A Multicriteria Simheuristic Approach for Solving a Stochastic Permutation Flow Shop Scheduling Problem

Abstract

This paper proposes a hybridized simheuristic approach that couples a greedy randomized adaptive search procedure (GRASP), a Monte Carlo simulation, a Pareto archived evolution strategy (PAES), and an analytic hierarchy process (AHP), in order to solve a multicriteria stochastic permutation flow shop problem with stochastic processing times and stochastic sequence-dependent setup times. For the decisional criteria, the proposed approach considers four objective functions, including two quantitative and two qualitative criteria. While the expected value and the standard deviation of the earliness/tardiness of jobs are included in the quantitative criteria to address a robust solution in a just-in-time environment, this approach also includes a qualitative assessment of the product and customer importance in order to appraise a weighted priority for each job. An experimental design was carried out in several study instances of the flow shop problem to test the effects of the processing times and sequence-dependent setup times, obtained through lognormal and uniform probability distributions with three levels of coefficients of variation, settled as 0.3, 0.4, and 0.5. The results show that both probability distributions and coefficients of variation have a significant effect on the four decision criteria selected. In addition, the analytical hierarchical process makes it possible to choose the best sequence exhibited by the Pareto frontier that adjusts more adequately to the decision-makers’ objectives.