Exact model for the cell formation problem
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The cell formation problem (CFP) consists in an optimal grouping of the given machines and parts into cells, so that machines in every cell process as much as possible parts from this cell (intra-cell operations) and as less as possible parts from other cells (inter-cell operations). The grouping efficacy is the objective function for the CFP which simultaneously maximizes the number of intra-cell operations and minimizes the number of inter-cell operations. Currently there are no exact approaches (known to the authors) suggested for solving the CFP with the grouping efficacy objective. The only exact model which solves the CFP in a restricted formulation is due to Elbenani and Ferland (Cell formation problem solved exactly with the dinkelbach algorithm. Montreal. Quebec. CIRRELT-2012-07, 1–14, 2012). The restriction consists in fixing the number of production cells. The main difficulty of the CFP is the fractional objective function—the grouping efficacy. In this paper we address this issue for the CFP in its common formulation with a variable number of cells. Our computational experiments are made for the most popular set of 35 benchmark instances. For the 14 of these instances using CPLEX software we prove that the best known solutions are exact global optimums.
KeywordsCell formation problem Exact model Grouping efficacy Fractional objective function
The authors are partially supported by LATNA Laboratory, NRU HSE, RF government grant, ag. 11.G34.31.0057.
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