A model proposal for shift scheduling and rostering in call centers based on constraint programming

It may be very difficult to achieve the optimal shift schedule in call centers which have highly uncertain and peaked demand during short time periods. Overlapping shift systems are usually designed for such cases. This paper studies shift scheduling and rostering problems for inbound call centers where overlapping shift systems are used. An integer programming model that determines which shifts to be opened and how many operators to be assigned to these shifts is proposed for the shift scheduling problem. For the rostering problem both integer programming and constraint programming models are developed to determine assignments of operators to all shifts, weekly days-off and meal and relief break times of the operators. The proposed models are tested on real data supplied by an outsource call center and optimal results are found in an acceptable computation time. An improvement of 15% in the objective function compared to the current situation is observed with the proposed model for the shift scheduling problem. The computational performances of the proposed integer and constraint programming models for the rostering problem are compared using real data observed at a call center and simulated test instances. In addition, benchmark instances are used to compare our constraint programming approach with the existing models. The results of the comprehensive computational study indicate that the constraint programming model runs more efficiently than the integer programming model for the rostering problem. In addition, our constraint programming approach has been shown to be sufficiently competitive with other methods in which benchmarking instances are tested. The originality of this research can be attributed to two contributions: (a) a model for shift scheduling problem and two models for rostering problem are presented in detail, compared using real and benchmarking data, (b) the rostering problem is considered as a task-resource allocation and considerably shorter computation times are obtained by modeling this new problem via constraint programming.