The task assignment problem for unrestricted movement between workstation groups

The purpose of this paper is to investigate the problem of assigning tasks to workers during their daily shifts. For a homogeneous workforce, a given set of workstation groups, and a corresponding demand for labor, the objective is to develop a disaggregated schedule for each worker that minimizes the weighted sum of transitions between workstation groups. In the formulation of the problem, each day is divided into 48 1/2-hour time periods and a multi-commodity network is constructed in which each worker corresponds to a unique commodity and each node represents a workstation group–time period combination. Lunch breaks and idle time are also included in the model. Initial attempts to solve large instances with a commercial code indicated a need for a more practical approach. This led to the development of a reduced network representation in which idle periods are treated implicitly, and a sequential methodology in which the week is decomposed into 7 daily problems and each solved in turn. To gain more computational efficiency, a tabu search procedure was also developed. All procedures were tested using data obtained from a U.S. Postal Service mail processing and distribution center. Depending on the labor category, anywhere from 3 to 28 workstation groups and up to 311 full-time and part-time workers had to be scheduled together. The results were mixed. While small problems could be solved to near-optimality with the integer programming approaches, tabu search was the best alternative for the very large instances. However, the excessive number of swaps needed to gain marginal improvements, undermined its effectiveness. Combining the two provided a good balance in most cases.