Parallel machines scheduling with simultaneous considerations of position-dependent deterioration effects and maintenance activities

This article considers identical parallel-machine scheduling problems with simultaneous considerations of position-dependent deterioration effects and maintenance activities. To counteract the deterioration effects on the machines, we assume that each machine must be maintained exactly once during the planning horizon and the maintenance can be scheduled immediately after completing the processing of any job. We further assume that, after the maintenance on a machine, the machine reverts to its initial condition and the deterioration effect starts anew. The objective is to find jointly the optimal maintenance positions and the optimal job sequences to minimize the total machine load. We provide polynomial time solutions for all the problems studied. Furthermore, we also show that the problem under study remains polynomially solvable when each machine is subject to multiple maintenance activities.