Title: Flexible shift scheduling for a call centre using column generation

Authors: Carlos Campos Amezcua; Omar G. Rojas; Emilio Zamudio Gutierrez; Elias Olivares-Benitez

Addresses: Facultad de Ingeniería, Universidad Panamericana, Prolongación Calzada Circunvalación Poniente 49, 45010 Zapopan, Jalisco, Mexico ' Escuela de Ciencias Económicas y Empresariales, Universidad Panamericana, Prolongación Calzada Circunvalación Poniente 49, Zapopan, Jalisco, 45010, México ' Facultad de Ingeniería, Universidad Panamericana, Prolongación Calzada Circunvalación Poniente 49, Zapopan, Jalisco, 45010, México ' Facultad de Ingeniería, Universidad Panamericana, Prolongación Calzada Circunvalación Poniente 49, Zapopan, Jalisco, 45010, México

Abstract: A shift scheduling problem for a call centre is solved by applying a column generation method. The objective is to find an employee schedule within the planning horizon that meets staffing requirements provided by the customer and that minimises the costs of excess-staffing and under-staffing. To solve the problem, two iterative models were used: the first being a mixed integer-linear programming model, the master problem, and the second being a column generation model. In a first approach, the master problem was solved considering a fixed number of shift patterns. The second approach was to use both models iteratively to generate shift patterns to be used in the master problem. Both approaches met all constraints relatively fast, but the column generation model decreased the cost considerably when cheaper shift patterns were generated. The models contribute to the current literature by providing flexibility to consider under-coverage and over-coverage at two levels.

Keywords: shift scheduling; call centre; staffing; mixed integer linear programming; master problem; column generation; shift pattern; flexibility.

DOI: 10.1504/IJOR.2021.114836

International Journal of Operational Research, 2021 Vol.40 No.4, pp.502 - 523

Received: 24 Jul 2017
Accepted: 06 Jul 2018

Published online: 29 Apr 2021 *

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