Four-Day Workweek Scheduling with Two or Three Consecutive Days Off

A four-day workweek days-off scheduling problem is considered. Out of the three days off per week for each employee, either two or three days must be consecutive. An optimization algorithm is presented which starts by utilizing the problem's special structure to determine the minimum workforce size. Subsequently, workers are assigned to different days-off work patterns in order to minimize either the total number or the total cost of the workforce. Different procedures must be followed in assigning days-off patterns, depending on the characteristics of labor demands. In some cases, optimum days-off assignments are determined without requiring mathematical programming. In other cases, a workforce size constraint is added to the integer programming model, greatly improving computational performance.