Abstract
We consider in this work a bicriteria scheduling problem on two different parallel machines with a periodic preventive maintenance policy. The two objectives considered involve minimization of job rejection costs and weighted sum of completion times. They are handled through a lexicographic approach, due to a natural hierarchy among the two objectives in the applications considered. The main contributions of this paper are first to present a new problem relevant to practice, second, to develop a mixed-integer-linear-program model for the problem, and third, to introduce two generalizable tabu-search metaheuristics relying on different neighborhood structures and solution spaces. Computational results for 120 instances (generated from a real case) are reported to empirically demonstrate the effectiveness of the proposed metaheuristics.
Highlights
Scheduling problems have been extensively studied in the literature under the assumption that all jobs have to be processed
The contributions of this paper are the following: (1) we propose a new problem relevant to practice; (2) we formulate the problem with a Mixed Integer Linear Program (MILP); (3) a diversified panel of solutions methods is proposed, namely a greedy constructive procedure, two tabu-search approaches relying on various neighborhood structures and different solution spaces, and a baseline local-search heuristic aimed at representing a current-practice rule
For each value of n and each objective function fi (i ∈ {1, 2}), we report the following information: the average value of fi obtained by Tabu Search with Multiple Neighborhoods (TSMN), the augmentation percentage (Gap(%)) of fi if TSMN is performed without Phase 2, and the augmentation percentage of fi if TSMN is performed without Phase 3
Summary
Scheduling problems have been extensively studied in the literature under the assumption that all jobs have to be processed. Journal of Scheduling tion is expected to be more efficient and revenues to increase when PM is well managed In this regard, we address a scheduling problem (P) with two different parallel machines (it is formally a 2-Parallel Machines problem with Periodic Maintenance, Job Rejection and Weighted sum of Completion Times). The first one is the total cost of rejected jobs, and the second one is the weighted sum of job completion times In the former case, jobs are rejected when the capacity of both machines is reached.
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