Mathematical models and solution approach for cross-training staff scheduling at call centers

Abstract

Call centers face demand variations over time across multiple service categories and typically employ a cross-trained workforce with flexible schedules to hedge against these fluctuations. In practice, it is often impossible to cross-train agents in each category, thus partial and limited cross-training are the norm. This adds another layer of complexity to determine the optimal mix of cross-trained workforce (on top of the shift and tour schedules) and has created a challenging problem in the optimization of staff schedules.To solve this problem to its fullest extent, an integer program that addresses cross-training, shift schedule, days off and break assignments across multiple service categories is proposed. The model is hard to solve and a two-phase sequential approach is developed. The first phase is to find the optimal mix of the workforce, i.e., the categories to be cross-trained and the time periods in which they are to be deployed; the second phase is a smaller staff scheduling model to find the composition of the workforce and to construct their weekly tours. For all the test cases, which are of practical sizes, the two-phase sequential approach provided better solutions than the solution of the original model with a state-of-the-art commercial solver subject to imposed time limits.Experimental results with data from a call center with nine categories clearly demonstrate the significance of cross-training. In fact, partial limited cross-training, where 30% of staff is cross-trained with two skills or 10% of staff is cross-trained with three skills, could result in considerable cost savings; however, these savings could diminish quickly with the increase of efficiency loss in secondary skills. Experiments also suggest that cross-training could be a more effective approach than part-time shifts to hedge against fluctuations across service categories.