Two-machine scheduling with aging effects and variable maintenance activities

This paper presents models and solution algorithms for a two-machine scheduling problem with position-dependent job processing times subject to both aging and maintenance effects. Aiming to minimize the overall makespan for two identical parallel machines, two cases are analyzed. In the first case, no maintenance is scheduled. In the second case, maintenance is scheduled within the job processing sequence, restoring the machine to as-new condition. Assuming the number and the positions of maintenance stops to be variable, machine maintenance and job processing are scheduled simultaneously. Integer linear programming (ILP) models are formulated to determine the optimal maintenance and job processing sequence on each machine. To solve large-size problems, six heuristic solution methods are developed and compared. The maximum delay penalty (MDP) heuristic is best for the no-maintenance case, while the variable neighborhood search (VNS) metaheuristic is best for the with-maintenance case. Both methods quickly produce near-optimal solutions for large-size problems.