Overlapping Start-Time Bands in Implicit Tour Scheduling

Many organizations face personnel scheduling decisions under conditions of variable demand for service across a seven-day planning horizon. These organizations must assign employees to daily shifts that efficiently satisfy the demand for labor, yet allow adequate time for rest between subsequent shifts of an employee's weekly tour schedule. To meet these diverse objectives, managers may permit shifts to begin (and end) in any planning period of the day, but place bands on shift-start times to which individuals may be assigned on each day of their tour schedule. We present a compact integer programming model that implicitly represents start-time band scheduling flexibility. We demonstrate the new model by applying it to requirements for toll collectors on the Illinois Tollway. Problems requiring up to two million variables using a general set covering formulation were represented using the new implicit programming model and often solved to optimality in just a few minutes on a Pentium-based microcomputer. The results indicate that start-time bands can provide an important improvement in scheduling efficiency when compared to the exclusive use of schedules that require workers to begin work on the same hour of the day on each day of their tour.