Makespan minimization for scheduling on two identical parallel machiens with flexible maintenance and nonresumable jobs

Abstract

This paper addresses the problem of scheduling on two identical parallel machines with flexible maintenance and nonresumable jobs; the objective is minimizing the makespan. The properties of the optimal solution of this problem are analyzed. Then, two mixed-integer programming (MIP) models are developed to provide a benchmark for evaluating the effectiveness of the heuristic algorithms presented. Next, three heuristic algorithms and four procedures to improve the quality of the solutions generated by these algorithms are proposed based on the properties of the optimal solution. Finally, the solutions of the heuristic algorithms are compared with those obtained by the MIP models in terms of time and optimality. The results show that the three heuristic algorithms and their improved algorithms can all obtain near-optimal solutions with very little computation time. In particular, the sorting while allocating (SWA) algorithm and its improved algorithms are satisfactory in terms of both solution efficiency and accuracy.