An exact algorithm for a workforce allocation problem with application to an analysis of cross-training policies

The evaluation of workforce staffing and scheduling policies is of paramount importance for meeting the challenge of simultaneously providing good customer service and low operational costs. Policy studies are particularly critical in workforce environments plagued by staffing shortages. The cross-utilization of employees among different departments or work centers is a well-recognized staffing policy for coping with shortages. We revisit a non-linear assignment problem for allocating cross-trained workers so as to maximize overall utility, which is measured using a quadratic function of labor shortages. We develop a branch-and-bound algorithm that efficiently provides optimal solutions for problems of practical size. This algorithm is then used to conduct a computational investigation of cross-training policies. Among the most critical factors affecting utility improvement are the coefficient of variation for demand, worker absenteeism, the percentage of cross-trained workers and cross-training breadth. Several important interactions among these and other factors are also identified.