This paper presents an integrated mathematical programming formulation of the manufacturing cell formation problem introduced by Nagi et al. The formulation incorporates critical production planning issues that include long-term projected production requirements, resource capacity constraints, functionally identical machines and alternative process plans in the cell formation problem, with a common objective of minimizing the resulting inter-cell material handling effort. This problem is NP-hard. The previous work presented a heuristic solution based on decomposing the integrated problem into capacitated route selection and cell formation sub-problems that are solved iteratively until convergence. Like all fast heuristics, the method may suffer from poor solution quality, and non-heuristic methods cannot address problems of typical industrial dimensions because they would require exorbitant amounts of computing time. To overcome both these deficiencies, this paper (i) presents a 0–1 Mixed Integer Linear Programming (MILP) formulation alternative to the integrated cell formation problem, (ii) based on this formulation, develops a branch-and-bound procedure that provides improved solutions compared to those obtained by the heuristic of Nagi et al., and (iii) makes possible derivation of lower bounds to assess the quality gap when optimal solutions are unavailable or require excessive computing time. This work is important because it allows for better solutions to realistic industrial-sized problem instances.
