Scheduling Jobs with Maintenance Subject to Load-Dependent Duration on a Single Machine

This paper investigates a scheduling problem on a single machine with maintenance, in which the starting time of the maintenance is given in advance but its duration depends on the load of the machine before the maintenance. The goal is to minimize the makespan. We formulate it as an integer programming model and show that it is NP-hard in the ordinary sense. Then, we propose an FPTAS and point out that a special case is polynomial solvable. Finally, we design fast heuristic algorithms to solve the scheduling problem. Numerical experiments are implemented to evaluate the performance of the proposed heuristic algorithms. The results show the proposed heuristic algorithms are effective.