On The Capacitated Scheduling Problem with Conflict Jobs

The paper is concerned with scheduling jobs on parallel identical machines under the restrictions imposed by a conflict graph. The nodes of this conflict graph represent jobs and each edge indicates that the jobs associated with the nodes, incident to this edge, can not be processed concurrently. The jobs have a common due date and each job has the associated weight. The goal is to maximise the total weight of jobs which completion times do not exceed the due date. The considered scheduling model was motivated by the problem arising in the telecommunication industry. The paper identifies polynomially solvable and NP-hard particular cases and presents two mixed integer linear programming formulations together with their comparison by means of computational experiments.