Solving a single-machine scheduling problem with maintenance, job deterioration and learning effect by simulated annealing

This paper presents a new nonlinear multi-objective mathematical model for a single-machine scheduling problem with three objectives: (1) minimizing the sum of the weighted jobs completion, (2) minimizing the sum of the weighted delay times, and (3) maximizing the sum of the job values in makespan. In addition, a number of constraints are incorporated in this presented model, such as repairing and maintenance periods, deterioration of jobs, and learning effect of the work process. Since this type of scheduling problem belongs to a class of NP-hard ones, its solution by common software packages is almost impossible, or at best very time consuming. Thus, a meta-heuristic algorithm based on simulated annealing (SA) is proposed to solve such a hard problem. At a final stage, the related results obtained by the proposed SA are compared with those results reported by the Lingo 8 software in order to demonstrate the efficiency and capability of our proposed SA algorithm.