Two-stage fuzzy-stochastic programming for parallel machine scheduling problem with machine deterioration and operator learning effect

This paper deals with the determination of machine numbers and production schedules in manufacturing environments. In this line, a two-stage fuzzy stochastic programming model is discussed with fuzzy processing times where both deterioration and learning effects are evaluated simultaneously. The first stage focuses on the type and number of machines in order to minimize the total costs associated with the machine purchase. Based on the made decisions, the second stage aims to schedule orders, while the objective is to minimize total tardiness costs. A dependent-chance programming (DCP) approach is used for the defuzzification of the proposed model. As the resulted formulation is a NP-hard problem, a branch and bound (B&B) algorithm with effective lower bound is developed. Moreover, a genetic algorithm (GA) is proposed to solve problems of large-sizes. The computational results reveal the high efficiency of the proposed methods, in particular the GA, to solve problems of large sizes.