Integrated planning of maintenance operations and workload allocation

Motivated by a practical problem, this paper investigates the integrated planning of maintenance operations and workload allocation on a set of machines in a workshop. Given quantities of products to be produced per period on a planning horizon must be processed on unrelated flexible machines. Moreover, each machine has to undergo one or more maintenance operations that must be planned within a given time window and impact products differently. The main goal is to find a feasible plan that satisfies the machine capacity by allocating the production quantities to machines and assigning maintenance operations as late as possible in their time windows. Various original mathematical models are presented. In particular, we propose models that allow maintenance operations and some production quantities to overlap two consecutive periods. Computational experiments based on industrial data show that allowing this overlapping helps the earliness of maintenance operations to be significantly reduced in the most difficult instances, going for example from a total of 14 periods to only 1 period, and by more than 35% on average.