinct number of
operations to be processed in a specified order. Each
operation has to be processed on one of a set of resources
(e.g. machines) with possibly different efficiency and
hence processing time. The objective was to minimize
the sum of the weighted quadratic tardiness of the jobs.
Most of the work done on integrated process planning
and scheduling consider only time aspects but Morad and
Zalzala [14] used a formulation based on multi objective
weighted-sums optimization, which are to minimize
makespan, to minimize total rejects produced and to
minimize the total cost of production. Weintraub et al.
[15] presented a procedure for scheduling jobs with
alternative process in a general N-job, M-machine job
shop. The objective of this procedure is to minimize
manufacturing costs while satisfying job due dates.
Usher [16] addressed the benefit of alternative process
plans and worked on the number of alternative process
plans. Jain et al [17] introduced a scheme for integration
of process planning and scheduling. In a job shop kind of
flexible manufacturing environment Wong et al [18]
presented the development of an agent-based negotiation
approach to integrate process planning and scheduling
(IPPS). Kumar and Rajotia [19] proposed a framework
for integration of process planning with production
scheduling. A new simultaneous process planning and
scheduling method is proposed by Ueda et al [20]. In a
supply chain, Moon et al [21] studied integrated process
planning and scheduling (IPPS).
Chan et al. [22] proposed an integrated process
planning and scheduling model inheriting the salient
features of outsourcing and leagile principles to compete
in the existing market scenario. Guo et al [23] developed
a unified representation model for integrated process
planning and scheduling (IPPS).
Li et al [24] presented a review on integrated process
planning and scheduling. A mathematical model of
integrated process planning and scheduling developed by
them and they developed evolutionary algorithm based
approach to facilitate the integration and optimization of
process planning and scheduling. In order to integrate
process planning and shop floor scheduling (IPPS)
Leung et al [25] presented an ant colony optimization
(ACO) algorithm in an agent-based system. Phanden et
al [26] presented a state-of-the-art review of IPPS
(Integration of process planning and scheduling). Due dates sometimes dictated by customer but most of
the time due dates are determined after the negotiation
with the customer. In latter case it is desired to find the
best due date that satisfy both customer and the company.
Recent years numerous works have been done on
concurrent scheduling and due date assignment. If
literature survey is done for the last decade about
concurrent scheduling and due-date assignment
numerous works can be found. Since to be a survivor in
the market, firms should be as strong as possible and
make use of every new ideas and technological
developments that is why determining a reasonable due-
date is very important. According to classical approach,
only tardiness is punished but according to just in time
philosophy earliness is also punished as well. Earliness
means inventory holding cost and costs related with
stock keeping. To be realistic these costs should be
considered too. Studies shows that tardiness is still the
major component in due-date related costs. Tardiness
causes some fixed and variable costs. These costs are
price reduction and loss of customer good will and worst
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losing good reputation and the customer. Therefore,
earliness should be punished as tardiness.
While some researches are conducted on single
machine environments, some other researches are done
on multiple machine environments. Multiple machine
environments could be job shop, flow shop, two
machines, n machines, identical or different machine etc.
Whether single or multiple machine environments
most of the studies tries to assign common due-date for
the jobs. This is because in many cases job should be
delivered to the customer at the same time or in some
cases finished parts or semi-assembled parts should be
ready at the same due-date for final assembly. Gordon et
al. [1] presented a state-of-the-art survey about
scheduling with common due-date assignment.
Ng et al [27], Cheng et al. [28], Qi et al. [29], Biskup
and Jahnke [30], Gordon and Strusevich [31], Gordon
and Kubiak [32] Ying [33], Li et al. [34], Nearchou [35],
Xia et al. [36], Lin [37], Panwalker [38], Wang [39],
Cheng et al. [40], and Ventura and Radhakrishnan [41]
studied scheduling with due-date assignment on single
machine environments.
Birman and Mosheiov [42], Mosheiov [43], Cheng
and Kovalyev [44], Adamapolous and Pappis [45], and
Lauf and Werner [46] studied multiple machine
problems.
Birman and Mosheiov [42] addressed a due-date
assignment and scheduling problem in a two-machine
flow-shop setting. Their objective was to find both job
schedule and common due-date that minimize maximum
earliness, tardiness, and due-date costs. Mosheiov [43]
addressed a job scheduling and due-date assignment
problem on parallel identical machines. All jobs share a
common due-date, which is to be determined. The cost of
a given schedule is a function of the maximum earliness
cost, the maximum tardiness cost, and the due-date cost.
Cheng and Kovalyev [44] tried to schedule n jobs on
parallel identical machines. They aimed to make
optimum scheduling while trying to assign best due-dates
to the jobs using PPW (Process plus wait) method.
Adamapolous and Pappis [45] tried to assign common
due dates to some jobs and schedule them on parallel and
unrelated machines. Min and Cheng [47] used genetic algorithm to
determine the optimal due date and optimal scheduling
policy for determining the job number and their
processing order on each machine. Lin et al [37] studied
single machine scheduling involving a common due date.
They minimized total job earliness and tardiness
penalties.
Nearchou [35] studied scheduling multiple jobs on a
single machine for common specified due date where
earliness and tardiness are punished..
Ying [33] studied scheduling jobs on a single machine
against common due dates with respect to earliness and
tardiness penalties.
Gordon and Strusevich [31] studied single machine
scheduling and due date assignment problems in which
the processing time of a job depends on its position in a
processing sequence. Vinod and Sridharan [48]
investigated the interaction between due-date assignment
methos and scheduling rules in a typical dynamic jop
shop production system.
Steiner and Zhang [49] studied a supply chain problem
where a common due date is assigned to all jobs and
number of jobs in delivery batches is constrained by
batch size. Li et al. [34] used CON/SLK (Common Due
Date/ Equal Slack) due date assignment rules with
scheduling deteriorating jobs on a single machine.
Most research on scheduling with due-date assignment
is focused on optimal sequencing of independent jobs.
But in practice some products are manufactured under
precedence constraints that reflects technological,
marketing or assembly requirements Gordon et al. [50].
III. DEFINITION OF THE PROBLEM
In this study integration of process planning,
scheduling and due-date assignment problem is studied.
There are alternative routes in order to improve inputs to
downstream (Scheduling and due-date assignment), to
provide flexibility in case of unexpected occurrences. We
have five alternative routes in case of small and medium
shop floor and we have three alternative routes in case of
big shop floor. One of these alternatives is going to be
selected to improve global (integrated solution)
performance. In case of scheduling we used ATC
(Apparent Tardiness Cost) dispatching rule to improve
global performance. We compared ATC with SIRO
(Service in random order) to see contribution of ATC
heuristic to the problem. We used different due-date
assignment rule at the related gene in a chromosome
(solution).These due-date assignment rules are used for
internal due-date assignment and we used RDM
(Random) due date assignment for external due-date
assignment. By comparing internal due date assignment
rules and external due date assignment we observed the
benefit of due-date determination and integration with
the problem. We compared seven different solutions each
has different level of integration and either makes genetic
or random search or ordinary solutions. These solutions
are explained in detail at section five.
Three shop floors are tested. First is small shop floor
with 50 jobs and 20 machines. At small shop floor there
are five alternative routes of each job and every job has
10 operations and operation time changes in between 10
and 19 minutes ( Processing times = ⌊(10 + |z| ∗ 3)⌋ =
nearest small integer. |z| is absolute value of standard
normal numbers). Processing times are randomly
produced.
Second shop floor is mid-sized shop floor with 100
jobs and 30 machines. At this shop floor again we have 5
alternative routes for each job and one is going to be
selected and each job has 10 different operations to be
performed. Operation times change in between 10 and 19
according to the same formula (Processing times
= ⌊(10 + |z| ∗ 3)⌋ = nearest small integer. |z| is absolute
value of standard normal numbers) with other shop floors.
Third shop floor is large sized shop floor with 200
jobs and 40 machines. At this shop 3 alternative routes
are used for each job and one of these routes is going to
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be selected for global (integrated) performance. Each job
has 10 operations in every route and operation times
changes according to following formula (Processing
times = ⌊(10 + |z| ∗ 3)⌋ = nearest small integer in
between 10 and 19. |z| is absolute value of standard
normal numbers). Features of shop floors are given at
Table I.
TABLE I. SHOP FLOORS
Shop floor Shop floor 1 Shop floor 2 Shop floor 3
# of machines 20 30 40
# of Jobs 50 100 200
# of Routes 5 5 3
Processing Times ⌊(10 + |z| ∗ 3)⌋ ⌊(10 + |z| ∗ 3)⌋ ⌊(10 + |z| ∗ 3)⌋ # of op. per job 10 10 10
In this study we penalized earliness, tardiness and due
date. We assumed one shift per day and 8 hours * 60
minutes = 480 minutes are considered as one day. If jobs
are early and tardy within one day then we punished
earliness and tardiness linearly, and if there are more
than one day earliness and tardiness then we punished
quadratically. This is because completion early or tardy
within one day makes very small quadratic punishment
that’s why we used in this range linear punishment. Due
dates are punished linearly. Punishment functions are
given below where PD is penalty for due-date, PE is
penalty for earliness and PT is penalty for tardiness;
IV. SOLUTION TECHNIQUES
In this search following solutions techniques are used
and compared with each other.
Random search: In this search, solutions are produced
randomly. Best of these solutions is recorded as the next
population. Since this technique produces brand new
solutions randomly in every generations and don’t get the
benefit of earlier generations by using previous solutions
to get better solution, That is why it is an undirected
search technique. Since this is an undirected search, it
scans the solution space randomly.
Genetic search: Genetic algorithm is thought to work
well for the studied problem. That’s why over randomly
produced initial population and over the following
generations genetic operators are applied to get a good
solution in a reasonable amount of time. This search
called genetic, because it uses crossover and mutation
operators and updated best population to get better
solutions. Since it tries to find better solution by using
the final best solution, it is called as directed search in
contrast to the random search.
For every types of shop floor population size is ten, in
each generation (iteration) eight new offspring are
produced using crossover operator, and five new
offspring are produced using mutation operator. From
old population, crossover and mutation populations best
ten distinct chromosomes are selected for the next
generation as the new population. Iteration goes like this
until a predetermined number is reached.
Figure 1. Sample chromosome.
Ordinary solution: We use randomly produced initial
populations as ordinary solutions. Each chromosome is
randomly produced and a valid value is assigned to each
gene in the chromosome and performance of the
chromosome is found. Average of these performance
measures are taken as the ordinary solution.
Due dates were assigned using mainly five different
types of rules. Considering different constants and
multipliers the first gene took one of nineteen values.
These rules are explained below at Table II:
TABLE II: DUE-DATE ASSIGNMENT RULES
Method Multiplier k Constant qx Rule no:
TWK k = 1,2,3 0,1,2
SLK qx = q1,q2,q3 3,4,5
PPW k =1,2,3 qx = q1,q2,q3 6,7,8,9,10,11,12, 13,14
NOP k = 1,2,3 15,16,17
RDM 18
In order to dispatch two different methods were used.
Considering different multipliers, the second gene took
one of four different values. Dispatching rules use are
given and explained at Table III.
TABLE III: DISPATCHING RULES
Method Multiplier Rule no
ATC k x =1,2,3 0,1,2
SIRO 3
V. SOLUTIONS COMPARED
ATC-DUE(Ordinary): Process planning, due date
assignment and ATC dispatching are integrated and
ordinary solution is taken. Ordinary means just one
iteration applied and initial population is taken without
making any directed and undirected search. ATC
dispatching means jobs are sequenced scheduled
according to ATC composite dispatching rule.
Dispatching (Scheduling) is integrated with due-date
assignment and route selection.
PE= 8*(E/480) If E <= 480 8*(E/480)* (E/480) If E > 480
PT= 8*(T/480) If T <= 480 8*(T/480)* (T/480) If T > 480
P.D= 8*(Due-date/480) (1)
(2)
(3)
DD DR R1j R2j . . . R nj
Where
DD: Due date assignment gene DR: Dispatching rule gene
R nj : j’th route of job n
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A sample chromosome can be illustrated as in Fig. 1.
There are (n+2) genes in one chromosome. First gene is
for due-date assignment and second gene for dispatching
rule and the rest for the routes of each job sequentially.
Journal of Industrial and Intelligent Information Vol. 3, No. 3, September 2015
SIRO-DUE (Ordinary): Process planning and due date
assignment are integrated, but scheduling is unintegrated
and SIRO dispatching rule is used. Ordinary solution is
taken. No directed or undirected search is applied.
SIRO-RDM (Ordinary): In this solution scheduling
and due-date determinations are unintegrated. One of
alternative routes is selected and SIRO (Service in
random order) dispatching rule is used to represent
unintegrated scheduling and RDM (Random) due-date
determination is used to represent unintegrated due-date
assignment.
ATC-DUE (Random): Above solutions were first
iteration solutions (No directed or undirected search are
applied) but this solutions apply undirected search. For
small shop floor we apply 200 random iterations, for
medium sized shop floor we apply 100 iterations and for
large shop floor we apply 50 random iterations. Here
due-date assignment and ATC scheduling are integrated
with process planning.
ATC-DUE (Genetic): Here due-date assignment and
ATC scheduling are integrated with process planning.
Genetic (Directed) search is applied to the problem. For
small shop we apply 200 genetic iterations, for mid-size
shop floor we apply 100 genetic iterations and for large
shop floor we apply 50 genetic iterations. Since genetic
(directed) search is better than random (undirected)
search we used genetic iterations for the solutions below.
SIRO-DUE (Genetic): Here due-date assignment is
integrated with process planning but scheduling is
performed randomly (SIRO) and genetic search is
applied.
SIRO-RDM (Genetic): In this solution scheduling and
due-date determination are unintegrated with process
planning. SIRO dispatching rule is used and RDM due-
date assignment is used and genetic search is applied.
We compared above seven solutions with each other
to determine whether integration of due-date assignment
with process planning is beneficial and whether
integration of scheduling with process planning and due-
date assignment is beneficial. We also tested directed and
undirected search for three shop floors and genetic search
is found better. Results are given at experimentation part
and interpreted at conclusion part.
VI. EXPERIMENTS AND RESULTS
We studied three shop floors which are small medium
and large shop floors. We produced data for three shop
floors and coded integrated process planning, scheduling
and due-date assignment problem and coded random and
genetic search. We coded integrated problem using C++
language and run the experiments on a Notebook with 2
GHz processor. For different shop floors we applied
given number of random and genetic iterations. For small
shop floor we used 200 iterations and it took
approximately 90 seconds to finish 200 iterations if we
use SIRO dispatching and 150 seconds if we use ATC
dispatching. For medium sized shop floor we applied 100
iterations and it took approximately 250 seconds to finish
100 iterations if we use SIRO dispatching and 450
seconds if we use ATC dispatching. For large shop floor
we applied 50 iterations and it took 520 seconds to finish
50 iterations if we use SIRO dispatching and 850
seconds if we use ATC dispatching.
We tested three shop floors for seven types of
solutions. We first looked at unintegrated process
planning scheduling and due-date assignment as SIRO-
RDM (Genetic) and SIRO-RDM (Ordinary). Later we
integrated due-date assignment with process planning
and used SIRO dispatching rule. At these solutions we
looked at SIRO-DUE (Genetic) and SIRO-
DUE(Ordinary) solutions. Finally we integrated process
planning, Due-date assignment and ATC scheduling and
looked at solutions ATC-DUE (Genetic), ATC-DUE
(Random), ATC-DUE (ordinary). Explanations of these
solutions are given at section 5.
TABLE IV: COMPARISON OF SEVEN TYPES OF SOLUTIONS FOR SMALL
SHOP FLOOR
Worst Avarage Best Cpu time
ATC-DUE (O) 612,1 320,07 251,52
SIRO-DUE(O) 625,47 323,33 254,37
SIRO-RDM(O) 430,92 423,04 413,05
ATC-DUE (R) 236,98 235,42 232,88 153sec
ATC-DUE (G) 226,92 226,22 224,48 148sec
SIRO-DUE(G) 241,62 240,85 237,43 87 sec
SIRO-RDM(G) 399,12 397,64 394,82 89sec
Figure 2. Small shop floor results
We tested three shop floors for seven types of
solutions. First shop floor is small shop floor and there
are 20 machines, 50 jobs with 10 operations each and
each job has 5 alternative process plans and processing
times of each operation changes in between 10 and 19
according to following formula . We
compared seven solutions and three of them are ordinary
solutions and use first step (initial step, can be considered
as first iteration) solutions. One of them use random
search and we make 200 random iterations. Three of the
solutions use genetic search and we apply 200 genetic
search iterations. Results are given below for the small
shop floor. Getting ordinary solution occurs at the very
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beginning of the iterations so negligible time required for
ordinary solutions. Applying 200 random or genetic
iterations require approximately 90 seconds (with SIRO)
or 150 seconds (with ATC) (cpu time). Times are given
at Table IV at the last column. Results of small shop
floor are given at Table IV and at Fig. 2. According to
results the more the solutions are integrated the results
are better and the more search iteration applied the
solution is better and directed search outperforms
undirected search.
Similar results are found for the second mid-size shop
floor and these results are given at the following Table V
and Fig. 3.
TABLE V: COMPARISON OF SEVEN TYPES OF SOLUTIONS FOR MEDIUM
SHOP FLOOR
Worst Avarage Best Cpu time
ATC-DUE (O) 1111,35 724,9 594,1
SIRO-DUE(O) 1138,97 746,06 649,05
SIRO-RDM(O) 830,59 806,89 784,22
ATC-DUE (R) 584,63 579,07 570,73 439sec
ATC-DUE (G) 555,73 554,32 551,25 427sec
SIRO-DUE(G) 618,9 615,85 612,07 259sec
SIRO-RDM(G) 774,45 772,71 768,9 250sec
Figure 3. Medium shop floor results
Third shop floor is the biggest shop floor and similar
results are found in this shop floor. Results are
summarized at the following Table VI and Fig. 4.
TABLE VI: COMPARISON OF SEVEN TYPES OF SOLUTIONS FOR LARGE
SHOP FLOOR
WORST AVG. BEST CPU
TIME ATC-DUE (O) 2141,55 1872,42 1690,84
SIRO-DUE(O) 2158,09 1965,85 1814,52
SIRO-RDM(O) 1936,56 1910,79 1886,14
ATC-DUE (R) 1639,88 1622,84 1598,17 855sec
ATC-DUE (G) 1565 1558,62 1539,9 848sec
SIRO-DUE(G) 1757,03 1752,86 1735,41 527sec
SIRO-RDM(G) 1813,14 1808,31 1797,27 515sn
Figure 4. Large shop floor results
VII. CONCLUSION
In this study we tried to integrate due-date assignment
process planning and ATC scheduling. We compared
different integration level. At first we took scheduling
and due-date assignment as unintegrated we solved
problem for SIRO-RDM (Genetic) and SIRO-RDM
(Ordinary). Here we assumed that scheduling is
unintegrated and we used SIRO dispatching. We also
assumed due-date determination is unintegrated and we
used RDM due-date assignment in place of external,
unintegrated due-date determination.
Later we integrated due-date assignment with process
pla selection. At solution, at due-date assignment gene
with multipliers and constants we used nineteen different
due-date assignment rules. These due-date assignment
rules are given at section 4. Here we still scheduled jobs
with SIRO we didn’t integrate scheduling with due date
determination and process plan selection. We solved
problem for SIRO-DUE (Genetic) and for SIRO-DUE
(Ordinary).
Later we integrated three functions (process planning,
scheduling and due-date assignment). At solution, at
scheduling gene with multipliers we used four
dispatching rules (ATC and SIRO heuristics) and at due-
date assignment gene we used 19 types of due-date
assignment rules. Here we solved problem for ATC-DUE
(Genetic), ATC-DUE (Random), and ATC-DUE
(Ordinary) cases. At genetic search we repeated genetic
iterations up to 200, 100 and 50 iterations for small,
medium and large sized shop floors. At Random search
we applied these many random iterations for three
different shop floors. Totally these seven types of
solutions and their explanations are given at section 5.
When we looked at the results as we increased
integration level the solution became better. If we look at
searches we found that search is very useful to find better
solution. When we compare directed (genetic) search and
undirected (random) search, genetic search always found
to be best. We proved that higher integration level is
better and if we don’t integrate these three functions then
each function will try to get local optima. Process
planning will not care about scheduling, shop floor
performance, workload level and balance and also will
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not care about due-date performance. If we don’t
integrate scheduling with due-date assignment then
scheduling will not take into account of earliness,
tardiness and length of due-date. So benefit of integration
will be substantial.
APPENDIX A: DUE-DATE ASSIGNMENT RULES
TWK (Total Work) Due =TPT * k
SLK (Slack) Due = TPT + qx
PPW (Processing plus Wait)Due=TPT * k + qx
NOP (Number of operations) Due = NOP * k
RDM (Random due assign.) Due = N ~
(3*Pav,(Pavg/2 )2)
TPT= total processing time
Pavg= mean processing time of all job waiting
APPENDIX B: DISPATCHING RULES
ATC(Apparent Tardiness Cost): This is composite
dispatching rule here and it is a kind of hybrid of MS
(Minimum Slack First) and SPT (Shortest Processing
Time First) dispatching rules. For each job, priority index
is calculated as.
Ij(t) = wj/pj*exp(-max(dj-pj-t,0)/Kpavg) .
Ij(t) is priority index,
pj is j’th job processing time,
max(dj-pj-t,0) is j’th job slack,
K is scaling parameter,
Pavg is avarage processing time of the jobs
SIRO(Service in Random order): A job among waiting
jobs is selected randomly to be processed.
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Halil Ibrahim Demir was born in Sivas, Turkey in 1971. In 1988 he
got full scholarship and entered Bilkent University, Ankara, Turkey to Industrial Engineering Department. He got his Bachelor of Science
degree in Industrial Engineering in 1993.
In 1993 he went to Germany for graduate study. He studied German up to intermediate level. In 1994 he got full scholarship for graduate study
in USA from ministry of Education of Turkey. In 1997 he got Master of
Science degree in Industrial Engineering from Lehigh University, Bethlehem, Pennsylvania, USA. He is accepted to Northeastern
University, Boston, Massachusetts for Ph.D. study. He finished Ph.D.
courses at this university and completed Ph.D. thesis at Sakarya University, Turkey in 2005 and got Ph.D. degree in Industrial
Engineering. He started to his academic position at Sakarya University and works as
an Assistant Professor at this university.
Tarık Cakar is an Associate Professor at Sakarya University
Mumtaz Ipek is an Assistant professor at Sakarya University
Ozer Uygun is an Assistant professor at Sakarya University
Murat Sari is a Research Assistant at Sakarya University
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and due date assignment with positionally dependent processing
times,” European Journal of Operational Research, vol. 198, pp.
57-62, 2009.
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