Service completion estimates for cross-trained workforce schedules under uncertain attendance and demand

Although cross-trained workers offer numerous operational advantages for extended-hour service businesses, they must first be scheduled for duty. The outcome from those decisions, usually made a week or more in advance, varies with realized service demand, worker attendance, and the way available cross-trained workers are deployed once the demands for service are known. By ignoring the joint variability of attendance and demand, we show that existing workforce scheduling models tend to overstate expected schedule performance and systematically undervalue the benefits of cross-training. We propose a two-stage stochastic program for profit-oriented cross-trained workforce scheduling and allocation decisions that is driven by service completion estimates obtained from the convolution of the employee attendance and service demand distributions. Those estimates, reflecting optimal worker allocation decisions over all plausible realizations of attendance and demand, provide the gradient information used to guide workforce scheduling decisions. Comparing the performance of workforce scheduling decisions for hundreds of different hypothetical service environments, we find that solutions based on convolution estimates are more profitable, favor proportionately more cross-trained workers and fewer specialists, and tend to recommend significantly larger (smaller) staffing levels for services under high (low) contribution margins than workforce schedules developed with independent expectations of attendance and demand.