Optimal selection of contracts and work shifts in multi-skill call centers

Abstract

This paper deals with the problem of finding the most suitable contracts to be used when hiring the operators of a call center and deciding their optimal working schedule, to optimize the trade-off between the service level provided to the customers and the cost of the personnel. In a previous paper (Cordone et al. 2011), we proposed a heuristic method to quickly build an integer solution from the solution of the continuous relaxation of an integer linear programming model. In this paper, we generalize that model to take into account a much wider class of working contracts, allowing heterogeneous shift patterns, as well as legal constraints related to continuously active working environments. Since our original rounding heuristic cannot be extended to the new model, due to its huge size and to the involved correlations between different sets of integer variables, we introduce a more sophisticated heuristic based on decomposition and on a multi-level iterative structure. We compare the results of this heuristic with those of a Greedy Randomized Adaptive Search Procedure, both on real-world instances and on realistic random instances.

Keywords

• Workforce management
• Call center optimization
• Integer linear programming
• GRASP