A genetic algorithm for a bi-objective mathematical model for dynamic virtual cell formation problem

Nowadays, with the increasing pressure of the competitive business environment and demand for diverse products, manufacturers are force to seek for solutions that reduce production costs and rise product quality. Cellular manufacturing system (CMS), as a means to this end, has been a point of attraction to both researchers and practitioners. Limitations of cell formation problem (CFP), as one of important topics in CMS, have led to the introduction of virtual CMS (VCMS). This research addresses a bi-objective dynamic virtual cell formation problem (DVCFP) with the objective of finding the optimal formation of cells, considering the material handling costs, fixed machine installation costs and variable production costs of machines and workforce. Furthermore, we consider different skills on different machines in workforce assignment in a multi-period planning horizon. The bi-objective model is transformed to a single-objective fuzzy goal programming model and to show its performance; numerical examples are solved using the LINGO software. In addition, genetic algorithm (GA) is customized to tackle large-scale instances of the problems to show the performance of the solution method.