Accounting for time-varying queueing effects in workforce scheduling

We developed a method for workforce scheduling that models both the structure of the set of permissible shifts, and the stochastic and time-varying demand process. A prototype implementation uses a genetic algorithm to search for good schedules, and evaluates the service level resulting from a schedule by numerically solving the equations of motion for a time-varying queueing system. Comparison with a traditional approach using a ‘stationary independent period-by-period’ (SIPP) assumption to set staffing requirements and an integer program (IP) to choose shifts indicates that the traditional approach can significantly overestimate the service level that results from a schedule. Further, our method sometimes generates schedules that result in both lower labor cost and higher service level than those found with the SIPP–IP approach. An additional benefit of our method is its applicability in ‘rush hour’ situations where the arrival rate to the system temporarily exceeds its capacity to serve customers.