Scheduling on uniform parallel machines with periodic unavailability constraints

Scheduling problems under unavailability constraints has become a popular research topic in the last few years. Despite it’s important application in the real world, the uniform parallel machine scheduling problem was the least studied due to its complexity. In this paper, we investigated the uniform parallel machine scheduling problem under deterministic availability constraints. Each machine is subject to one unavailability period. Different versions of the problem regarding the type of jobs (identical and non-identical) and the performance measures (the total completion times and the makespan) were studied. For the case of identical jobs and for both performance measures, we developed linear programming models and optimal algorithms to provide a solution to the problem. For the case of non-identical jobs, we proved that the problem is NP-hard and propose a quadratic program. Because, this later cannot solve problems with very large number of jobs and machines, a heuristic was developed to find near optimal solutions to the problem especially with very large number of jobs and machines. The computational results showed that the heuristic’s performance is very high regardless the dimensions of problem instances.