The Capacitated Scheduling Problem with Conflicts Jobs (CSPCJ) requires to find a feasible schedule, on a set of parallel identical machine without preemption, that maximizes the total weighted value of jobs completed before a common deadline. The schedule is subject to conflict constraints limiting the set of jobs that can be processed concurrently. In this work we present a new arc-flow inspired mathematical formulation and a three-step heuristic algorithm combining randomization, greedy construction and local search improvement for the CSPCJ. The effectiveness of our approaches is tested through extensive computational experiments. The results demonstrate that our formulation outperforms existing models proposed in the literature and that our simple heuristic algorithm is able to find very good solutions in limited computational time.
Keywords: Scheduling, Parallel Machines, Conflicts, Arc-flowScheduled
TD1 Scheduling 3
June 10, 2021 2:45 PM
1 - GB Dantzig