Title: Shift scheduling and rostering with same shift-type and weekend-off fairness constraints in call centres

Authors: Ruicheng Wang; Yue Xu; Xiuli Wang

Addresses: School of Economics and Management, Nanjing University of Science and Technology, Nanjing, China ' School of Architectural Science and Engineering, Yangzhou University, Yangzhou, China ' School of Economics and Management, Nanjing University of Science and Technology, Nanjing, China

Abstract: Based on the actual operational situation of call centres, this paper incorporates the constraints of the same shift-type within a week and the fairness of weekends-off into scheduling. Utilising the progressive decomposition structure of the same shift-type constraint, this paper constructs an integer programming model for multi-week scheduling optimisation problem of call centre agents. We first analyse the maximum lower bound of the problem and prove the optimality of its relaxation problem. Then we propose a two-stage algorithm which combines a constructive heuristic with neighbourhood search incorporating simulated annealing. Experimental results show that the integer programming model is only suitable for achieving optimal solutions for small-scale problems, while our two-stage algorithm can obtain (sub-)optimal solutions for large-scale problems. The impact of employment policy on labour costs is also discussed. [Received: 21 March 2023; Accepted: 12 November 2023]

Keywords: call centre; shift scheduling; rostering; integer programming; optimal algorithm; heuristic algorithm; neighbourhood search; weekend-off fairness; same shift-type; operations management.

DOI: 10.1504/EJIE.2025.145292

European Journal of Industrial Engineering, 2025 Vol.19 No.3, pp.340 - 373

Received: 21 Mar 2023
Accepted: 12 Nov 2023
Published online: 31 Mar 2025 *

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