Article

Journal of Scheduling

, Volume 17, Issue 2, pp 185-197

First online:

A branch-and-price algorithm for the multi-activity multi-task shift scheduling problem

  • Vincent BoyerAffiliated withCentre interuniversitaire de recherche sur les réseaux d’Entreprise, la logistique et le transport, Université de MontréalGraduate Program in Systems Engineering, Universidad Autónoma de Nuevo León (UANL) Email author 
  • , Bernard GendronAffiliated withCentre interuniversitaire de recherche sur les réseaux d’Entreprise, la logistique et le transport, Université de Montréal
  • , Louis-Martin RousseauAffiliated withCentre interuniversitaire de recherche sur les réseaux d’Entreprise, la logistique et le transport, Université de Montréal

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Abstract

The multi-activity multi-task shift scheduling problem requires the assignment of interruptible activities and uninterruptible tasks to a set of employees in order to satisfy a demand function. In this paper, we consider the personalized variant of the problem where the employees have different qualifications, preferences, and availabilities. We present a branch-and-price algorithm to solve this problem. The pricing subproblems in column generation are formulated with context-free grammars that are able to model complex rules in the construction of feasible shifts for an employee. We present results for a large set of instances inspired by real cases and show that this approach is sufficiently flexible to handle different classes of problems.

Keywords

Multi-activity multi-task shift scheduling problem Precedence constraints Branch-and-price Context-free grammar