A single-machine scheduling problem with multiple unavailability constraints: A mathematical model and an enhanced variable neighborhood search approach

•A scheduling problem with multiple unavailability is proposed and formulated.•A knowledge-based variable neighborhood search algorithm is proposed.•Extensive computational tests confirm the good capability of the proposed model and algorithm.

This research focuses on a scheduling problem with multiple unavailability periods and distinct due dates. The objective is to minimize the sum of maximum earliness and tardiness of jobs. In order to optimize the problem exactly a mathematical model is proposed. However due to computational difficulties for large instances of the considered problem a modified variable neighborhood search (VNS) is developed. In basic VNS, the searching process to achieve to global optimum or near global optimum solution is totally random, and it is known as one of the weaknesses of this algorithm. To tackle this weakness, a VNS algorithm is combined with a knowledge module. In the proposed VNS, knowledge module extracts the knowledge of good solution and save them in memory and feed it back to the algorithm during the search process. Computational results show that the proposed algorithm is efficient and effective.

Graphical abstract