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A graph-based formulation for the shift rostering problem

A graph-based formulation for the shift rostering problem
A graph-based formulation for the shift rostering problem

This paper investigates a shift rostering problem – the assignment of staff to shifts over a planning horizon such that work rules are observed. Traditional integer-programming models are not able to solve shift rostering problems effectively for large number of staff and feasible shift patterns. We formulate work rules in terms of newly-proposed prohibited meta-sequences and resource constraints. A graph-based formulation and a specialized graph construction algorithm are proposed where the set of feasible shift patterns is represented by paths of a graph. The formulation size depends on the structure of the work-rule constraints and is independent of the number of staff. This approach results in smaller networks allowing large-scale rostering problems with hard constraints to be solved efficiently using standard commercial solvers. Moreover, it allows finding multiple optimal solutions which are beneficial for managerial decision makers. Computational results show that the proposed approach can obtain new best-known solutions and identify proven optimal solutions for almost all NSPLIB instances at significantly lower CPU times.

0377-2217
285-300
Lai, David S.W.
9e095afb-da7c-42e3-9e3e-a609bf12da57
Leung, Janny M.Y.
f37e71c0-e2fc-4f2c-9dd5-bb897b1311da
Dullaert, Wout
315bc5f3-4982-42d7-a659-2bf8e910b7ba
Marques, Inês
b106969d-8638-4e26-9166-3c5652e3b90e
Lai, David S.W.
9e095afb-da7c-42e3-9e3e-a609bf12da57
Leung, Janny M.Y.
f37e71c0-e2fc-4f2c-9dd5-bb897b1311da
Dullaert, Wout
315bc5f3-4982-42d7-a659-2bf8e910b7ba
Marques, Inês
b106969d-8638-4e26-9166-3c5652e3b90e

Lai, David S.W., Leung, Janny M.Y., Dullaert, Wout and Marques, Inês (2020) A graph-based formulation for the shift rostering problem. European Journal of Operational Research, 284 (1), 285-300. (doi:10.1016/j.ejor.2019.12.019).

Record type: Article

Abstract

This paper investigates a shift rostering problem – the assignment of staff to shifts over a planning horizon such that work rules are observed. Traditional integer-programming models are not able to solve shift rostering problems effectively for large number of staff and feasible shift patterns. We formulate work rules in terms of newly-proposed prohibited meta-sequences and resource constraints. A graph-based formulation and a specialized graph construction algorithm are proposed where the set of feasible shift patterns is represented by paths of a graph. The formulation size depends on the structure of the work-rule constraints and is independent of the number of staff. This approach results in smaller networks allowing large-scale rostering problems with hard constraints to be solved efficiently using standard commercial solvers. Moreover, it allows finding multiple optimal solutions which are beneficial for managerial decision makers. Computational results show that the proposed approach can obtain new best-known solutions and identify proven optimal solutions for almost all NSPLIB instances at significantly lower CPU times.

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More information

Accepted/In Press date: 11 December 2019
e-pub ahead of print date: 16 December 2019
Published date: 1 July 2020

Identifiers

Local EPrints ID: 457647
URI: http://eprints.soton.ac.uk/id/eprint/457647
ISSN: 0377-2217
PURE UUID: d3a885a1-b1e3-4ba9-9219-f96968a031f6
ORCID for David S.W. Lai: ORCID iD orcid.org/0000-0002-9989-1485

Catalogue record

Date deposited: 14 Jun 2022 16:56
Last modified: 23 Jul 2022 02:32

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Contributors

Author: David S.W. Lai ORCID iD
Author: Janny M.Y. Leung
Author: Wout Dullaert
Author: Inês Marques

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