Using metaheuristic algorithms to solve a dynamic cell formation problem with consideration of intra-cell layout design

Abstract

This paper proposes a new nonlinear integer mathematical model to address the cell formation and intra-cell layout problem, as two main steps of designing a cellular manufacturing system, concurrently. The problem is formulated under dynamic condition, where product demands may vary from one period to another and consequently machine-part grouping and machine layout design within each cell are determined for each period of the planning horizon. In addition to forming the machine-part groupings, the proposed model determines the best layout within each cell in each period; few numbers of previous studies have been dedicated to concurrent problem of dynamic cell formation and intra-cell layout design. Machine relocation cost, as a main objective function of a dynamic cell formation problem, is formulated based on the location where machines are being relocated. Intra-cell and inter-cell part movement costs are also calculated based on the distance between machine positions and cell positions, respectively. Exhaustive numerical analyses are reported in order to validate the proposed mathematical model. Then, two well-known algorithms and one hybrid algorithm including developed simulated annealing algorithm (SA), particle swarm optimization (PSO), and hybrid particle swarm optimization (HPSO) are applied to tackle the problem. Mutation operator is combined with the operators of particle swarm optimization to enhance the algorithm. The results show that simulated annealing outperforms other algorithms in this problem.