A robust optimization method for hybrid flow shop scheduling with uncertain setup times

Abstract

This research focuses on modeling and solving a bi-objective hybrid flow shop scheduling problem, considering uncertain job-dependent setup times and worker constraints. The main objective of the mathematical model is to simultaneously minimize the Maximum Completion Time (Cmax) and minimize the total tardiness. To achieve both objective functions simultaneously, various decisions are made, including scheduling the processing of jobs in each stage, assigning jobs to machines, and assigning workers in each stage. Uncertainty in the job-dependent setup time leads to the use of a robust-box optimization method to control this parameter. In addition, this paper proposes four algorithms, Non-dominated Sorting Genetic Algorithm II (NSGA-II), Multi Objective Particle Swarm Optimization (MOPSO), Multi-Objective Grey Wolf Optimizer (MOGWO), and Multi-Objective Flow Direction Algorithm (MOFDA), to solve the problem. The results of solving the problem on 15 sample problems show that decreasing the total tardiness value increases the Cmax value. This is due to changes in the scheduling of job processing by machines and workers in different stages. Also, by comparing the efficient solutions obtained from different algorithms and examining the indices, it was observed that the MOFDA has higher efficiency in obtaining the Number of Pareto Front (NPF) and Maximum spread Index (MSI) indices. However, the Computational time (CPT) and Space Metric (SM) indices in this algorithm was higher compared to other algorithms. Also, the quality of the solutions obtained from this algorithm was higher compared to other algorithms and was selected as the more efficient algorithm. By examining the uncertainty rate in the job-dependent setup time analysis, it was observed that increasing this rate increases the Cmax and total tardiness values. So that, increasing the uncertainty rate from 0.5 to 0.9 leads to an 8.36% increase in the Cmax value and a 15.81% increase in the total tardiness value. The results of this model can help managers in appropriate scheduling of job processing in production units.