Multi-objective control chart design optimization using NSGA-III and MOPSO enhanced with DEA and TOPSIS

• We use NSGA-III and MOPSO algorithms to solve a multi-objective X-bar control chart design problem.
• NSGA-III and MOPSO are modified to handle a constrained multi-objective problem with discrete and continuous variables.
• Four DEA models are proposed to reduce the number of Pareto optimal solutions to a manageable size.
• TOPSIS is used to prioritize the efficient optimal solutions.
• Several metrics are used to compare the performance of NSGA-III and MOPSO algorithms.

X-bar control charts are widely used to monitor and control business and manufacturing processes. This study considers an X-bar control chart design problem with multiple and often conflicting objectives, including the expected time the process remains in statistical control status, the type-I error, and the detection power. An integrated multi-objective algorithm is proposed for optimizing economical control chart design. We applied multi-objective optimization methods founded on the reference-points-based non-dominated sorting genetic algorithm-II (NSGA-III) and a multi-objective particle swarm optimization (MOPSO) algorithm to efficiently solve the optimization problem. Then, two different multiple criteria decision making (MCDM) methods, including data envelopment analysis (DEA) and the technique for order of preference by similarity to ideal solution (TOPSIS), are used to reduce the number of Pareto optimal solutions to a manageable size. Four DEA methods compare the optimal solutions based on relative efficiency, and then the TOPSIS method ranks the efficient optimal solutions. Several metrics are used to compare the performance of the NSGA-III and MOPSO algorithms. In addition, the DEA and TOPSIS methods are used to compare the performance of NSGA-III and MOPSO. A well-known case study is formulated and solved to demonstrate the applicability and exhibit the efficacy of the proposed optimization algorithm. In addition, several numerical examples are developed to compare the NSGA-III and MOPSO algorithms. Results show that NSGA-III performs better in generating efficient optimal solutions.