Solving a dynamic virtual cell formation problem by linear programming embedded particle swarm optimization algorithm

In this paper, a new mathematical model for virtual cell formation problem (VCFP) under condition of multi-period planning horizon is presented where the product mix and demand are different in each period, but they are deterministic moreover production planning decisions are incorporated. The advantages of the proposed model are as follows: considering operation sequence, alternative process plans for part types, machine time-capacity, lot splitting, maximal virtual cell size and balanced workload for virtual cells. The objective of the model is to determine the optimal number of virtual cells while minimizing the manufacturing, material handling, subcontracting, inventory holding and internal production costs in each period. The proposed model for real-world instances cannot be solved optimally within a reasonable amount of computational time. Thus, an efficient linear programming embedded particle swarm optimization algorithm with a simulated annealing-based local search engine (LPEPSO-SA) is proposed for solving it. This model is solved optimally by the LINGO software then the optimal solution is compared with the proposed algorithm.