Implicit optimal tour scheduling with flexible break assignments

In service organizations, customer demand varies over the course of an operating day and across the days of an operating week. These organizations must assign employees to weekly tour schedules in an attempt to satisfy the fluctuating customer demand. The tour-scheduling problem has been traditionally formulated by the set-covering approach. However, this approach requires a separate integer variable for each variation in the tour schedule due to different work days and different shift and break start times on these days, and this explicit representation results in an enormously large number of decision variables. In this paper, an implicit integer-programming model is presented, which combines daily shift assignments and alternate day-on patterns and also schedules break periods for shifts within the specified break windows. The implicit form of the model requires very few integer variables compared to the set-covering approach.