Multi-objective parallel machine scheduling problem with job deterioration and learning effect under fuzzy environment

The current paper investigates a non-identical parallel machine multi-objective scheduling problem in which both the deterioration and learning effects have been considered. Due to uncertainty of the parameters in real-world systems, processing times and due dates of jobs are represented here with triangular fuzzy numbers. Using the credibility measure, a nonlinear mathematical model is provided based on fuzzy chance-constrained programming (FCCP) with the aim to minimize two objective functions, namely total earliness/tardiness (ET) and maximum completion time of jobs (makespan). Since it is a mixed integer nonlinear mathematical model, there is no guarantee that the solution will obtain a global optimum. Therefore, a multi-objective branch and bound algorithm is provided by introducing an effective lower bound in order to obtain a Pareto optimal front. Computational results show that the algorithm proposed is especially useful to solve large-scale problems.