In this paper, a multi-objective model for the economic-statistical design of the C-control charts is presented. The proposed model considers that multiple assignable causes can occur during the production process. Then, a hybrid meta-heuristic algorithm is developed to solve the model. The proposed algorithm consists of an improved version of the non-dominated sorting genetic algorithm II (NSGA-II) and the data envelopment analysis (DEA) which is called the IM-NSGA-II-DEA. For the proposed algorithm, new crossover and mutation operators based on the technique for order preference by similarity to ideal solution (TOPSIS) have been designed. After obtaining the non-dominated solutions, the DEA is employed to find the efficient ones. The performance of the IM-NSGA-II is evaluated in comparison with the classical NSGA-II and NRGA. The results of numerical experiments imply that the proposed method is superior to other algorithms in terms of objective function values and several multi-objective metrics.
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Zandieh et al. (2019) studied this question.