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South African Journal of Industrial Engineering

versão On-line ISSN 2224-7890
versão impressa ISSN 1012-277X

S. Afr. J. Ind. Eng. vol.22 no.1 Pretoria  2011


A multi-objective genetic algorithm approach to the probabilistic manufacturing cell formation problem



V. JayakumarI; R. RajuII

ISchool of Mechanical and Building Sciences, VIT University, India.
IIDepartment of Industrial Engineering, Anna University, Chennai, India.




Due to customised products, shorter product life-cycles, and unpredictable patterns of demand, manufacturing industries are faced with stochastic production requirements. It is unlikely that the production requirements (product mix and demand) are known exactly at the time of designing the manufacturing cell. However, a set of possible production requirements (scenarios) with certain probabilities are known at the design stage. Though a large number of research works on manufacturing cells have been reported, very few have considered random product mix constraints at the design stage. This paper presents a nonlinear mixed-integer mathematical model for the cell formation problem with the uncertainty of the product mix for a single period. The model incorporates real-life parameters like alternate routing, operation sequence, duplicate machines, uncertain product mix, uncertain product demand, varying batch size, processing time, machine capacity, and various cost factors. A solution methodology for best possible cell formation using a genetic algorithm (GA) is presented, and the computational procedure is illustrated for the case study undertaken.


Vanweë doelgemaakte produkte, korter produklewensiklusse en onvoorspelbare vraagpatrone, staar vervaardigingsindustrieë stochastiese produksiebehoeftes in die gesig. Dit is onwaarskynlik dat produksiebehoeftes (produkmengsel en vraag) presies bekend sal wees wanneer die vervaardigingsel ontwerp word. Desnieteenstaande sal 'n stel moontlike produksiebehoeftes (scenarios) met bepaalde waarskynlikhede tog op hierdie stadium bekend wees. Alhoewel heelwat navorsing reeds op vervaardigingselle gedoen is, is daar weinig gerapporteer waar lukraak produkmengselrandvorwaardes by die ontwerpfase oorweeg is. Hierdie artikel hou 'n nie-lineêre gemengde-heeltal- wiskundige model voor vir die selformasieprobleem met onsekerheid oor die produkmengsel in 'n enkelperiode. Die model inkorporeer werklike parameters soos alternatiewe roetes, bewerkingsvolgordes, duplikaat toerusting, onsekere produkmengsels, onsekere produkvraag, wisselende lotgroottes, prosesseertye, toerustingkapasiteit en verskeie kostefaktore. 'n Oplossings-metodologie aan die hand van 'n genetiese algoritme vir die beste moontlike selformasie word voorgehou en die prosedure word by wyse van 'n gevallestudie geïllustreer.



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