Meij, J. T.
A icle
Compa ing wo compu e sea ch models o agg ega e
p oduc ion planning
Sou h A ican Jou nal o Business Managemen
P o ided in Coope a ion wi h:
Uni e si y o S ellenbosch Business School (USB), Bell ille, Sou h A ica
Sugges ed Ci a ion: Meij, J. T. (1982) : Compa ing wo compu e sea ch models o agg ega e
p oduc ion planning, Sou h A ican Jou nal o Business Managemen , ISSN 2078-5976, A ican
Online Scien i ic In o ma ion Sys ems (AOSIS), Cape Town, Vol. 13, Iss. 2, pp. 67-69,
h ps://doi.o g/10.4102/sajbm. 13i2.1175
This Ve sion is a ailable a :
h ps://hdl.handle.ne /10419/217795
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Compa ing
wo
compu e
sea ch
models
o
agg ega e
p oduc ion
planning
J.T.
Meij
Depa men
o
Indus ial Enginee ing, Uni e si y
o
S ellenbosch
In
his pape a compa ison is made be ween he esul s and
he
cos -e ec i eness
o
wo
compu e sea ch models o
ag-
g ega e p oduc ion planning when applied o a e y sensi i e
high-o de cos s uc u e. The Sea ch Decision Rule
(SOR)
model
de eloped by Taube
ou pe o ms
he Sec ioning
Sea ch
Model
(SECT)
o
Goodman in bo h he a eas
o
o al
op imum cos . and cos -e ec i eness.
S.
A .
J.
Bus. Mgm . 1982,
13:
67-69
In
hie die a ikel wo d 'n e gelyking ge e ussen die
esul a e
en
die kos e-doel e endheid an wee ekenaa -
soekmodelle i geheelskedule-p oduksiebeplanning, soos
oegepas op 'n baie sensi iewe hoe-o de kos es uk uu . Die
'Sea ch Decision Rule'-model
(SOR)
on wikkel deu Taube
lewe
in albei a eas, naamlik
o ale
op imale kos e
en
kos e-
doel e endheid, be e esul a e as die 'Sec ioning Sea ch
Model'
(SECT)
an Goodman.
S.-A .
Tydsk . Bed y sl. 1982,
13:
67-
69
Second
in
a se ies
o
h ee a icles
P o .
J.T.
Meij
Head
o
Indus ial Enginee ing, Uni e si y
o
S ellenbosch,
S ellenbosch
7600, Republic
o
Sou h A ica
Recei ed
Oc obe
1981;
accep ed No embe
1981
In oduc ion
Many p oduc ion manage s a e aced wi h he p oblem
o
planning p oduc ion, in en o y and wo k o ce unde
he cons ain
o
limi ed ecou ces o mee a seasonal de-
mand. In hose cases whe e linea i y
o
he cos unc ions
o
an unde aking may easonably be assumed, an o -
dina y linea p og amming model su ices. In many
cases, howe e , his simple linea app oach o ce ain
essen ially non-linea cos unc ions
is
unaccep able
owing o he g oss app oxima ion made. Conside able
esea ch has been done on his planning p oblem and
a ious models ha e been p oposed. These models can be
di ided in o h ee b oad ca ego ies, namely heu is ic
models, ma hema ical op imiza ion models and com-
pu e sea ch models.
In his pape a compa ison
is
made be ween he esul s
o
wo
o
he published compu e sea ch models on a
high-o de cos unc ion. One
o
he ollowing ou basic
s a egies can be ollowed o mee he luc ua ions in de-
mand.
1.
Wo k- o ce le el and p oduc ion a e a e kep con-
s an and in en o y
is
used o abso b luc ua ions in
demand.
2.
Wo k- o ce le el and in en o y a e kep cons an
and demand luc ua ions a e handled
by
changing
he p oduc ion a e, i.e. wo king o e ime o allow-
ing idle ime.
3. P oduc ion a e and in en o y a e kep cons an and
he wo k o ce
is
a ied o sui he demand.
4. A combina ion
o
he h ee s a egies gi en abo e.
In mos cases in indus y he combina ion ype
o
s a egy
(4)
is
usually he mos app op ia e. The ex en
o
which he di e en s a egies should be mixed o p esen
an o e all plan
is
dependen on he cos s uc u e
o
he
pa icula indus y.
Cos s uc u es a y, and may ha e any hing om
linea
o
almos linea , o highly non-linea ela ionships.
In many cases o dina y linea o piecewise linea unc-
ions may be adequa e o desc ibe he ela ionship be-
ween cos and one
o
he abo e-men ioned a iables. On
he o he hand
i
may well be ha o ce ain cos s a
linea app oach
is
un ealis ic and a emo ed om he
eal wo ld si ua ion. In he la e case i becomes ex eme-
ly
di icul o ob ain a p o en op imum solu ion. Va ious
me hods ha e been sugges ed o sol e his p oblem.
Fo a solu ion me hod o be p ac ical i mus comply
68
wi h he ollowing p ima y p ope ies:
I
mus be cos e ec i e.
I
mus assu e, wi h easonable con idence,
ha
a
global op imum will be eached.
I mus be uni e sally applicable.
Wi h he de elopmen
o
he high-speed digi al com-
pu e , compu e sea ch me hods ha e been de eloped
and
implemen ed
o
comply, in he ield
o
agg ega e p o-
duc ion planning, wi h hese p ope ies. Taube I com-
pa ed a ious sea ch algo i hms
and
ound he Hooke-
Jee es algo i hm2 pa icula ly sui able o he solu ion
o
high-o de unc ions. He made use
o
his algo i hm in
he de elopmen
o
his compu e sea ch sys em, Sea ch
Decision Rule (SOR). Goodman3 applied a modi ied Sec-
ioning Sea ch Model (SECT) o a high-o de cos unc-
ion.
The au ho applied he SOR model
o
he high-o de
cos unc ion used by Goodman and compa ed he esul s
wi h hose
o
he SECT.
Desc ip ion
o
he
cos
s uc u e
In o de o es he Sec ioning Sea ch Model, Goodman
de eloped a ou h-o de cos model. The eal wo ld
cos s,
o
which his model
is
an app oxima ion, a e gi en
in Table
1.
The cos componen s conside ed in his model
a e: di ec pay oll, o e ime
and
idle ime, hi ing
and
lay-
o ,
change
o
p oduc ion a e and in en o y holding
and
sho ages. The objec i e cos unc ion
o
be minimized is:
C = 1
[340
W,
+ 0,2 (P, -
6W,)
4
+ 64(W1 -W1
_.>4
+ 0,1
(P,
-
P,_.)4
+ 0, 1 (320 -
1,)1
Whe e
W,
is
he wo k o ce in pe iod ,
P,
is
he p oduc ion in pe iod ,
and
/1
is
he in en o y in pe iod
;
subjec o he ollowing cons ain s:
/1 = /1_ 1 + P, -D,
0
'-
W,<
150
(
= 1
o
N)
(
= 1
o
N)
S.-M .
I
yJ,k .
Bcd y sl.
1982,
IJ(i)
(
= 1
o
N)
whe e D,
is
he
demand
in pe iod .
Wo k
o ce
and
p oduc ion
quan i y
in each
pe iod
a e
he independen a iables.
F om
hese a iables,
as
well
as he gi en
demand
(D,),
he
o he
a iable
con ibu ing
o
he
cos ,
ha
is
in en o y,
is
calcula ed.
Resul s
In Table 2
he
mon hly
p oduc ion
plans and
co espon-
ding cos s gi en by
SOR
and
SECT
a e compa ed
o
a
24-mon h planning
ho izon.
SOR
ga e an
imp o emen
o
nea ly
6%
on
he
o al
cos
o
$14 196 488 ob ained
by
Goodman's
SECT.
I
can
also be seen
ha
he cos
model
is
e y sensi i e
o
small changes in any
o
he
a iables
-
compa e
o example
he
mon hly
cos s o
mon hs
3
(SECT
53"7o
highe
han
SOR), 4 (SECT 52% highe
han
SOR)
and
8 (SECT
52%
highe
han
SOR). The e
a e
no
majo
di e ences be ween
he
wo plans. F om a
p ac-
ical poin
o
iew
any
one
o
he
wo plans could
be
adop ed.
I mus
hus
be
emphasized ha o
highly-
sensi i e cos s uc u es as
he
one
used he e,
ex eme
ca e mus be
aken
in
he
choice
o
an
op imiza ion
me hod.
To
measu e
he
cos -e iciency
o
he
wo sea ch
ech-
niques,
he
compu e
ime equi ed
pe
decision
(inde-
penden a iable)
is
compa ed.
I should be kep
in
mind,
howe e ,
ha
as
Goodman
s a es, '
...
compu e
ime
usage is a unc ion
o
bo h
he
compu e
used and
p o-
g amming e iciency
and
me hod
used'.
3 He s a es
ha
on
a e age
he
Sec ioning Sea ch Model uses 0,
75
s
pe
decision. I was
ound
ha
SOR
used only 0,38 s
pe
decision
on
a UNIV
AC
1110
compu e .
By
dec easing
he
numbe
o
sea ch epe i ions
o
he
SOR p ocedu e, a
plan was ob ained using only 0,24 s
pe
decision
(a
680/o
sa ing in
compu e
ime).
The
o al
cos
o
his plan
was
only 0, 14% highe
han
he
esul s p e iously ob ained.
Conclusion
In his
pape
a
compa ison
is
made
be ween he esul s
o
wo well-known sea ch models de eloped o
agg ega e
p oduc ion planning.
Fo
compa ison
pu poses a
high-
o de cos model has been used.
The
SOR-model
o
Taube
ou pe o ms
he
SECT-model
o
Goodman
when
compa ed
on
he
basis
o
o al
op imum
cos
and
cos -e ec i eness.
Table
1
Real
wo ld cos
on
which he cos model is based (Rand)
1w,-w
1_11 Cos
IP,-P,_,,
Cos
II,
-
3201
Cos
IP,-6W,I
Cos
0 0 1 I I I 0 0
I
66
2 2 2 2 I
2
1001
4
24
3 9 2 4
3
5210
s
68
4
28
3
14
4
20100
7
22S
6
122
s
131
s
38120
10
1049
8
392
7
457
7
86300
16
6310
11
1370
1876
10
9
139200
22
26100
IS
5417
12
3780
12
224400
34
123400
21
18240
14
7795
14
279600
S2
487200
39
231200
18
20600
19
401100
87
1140000
SI
474400
22
34900
2S
698700
ISO
2224000
70
762500
30
58200
S.
A . J. Bus. Mgm
1982,
13(2)
69
Table 2 P oduc ion plans, Sea ch Decision Rule
(SOR)
and Sec ion-
ing Sea ch
(SECT)
Wo k o ce P oduc ion In en o y Pe iod cos
Pe iod Demand SDR SECT SDR SECT SDR SECT SDR SECT
(Rand) (Rand)
I
430
73 75
447
431
337
301
36205
160572
2
447
70
72
431
440
321
294
36187
76836
3
440
67
69
406
426
287
280
182702
392632
4
316
64
65
376
392
347
356
163305
340082
5
397
62 62
362 374
312 333
29178
39620
6
375
60
59
352 348
289
306
109783
75042
7
292
62
60
364
348
361
362
305626
335780
8
458
64
63
395
386
298
290
151989
316936
9
400
63
64
383
391
281
281
244834
253710
10
350
61 61
353 355
284
286
273730
330447
II
284
63 63
359
356 359
358
278352
277808
12
400
68 68
399
399
358 357
532877
593728
13
483
73 73
442
444
317 318
414825 475143
14
509
78 78
477
481
285
290
362126
340645
15
500
83
83
491
488
276
278
432210
381629
16
475
88
88
510
508
311 311
103618
118576
17
500
94 94
553
552
364
363
853346
835740
18
600
101
IOI
608
607
372
370
1752367
1728065
19
700
107 107
662
662
334
332
1090724 1068460
20
700
112
112
698 699
332
331
315675
373248
21
725
107
107
658
659
265 265
1273906
1264146
22
600
IOI
IOI
600 600
265
265
2171033
2244341
23
432
95
95
545 545
378 378
2222244
2240081
24
615
93
93
552
553
315
316
32637
33204
To al
cos
13368479
14196458
Re e ences
and s a is ical p oblems,
J.
Assoc. Comp., Ap il
1961,
pp.
I.
Taube ,
W.H.
A sea ch decision ule o he agg ega e scheduling 212-229.
p oblem, Manage. Sci., Feb.
1968,
14(6), pp.
8343-
8359.
3.
Goodman,
D.A. A Modi ied Sec ioning Sea ch App oach o Ag-
2.
Hooke,
R.
& Jee es,
T.A.
'Di ec
Sea ch'
solu ion
o
nume ical g ega e Planning. Ph.D-disse a ion, Yale Uni e si y,
1972.