Publication Date


Document Type


Committee Members

Nan Kong (Committee Member), Yan Liu (Committee Member), Pratik Parikh (Committee Member), George Polak (Committee Member), Xinhui Zhang (Advisor)

Degree Name

Doctor of Philosophy (PhD)


Call centers face demand that varies throughout the week across multiple service categories and typically employ non-standard workforce schedules to meet this demand. In call centers, cross-training provides a buffer against fluctuation of demand between categories and is widely used. Full cross-training, however, is financially impractical in most cases, which has created a challenging problem in how to optimize a cross-trained workforce, i.e., a) what categories should be cross-trained, b) what portion of the workforce should be cross-trained, and c) how to schedule their weekly assignments. This problem is motivated by the need of a Fortune 50 company's technology support center to schedule its workforce with multiple service categories. To solve this problem to its fullest extent, a mixed integer programming model that addresses staff assignment composition, shift scheduling, days off assignment, and break assignment across multi-skilled agents is proposed. The model is gigantic in size with thousands of general integer variables and is hard to solve. To improve computational efficiency, a two-phase sequential optimization approach is developed. The first phase is to find the optimal composition of the workforce to decide what categories should be cross-trained and when they should be deployed; the second phase is a staff scheduling model to find the size of the workforce with their skill sets and their shifts and weekly tours. The two-phase approach is an order of magnitude faster than the original model and is able to obtain better solutions orders of magnitude faster. Experimental results with real data from the company clearly demonstrate the significance of cross-training; even partial limited cross-training, where 30% - 40% of the workforce is cross-trained with limited (two out of nine) skills per agent, results in considerable performance improvements. The model, when tested in the strategic analysis of the staff composition, suggested an estimated savings of 4% - 9% on staffing cost with an improved service level. Compared with other flexibility options such as part-time shifts, experiment results seem to suggest that cross-training could be a more effective approach to hedge against demand fluctuations when multiple service categories are involved.

Page Count


Department or Program

Ph.D. in Engineering

Year Degree Awarded


Included in

Engineering Commons