Multi-objective green flowshop scheduling problem under uncertainty: Estimation of distribution algorithm

Abstract Flowshop scheduling is a well-known NP-hard problem. Sustainable scheduling problem has recently attracted the attention of researchers due to the importance of energy and environmental issues. Moreover, considering uncertainty in the real-world manufacturing environment makes the problem more realistic. Insufficient researches on energy issue under uncertainty were encouraging to conduct this study. In this paper, a mathematical formulation and a scenario-based estimation of distribution algorithm (EDA) are proposed to address the flowshop scheduling problem to optimize makespan and energy consumption under uncertainty. To the best of knowledge, scenario-based EDA has not been used to solve this problem. In this study, it is assumed that the processing times are stochastic and follow the normal distribution with known average and variance. In this problem, the machines have different processing speeds and reducing machine speeds increase makespan and decrease energy consumption and conversely. So, machine speeds affect the objective values which are conflicting. The proposed formulation assigns speeds to machines as well as decides about job sequencing. Different scenarios are used to consider stochastic processing times; so, the E-model approach is used for evaluation of objective functions. At the end, the computational experiment is presented and its results show promising performance of EDA in comparison to another algorithm. The proposed algorithm as practical method gives through insight about the problem and because of the suitable number of solutions in the Pareto set, the decision maker has more choice compared to the competing algorithm.