Uniform Parallel Machines Scheduling with Setup Time, Learning Effect, Machine Idle Time, and Processing Set Restrictions to Minimize Earliness/Tardiness Costs

Abstract

Inspired by a real industrial case, this study deals with the problem of scheduling jobs on uniform parallel machines with past-sequence-dependent setup times to minimize the total earliness and tardiness costs. The paper contributes to the existing literature of uniform parallel machines problems by the novel idea of considering position-based learning effects along with processing set restrictions. The presented problem is formulated as a Mixed Integer linear programming (MILP) model. Then, an exact method is introduced to calculate the accurate objective function in the just-in-time (JIT) environments for a given sequence of jobs. Furthermore, three meta-heuristic approaches, (1) a genetic algorithm (GA), (2) a simulated annealing algorithm (SA), and (3) a particle swarm optimization algorithm (PSO) are proposed to solve large size problems in reasonable computational time. Finally, computational results of the proposed meta-heuristic algorithms are evaluated through extensive experiments and tested using ANOVA followed by t-tests to identify the most effective meta-heuristic.