OVERLAPPING START-TIME BANDS IN IMPLICIT TOUR SCHEDULING

Many organizations face personnel scheduling decisions under condition s of variable demand for service across a seven-day planning horizon. These organizations must assign employees to daily shifts that efficie ntly satisfy the demand for labor, yet allow adequate time for rest be tween subsequent shifts of an employee's weekly tour schedule. To meet these diverse objectives, managers may permit shifts to begin (and en d) in any planning period of the day, but place bands on shift-start t imes to which individuals may be assigned on each day of their tour sc hedule. 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 I llinois Tollway. Problems requiring up to two million variables using a general set covering formulation were represented using the new impl icit programming model and often solved to optimality in just a few mi nutes on a Pentium-based microcomputer. The results indicate that star t-time bands can provide an important improvement in scheduling effici ency when compared to the exclusive use of schedules that require work ers to begin work on the same hour of the day on each day of their tou r.