Flexible 4-day workweek scheduling with weekend work frequency constraints

A new integer programming model and a two-stage solution method are presented for the flexible 4-day workweek days-off scheduling problem with weekend work frequency constraints. In this problem, employees are given 3 days off per week, out of which either 2 or 3 must be consecutive. Two alternative constraints are imposed to ensure that employees get a sufficient proportion of weekends off. In the first stage, the dual solution is utilized to determine the minimum workforce size. In the second stage, a constraint specifying the minimum workforce size is appended to the IP model, greatly improving computational efficiency. Moreover, multiple-week rotation schedules are generated to ensure that all conditions are satisfied as employees switch from one work pattern to another in successive weeks.