Goal 10 Maybe

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P e r g a m o n

Computers ind. EngngVoL 31, No. 1/2, pp. 363 - 366,1996Copyright © 1996 ElsevierScience Ltd

Printed in GreatBrita~ All dghw ~z r¢ ~

S0 36 0- 83 52 (9 6) 00 15 2- 0 o36o- 8352/96 $15.00 + 0.00

A G O A L P R O G R A M M I N G M O D E L T O E V A L U A T E T H E P R O D U C T I O N

D E C I S I O N T H R O U G H T H E P R O D U C T I V I T Y O F S U B - S Y S T E M S

N . A L P a n d S . L . M U R R A Y

E n g i n e e r i n g M a n a g e m e n t D e p a r t m e n t , U n i v e r s i ty o f M i s so u r i -R o l l a ,

R o l l a , M O 6 5 4 0 9 - 0 3 7 0 U . S . A .A B S T R A C T

Produ ctivity is co ncern ed with the effectiv e and efficient utilization o f resources in producing goo ds

and/or services. In this study, productivity has bee n viewed in a broader perspective to present the

deg ree of acc om plishm ent of perform ance objectives, recon ciled optimally thro ugh goal-programm ing.

K E Y W O R D S

Go al-Pr ogr am m ing, productivity, production, productivity analysis, sub-system.

T H E G O A L P R O G R A M M I N G M O D E L

The resea rch has been don e in an electronics organization (BEKO) in Turkey. The co mp any has six

differen t products.

Their products are:

X ~ : T V T e l e t e x t :

X z : T V N o n t x :

X 3 : T V S k d I m p o r t :

X 4 : T V S k d E x p o r t :X s : C a s h R e g i s t e r

X 6 : A u d i o - V i d e o

The com plete assembly TV with teletext

The complete assembly TV without teletext

The partial assembly import TV

The partial assembly export TV

The mo del has three sub-systems, d efined as production, marketing, and m aterials sub-systems, with

differen t objectives.

It was de cide d to accord the following priorit ies to goals according to the production level ( Re tzlaff

e t a L , 1 9 9 3 ) :

P~: Ac hie vin g that cap acity utilization w ill not violate the upper limit. Products X 3, X,, X s, and

X~, wi l l not b e p roduced m ore than demand.

P2: M axim ization of turnover and added value. Product XI will satisfy the max im umdemand.

1'3: Product X 2 will sat is fy the ma ximum demand.

P4: Products XI and X 2 will not be produced less than the minim um demand.

363

7/27/2019 Goal 10 Maybe


364 19th International Conference on Com puters and Industrial Engineering

P s: Ach ieving that e nergy ut i l ization wil l not violate the upper l imit.

The m ain priori t ies to goals are; the capaci ty uti lizat ion and the maximization of turno ver and ad ded

value a re two t imes mo re than the other goa ls .

In thi s case the Goal Programming M odel wi l l be as be low:

M i n . Z = 2 P l . d l * , P l . d l o + , P l .d 1 2 * , P p d u ÷ , P p d l ~ ÷ , 2P2.d2", P2 .d3- P2 .ds ' , P 3 .~ ' ,P 4 .d ~' , P4 .ds ÷ , Ps . (d4"+d 4 ÷)

The goal programming mo del is subject to the fol lowin g goal const iaints (Inuiguchi e t a l . , 1991) :

The formulations for constraints:

I . C a p a c i t y C o n s t r a i n t :

3.11X1+ 2.981X2+ 2.09X3+ 1.56X4+ 0.65Xs+ 0.09X~+d: - d : = 1,636,000

H . A d d e d V a l u e C o n s t r a i n t :

1.7X1+ 1.8X2+ 1.8X3+ 1.75X4+ 1.2X5+ 0.85X~+d2-- @ = 1.287"109

m . T u r n o v e r C o n s tr a in t :

3.8Xt+ 3.65X2+ 3.65X3+ 3.7X4+ 2.83X5+ 1.84X6+d3- -d 3 ÷ = 2.714"109

I V . E n e r g y C o n s t r a i n t :

5X t+ 2.2X2+ 2.1X 3+ 1,54X4+ 0.75Xs+ 0.50X6+d~- - d : = 10,000

V . D e m a n d C o n s t r ai n t :

3 0 0 < X l -< 3 5 0 , X l + d s " = 3 0 0 ,

2 0 0 < X 2 - < 2 3 0 , X 2 + d 7 " = 2 0 0 ,

3 5 ' < X 3 '< 4 0 , X 3 - d l o " ff i4 0

0.90 -< X4"< 0 . 9 5 , X4 - d l 2 * = 0 . 9 5

2 0 "< X s < 2 5 , X s - d 1 4 = 2 5

130 "< X~ '~ 1 50, X 6 -d 1~ ÷ = 150

XlX2

H j , ~ " , di" a re a lways pos i tive for a ll i and j .

- d~" = 350

- ds" -- 2 30

Acco rding to the abo ve formulations, there are three different goal programming solut ions

whi c h ha s be e n show e d in Ta b l e 1 .

P R O D U C T

C O D E

X~

X2

T h e p r o d u c t i o n

p l a n o f t h e f i rs ta l t e r n a t i v e

( x I ~ X ) )

2 9 9

2 0 2

X~ 4 0

X4 0.95

X ~ 2 4

T h e p r o d u c t i o n

p l a n o f t he s e c o n d

a l t e r n a t i v e(x 1,ooo)

3 02

2 0 2

T h e p r o d u c t io np l a n o f t h e t h i r a

a l t e r n a t i v e(x t,{}00)

3 5 0

1 5 0

4 0 4 0

0.95 0.95

24 25

X6 150 150 150

Table l .The p rodu ct ion plans o f the three alternat ive solut ions

7/27/2019 Goal 10 Maybe


19th International Conference on Computers and Industrial Engineering

T H E P R O D U C T I V I T Y A N A L Y S I S

365

T h e f o l l o w i n g p r o d u c t i v i t y i n d i c e s o f d i f f e re n t s u b - s y s t e m s w e r e c a l c u l a t e d t o e v a l u a t e t h e t h r e e

a l t e r n a t iv e p r o d u c t i o n p l a n s ( S u m a n t h , 1 9 85 ).

1 . Product ion sub-system:

- L a b o r u t i l i z a t io n- A s s e t u t i l i z at i o n

Q u a l i t y

- S c h e d u l e c o m p l e t i o n

= S t a n d a r d h o u r s / A t t e n d a n c e h o u r s ( D i r e c t l a b o r )= S t a n d a r d h o u r s / C a p i t a l i z e d c o s t

= V a l u e o f f l a w l e s s p r o d u c t / V a l u e o f t o t al p r o d u c t

-- O r d e r s c o m p l e t e d i n t i m e / O r d e r s s c h e d u l e d

2 . M a r k e ti n g s u b s y s t e m :

- S a l e s = P r o f i t / S a l e s

3 . Personnel sub-system:

- I n d u s t r i a l r e l a t i o n s

- V a l u e o f i n d i r e c t l a b o r

- V a l u e o f d i r e c t l a b o r

- V a l u e o f l a b o r

= L a b o r h o u r s w o r k e d / A t t e n d a n c e h o u r s

= I n d i r e c t l a b o r / T o t a l l a b o r

= D i re c t l a b o r / T o t a l l ab o r

= T o t a l l a b o r c o s t / T o t a l l a b o r h o u r s

4 . Materia ls sub-system:

- P u r c ha s e o f m a n a g e m e n t

- I n v e n t o r y c o n t r o l

- D o m e s t i c m a t e r i a l r a t i o

- I m p o r t m a t e r i a l r a t i o

= M a t e r i a l p a y m e n t i n t i m e / T o t a l m a t e r i a l c o s t

ffi A v e r a g e m a t e r i a l c o n s u m p t i o n / A v e r a g e s t o c k

= D o m e s t i c m a t e r i a l c o s t / T o t a l c o s t

= I m p o r t m a t e r i a l c o s t / T o t a l c o s t

5 . Goals & Values sub-system:

- F i n a n c i a l g o a l s = P r o f i t / I n v e s t m e n t

- S u p p l i e r s a t i s f a c ti o n = P a y m e n t s i n t i m e / T o t a l p a y m e n t s

I n p r o d u c t i v i t y a n a l y s i s , t h e k e y p e r f o r m a n c e a r e a s a n d e x p e c t e d v a l u e s h a v e b e e n c a l c u l a t e d f o r th r e e

d i f f e r e n t a lt e r n a t i v e so l u t i o n s w h i c h h a s b e e n s h o w e d i n T a b l e 2 .

T h e P r o d u c t i v i t y I n d i c e o f t h e F i r s t A l t e r n a t iv e :

0 . 2 5 * 0 . 9 6 7 + 0 . 2 5 * 1 . 0 + 0 . 1 5 * 0 . 9 4 8 + 0 . 2 0 * 0 . 9 5 6 + 0 . 1 5 * 0 . 9 4 4 - 0 . 9 5 8

T h e P r o d u c t i v i t y I n d i c e o f t h e S e c o n d A l t e r n a ti v e :

0 . 2 5 * 0 . 9 7 7 + 0 . 2 5 * 1 . 0 + 0 . 1 5 * 0 . 9 8 8 + 0 . 2 0 * 0 . 9 0 9 + 0 . 1 5 * 0 . 9 2 4 = 0 . 9 4 6

T h e P r o d u c t i v i t y I n d i c e o f t h e T h i r d A l t e r n a t i v e :

0 . 2 5 * 0 . 9 5 4 + 0 . 2 5 * 1 . 0 + 0 . 1 5 * 0 . 9 9 5 + 0 . 2 0 * 0 . 8 7 6 + 0 . 1 5 * 0 . 9 2 4 = 0 . 9 3 7

T h e h i g h e s t p r o d u c t i v i t y i n d i c e i s i n t h e f i r s t a l t e r n a t i v e , t h e r e f o r e t h i s p r o d u c t i o n p l a n i s t h e b e s t f o r

t h e c o m p a n y a m o n g t h e o th e r s .

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19 t h I n t er na t i ona l Con f e r enc e on Com pu t e r s and I n dus tr i a l En g i neer i ng66

I U B - S Y S TE I V ~ W E I G H T

1 2

PRODUCrIoI~ 0.25

X~a~nNO 0.25

PERSONNEL 0.15

MAa'~X:ALS 0.20

C,OALS & 0. 15VALUES

PERFORMANCE AREA VEIOI-l'I

3

L A B O R U T I L I Z A T I O N

A S S E rr ~ZA TI O N

Q U A L I T Y

S C I I E D U L E C O M F L E T I O N

S A L E S

I N D U S T R I A L R E L A T I O N S

V AL U E O F I N D ~ L A BO R

V A L U E OF DIRECTLABOR

VALUI~ /~ LABOK

PURCHASEMANAGEMENT

INVENTORYCONTROL

DOMESTIC MATERIALRATK! I~POIRTMATIN~IAL ~. TI0

F I N A N C I A L G O A L S

SUPpLIERSATISFACTION

4

0.25

0.35

0.25

0.15

1. 0

0.30

0.25

0.25

0.20

0.400.30

0.15

0.15

0.60

0.40

EXI'Er~-I~I.J V A L U E

a : F o r t h e f i r s t a l te r n a t i v e

b : F o r t h e s e c o n d a l t e r n a t i v e REALVALUEc : F o r t h e t h i r d a l t e r n a t i v e

5 6

a.0.977, b.0.974, c.0.982 0.952

a.4.66, b.4.65, c.4.69 4.67

a.0.972, b.0.979, c.0.985 0.96

2..229.2 .24, b .2 .23 , c .2 .24

a.0.412, b.0.465, c.0.462

a.0.758, b.0.760, c.0.758

a .0 .69, b .0 .68 , c .0 .67

a.0.308, b.0.309, c.0.307

a.62.06~ b.66.5r c.68.3

a.0.89, b.0.88, c.0.87

a . l ~ , b . l ~ , c . 1~

a.0.40, b.0.39, c. 0.41

0.466

0.7800.690.310

72.330.66

85.7

0. 3a.0.60, b.0.61, c.0.61 0.7

a.0.003, b.0.004, c.0.004 0.0042

a.0.8, b.0.8, c.0.8 0.66

Table 2 . The sub-systems of the company, their performance areas , and their weights

C O N C L U S I O N

Fiv e dif ferent constraints: capacity, prof it, sales, energy, and material , ha ve been u sed for the goa l

programm ing formulat ion. Three dif ferent product ion plans hav e bee n obtained according to the goal

programm ing. By these product ion plans, the item s which are important for the organizat ion, the sub-

system s, and the key performance areas have been determined. Through the weigh tage factors ,

productiv ity m easurement o f each sys tem and sub-system have been ca lculated. As a conclu s ion, the

high est product ivity indice has be en obtained in the f irst alternat ive solu t ion, therefore this product ionplan is the best for the organizat ion.

This method provide a useful tool to evaluate alternat ive product ion plans with respect to product ivity

ga ins, and enables plant managem ent to make de cis ions on di f f erent sys tem and sub-system o bject ives .

R E F E R E N C E S

Inuiguchi, M ., Ya sufun i, K. (1991) . Goal Programming Problems With Interval Co eff icien ts and

Target Intervals , E u r opean Jou rn a l o f O pera t i ona l Resea r ch 5 2 , pp .3 4 5 - 3 6 0 .

Retzla f f, R .L. , Mo rey , D . , and Richard, C . (1993) . A G oal Programming Me thod of Stochast ic

A l l o ca t i v e D a ta E nv e l o pm ent A na l y s i s , Eu ropean Jou r na l o f Ope ra t i ona l Resea r ch 71 , pp .3 7 9 - 3 9 7 .

Sum anth, J.D. (198 5) . Product ivity Engineering and Man agement, M c .G r a w -H i U , pp .5 7 - 1 6 0 .

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Goal 10 Maybe