A queuing approach for a tri-objective manufacturing problem with defects: a tuned Pareto-based genetic algorithm

In this research, a manufacturing facility with independent workstations to remanufacture nonconforming products is investigated. Each workstation is first modeled as an M/M/m queuing system with m being a decision variable. Then, a tri-objective integer nonlinear programming models is developed to formulate the problem. The first objective tries to minimize the waiting times of products, while the second one tries to maximize the minimum reliability of machines at the workstations. Since minimization of the waiting times results in using a large number of machines with higher idle times, the third objective is considered to minimize the mean idle time of the machines. The aim is to determine optimal number of machines at each workstation. Since the problem belongs to the class of NP-hard problems, the non-dominated sorting genetic algorithm-II (NSGA-II) is utilized to find Pareto fronts. Because there is no benchmark available in the literature to validate the results obtained, the non-dominated ranked genetic algorithm (NRGA) is used as well. In both algorithms, not only the best operators are selected but also all of their important parameters are calibrated using statistical analysis. The performances of the algorithms are statistically compared using the t test. Besides, the multiple attribute decision-making method of TOPSIS is used to determine the better algorithm. The applicability of the proposed model and the solution algorithms is demonstrated via some illustrative examples.

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