A mathematical model for unrelated parallel-machine scheduling with two competing agents and a fixed non-availability interval

Competitive multi-agent scheduling has attracted growing attention recently. In this paper, two-agent scheduling problem on unrelated parallel-machine involving setup and release date considerations is studied. We also consider a fixed non-availability interval for this scheduling problem so that no machine can process jobs in a specified non-availability interval. Each agent has its own set of jobs and objective function, but both share the same processor. A mixed integer programming model is proposed and its goal is to minimize the maximum completion time of jobs from the first agent subject to a constraint that the other agent’s maximum completion time cannot exceed a prescribed upper bound. Finally, numerical studies are performed using GAMS to examine the effectiveness and the efficiency of the proposed model. Also, an upper bound is developed to increase the efficiency of the model.

Keywords:

Scheduling , Two agents , Unrelated parallel machines , Sequence-dependent setup , Machine non-availability