A matheuristic based on Lagrangian relaxation for the multi-activity shift scheduling problem

Noberto A. Hernández-Leandro, Vincent Boyer, M. Angélica Salazar-Aguilar and Louis-Martin Rousseau

European Journal of Operational Research, 2019, vol. 272, issue 3, 859-867

Abstract: The multi-activity shift scheduling problem involves assigning a sequence of activities to a set of employees. In this paper, we consider the variant where the employees have different qualifications and each activity must be performed in a specified time window; i.e., we specify the earliest start period and the latest finish period. We propose a matheuristic in which Lagrangian relaxation is used to identify a subset of promising shifts, and a restricted set covering problem is solved to find a feasible solution. Each shift is represented by a context-free grammar. Computational tests are carried out on two sets of instances from the literature. For the first set, the matheuristic finds a solution with an optimality gap less than 0.01% for 70% of the instances and improves the best-known solution for 16% of them; for the second set, the matheuristic reaches the best-known solutions for 55% of the instances and finds better solutions for 37.5% of them.

Keywords: Scheduling; Shift scheduling problem; Context-free grammar; Lagrangian relaxation; Matheuristic (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:272:y:2019:i:3:p:859-867

DOI: 10.1016/j.ejor.2018.07.010

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