Staff scheduling at the United States Postal Service

The purpose of this paper is to present a full-scale model of the tour scheduling problem as it arises in the United States Postal Service, and to examine several scenarios aimed at reducing the size of the workforce. The problem is formulated as a pure integer linear program and solved with CPLEX. The baseline model includes both full-time and part-time workers, as well as the principal constraints defined by the union contract. The scenarios include requirements for two days off in a row, variable daily start times, the use of part-time flexible workers, and a parametric analysis of full-time to part-time restrictions. The results indicate that problem instances of realistic size can be solved within 1 h , and that measurable savings can be achieved by departing from current practice. Effective personnel scheduling has become one of the primary means by which service entities remain competitive. Unlike manufacturing, where standard shifts and days off are the rule, the service industry often operates 24 h a day, 7 days a week and faces widely fluctuating demand. Poor personnel schedules can lead to an oversupply of workers with too much idle time, or an undersupply with an attendant loss of business. In this paper, we present an integrated model that can be used to find optimal schedules for a homogeneous workforce. The objective is to meet daily staffing requirements at minimum cost without violating labor agreements and government regulations. The approach requires the solution of a large-scale integer linear program to determine general staffing needs for both full-time and part-time employees. Weekly tours are then constructed, and each employee is assigned a lunch break. Extensions to the model include different days off policies, variable start times, and the use of part-time flexible workers. Test data were provided by the United States Postal Service for one of their processing and distribution centers. The main conclusions of the study are that problems of realistic size can be solved quickly, and that substantial savings can be achieved by considering less restrictive policies. While the latter is not surprising, many organizations adopt costly practices, such as providing weekly schedules with the same start times every day for each employee, without fully realizing their implications.