Comparing two computer search models for aggregate production planning

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 S anda d-Nu zungsbedingungen: Die Dokumen e au EconS o dü en zu eigenen wissenscha lichen Zwecken und zum P i a geb auch gespeiche und kopie we den. Sie dü en die Dokumen e nich ü ö en liche ode komme zielle Zwecke e iel äl igen, ö en lich auss ellen, ö en lich zugänglich machen, e eiben ode ande wei ig nu zen. 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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.