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In this paper,a novel bi-objectivemathematical model is proposed to designa four-dimensional (i.e.,part, machine, operator, and tool) cellular manufacturing system (CMS) in a dynamic environment. The main objectives of this model are to 1) minimize total costs including tools processing cost, costs of transporting cells between various cells, machine setup cost, and operators’ educational costs, and 2) maximizing skill level of operators. The developedmodel is strictly NP-hard and exact algorithms cannot find globally optimal solutions in reasonably computational time. So, a multi-objective vibration damping optimization algorithm (MOVDO) with a new solution structure that satisfies all the constraints and generates feasible solutions is proposed to find near-optimal solutions in reasonablycomputational time. Since there is no benchmark available inthe literature, three other meta-heuristic algorithms (i.e., non-dominated sorting genetic algorithm (NSGA-II), multi-objective particle swarm optimization (MOPSO) and multi-objective invasive weeds optimization (MOIWO)) with the similar solution structure are developed to validate theperformance of the proposedMOVDOalgorithm for solving various instances of the developed model. A Taguchi method is employed to calibrate the main parameters ofthese fouralgorithms. The result of comparing theirperformances based on statistical tests and different measuring metrics reveals that theproposed MOVDO algorithm outperforms remarkably better than other meta-heuristics used in this paper.

A multi-objective vibration damping optimization algorithm for solving a cellular manufacturing system with manpower and tool allocation