This paper is concerned with the problem of determining the optimal size and composition of a permanent workforce needed to run a facility when demand is specified by a workstation group (WSG) for up to 24 hours a day, 7 days a week. For full-time employees, a solution is characterized by a bid job, which consists of a five-day-a-week schedule, a lunch break for all shifts, and a set of WSG task assignments for each of the half-hour periods in a shift. In contrast, each part-time employee may be given anywhere from one to six shifts during the week, and each shift may vary from four to eight hours in length. To facilitate supervision, all employees must be assigned to a home WSG, but when idle time exists in their schedules, they can be redeployed to other WSGs for a portion of the day.
One of the complicating and unique factors addressed in this paper is the existence of nonsymmetric movement restrictions between WSGs. For example, an employee whose home base is A may be permitted to perform tasks at B, but not vice versa. Because the full problem could not be reduced to a single model, a multistage solution approach was developed. In the first stage, an extended shift-scheduling problem is solved to determine the optimal number of employees and their shifts. The results are postprocessed in subsequent stages to obtain lunch breaks, days off, and task assignments under WSG movement restrictions.
In the implementation of the multistage approach, two alternatives were explored. The first was based on the idea of partitioning the WSGs into manageable clusters and then solving them in series. The second involved the direct solution of an integer programming formulation of the task assignment problem with home-base restrictions and WSG movement restrictions, but for a fixed workforce. An iterative scheme was used to adjust the size of the workforce until all constraints were satisfied and overall optimality was achieved. Testing was done with data provided by the U.S. Postal Service (USPS) mail processing and distribution center (P&DC) in Dallas. The computations showed that the second alternative always yielded the smaller workforce and was always able to find good solutions within 30 minutes.
