Unrelated parallel machine scheduling models with machine availability and eligibility constraints

In this paper, we address the unrelated parallel machine scheduling problem with calendar, which consists of a generic intermittent availability scheme with non-regular active and inactive time windows in sequence. The problem additionally considers machine eligibility and release date constraints, as well as the possibility of pausing or not the processing of the jobs between successive active time windows. This problem is quite frequent and relevant in several practical settings in which it is necessary to schedule parallel resources with different calendars, such as different weekly and daily shifts, non-regular not worked days, holidays, and preventive maintenance periods, among others, while considering the resources eligibility. We present novel mixed integer linear programming models for this problem with the aim of minimizing the makespan. Basic formulations of these models are presented as well as tight lower bounds for the objective, including enhanced formulations. To the best of our knowledge, there are no other works that tackled this problem and that proposed optimization models with the level of detail and generality here considered. The models presented are evaluated using a state-of-the-art general-purpose solver, and the computational tests are performed on a variety of instances. The results validate the models and show that they are can handle instances in realistic situations where the problem occurs. The results also show that the enhanced formulations are able to find several optimal solutions, and that within acceptable computational times they are able to sharply reduce the optimality gaps when compared to the more basic formulations.