A multi-objective mathematical model for cellular manufacturing systems design with probabilistic demand and machine reliability analysis

This paper presents a dynamic multi-objective mixed integer mathematical model for cell formation problem with probabilistic demand and machine reliability analysis, where the total system costs, machine underutilization cost, and maximum system failure rate over the planning time periods are to be minimized simultaneously. The total system cost objective function calculates machine operating, internal part production, intercellular material handling, and subcontracting costs. Since in this type of problems, objectives are in conflict with each other, so finding an ideal solution (a solution that satisfies all objectives simultaneously) is not possible. Therefore, this study uses the augmented ε-constraint method (to solve small size problems) and a nondominated sorting genetic algorithm (NSGAII) (to solve large size problems) to find the Pareto optimal frontier that decision makers can select her/his preferred solution. Numerical examples will be solved to demonstrate the efficiency of the proposed algorithm.

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