Compressed workweek scheduling with days-off consecutivity, weekend-off frequency, and work stretch constraints

This paper presents a three-day workweek scheduling problem with four types of days-off scheduling constraints: (1) out of the four off days given to each employee per week, at least two must be consecutive, (2) two alternative types of constraints are imposed to ensure that employees get a sufficient proportion of weekends off, (3) the maximum work stretch is four consecutive workdays for each employee, and (4) the maximum number of successive weeks with weekend work is specified. A mathematical model of this problem is formulated and efficiently solved by introducing a bound on workforce size. First, the problem structure is used to determine the minimum workforce size. Subsequently, a workforce-size constraint is added to the integer programming model in order to facilitate solution. Finally, multiple-week rotation schedules are produced to satisfy all constraints and limit or minimize the number of successive weeks with weekend work.