Equipment scheduling at mail processing and distribution centers

Mail Processing and Distribution Centers (P&DCs) run 24 hours a day, 7 days a week and are staffed by a skilled complement of full-time, part-time, and temporary employees. A recurrent problem faced by facility managers involves the development of daily schedules for the automation equipment used to process the mail. The ultimate goal is to minimize the labor costs associated with running the facility while ensuring that all service standards are met. The focus of this paper is on the equipment scheduling aspect of the problem. In particular, we seek a weekly schedule that satisfies all operational, technological, and legal constraints of the system at a minimum cost. The problem is modeled as a large-scale mixed-integer linear program and solved sequentially using a three-stage methodology. In each stage, a separate criterion is optimized and the corresponding objective function value is used as a constraint in subsequent stages. To ease the computational burden, two major enhancements are developed. The first is a pre-processor designed to reduce the number of integer variables; the second is a heuristic that uses the linear programming solution as a target and attempts to find a feasible integer point as close to it as possible. The methodology is demonstrated with data obtained from the Dallas P&DC. The computations indicate that for letter operations alone the annual savings will be on the order of $1.6 million per facility when the system is implemented nationwide over the next 3 years.