Modeling and Solving Scheduling Problem with m Uniform Parallel Machines Subject to Unavailability Constraints

The problem investigated in this paper is scheduling on uniform parallel machines, taking into account that machines can be periodically unavailable during the planning horizon. The objective is to determine planning for job processing so that the makespan is minimal. The problem is known to be NP-hard. A new quadratic model was developed. Because of the limitation of the aforementioned model in terms of problem sizes, a novel algorithm was developed to tackle big-sized instances. This consists of mainly two phases. The first phase generates schedules using a modified Largest Processing Time (LPT)-based procedure. Then, theses schedules are subject to further improvement during the second phase. This improvement is obtained by simultaneously applying pairwise job interchanges between machines. The proposed algorithm and the quadratic model were implemented and tested on variously sized problems. Computational results showed that the developed quadratic model could optimally solve small- to medium-sized problem instances. However, the proposed algorithm was able to optimally solve large-sized problems in a reasonable time.