Personnel tour scheduling when starting-time restrictions are present

This paper presents an effective solution strategy for an important category of personnel scheduling problems. Specifically, we address the restricted starting-time tour-scheduling problem (RSTP), which involves the determination of the hours of the day (shifts) and days of the week (days on) that employees are assigned to work. RSTP is characterized by restrictions on the number of daily time periods in which employees may begin their shifts. Moreover, the RSTP we consider contains constraints that require separation of starting times. Such restrictions are widely encountered in practice and are based on a number of factors including managerial concerns for control of employee movements, union contractual obligations, and employee preferences for common shift starting times. A two-stage heuristic solution strategy is proposed for RSTP. We developed eight heuristic procedures based on this strategy and applied them to four sets of labor requirements, for each of 27 United Airlines (UA) airport ground stations. One of the best of these procedures yielded solution costs that averaged only 1.36 full-time-equivalent employees above very conservative LP-based lower bounds. Moreover, the solution costs obtained using this procedure were, on average, 28 percent closer to the lower bounds than solution costs obtained using UA's current scheduling system. We conclude that the two-stage heuristic solution strategy is a valuable platform from which to develop procedures for generating near-optimal solutions to this difficult class of personnel scheduling problems.