Staff Scheduling with Day-Off and Workstretch Constraints

A set-processing algorithm for scheduling staff on 4-day or 3-day work weeks

“…Burns and Carter [5] use an iterative approach to deal with a situation where the employee requirement varies for each day of the week, each employee gets exactly 2 days off in a week, receives at least A out of every B weekends off, and has a maximum work stretch of 6 days. Their research generalizes the works of Brownell and Lowerre [3], Lowerre [10], Baker and Magazine [1], Burns [4], and Baker, Burns, and Carter [2]. Iterative scheduling algorithms differ from cyclic scheduling algorithms in that the long-run schedules experienced by individual workers need not be identical.…”

“…R3: The first day off for a T 3 employee may be shifted right with any compensatory leftward shift, provided that the first day off for all T 3 employees occurs more than 1 day earlier in the week than the last days off for all T 2 and T 4 employees [X 3 (1) shifted right with any compensatory leftward shift, provided that Max{X 3 (1)} / 1 õ Min{X 2 (2)} and Max{X 3 (1)} / 1 õ Min{X 4 (3)}]. R4: The last day off for a T 2 employee may be shifted left with any compensatory rightward shift, provided that the last day off for all T 2 employees occurs more than 1 day later in the week than the first day off for all T 3 and T 4 employees [X 2 (2) shifted left with any compensatory rightward shift, provided that Min{X 2 (2)} ú Max{X 3 (1)} / 1 and Min{X 2 (2)} ú…”

“…First define T s (r) as the subset of employees in set s that have yet to be assigned their rth additional day off this week, where r Å 1, (2), and T 4 (3). As a day off is assigned, the employee is removed from the corresponding subset and the surplus for that day is reduced by 1.…”

“…E2: The second day off in the week for a T 3 employee may be shifted left or right with a compensatory shift of the second day off for a T 2 , T 4 , or T 3 employee [X 3 (2) shifted left or right with a compensatory shift of X 2 (1) or X 4 (2), or X 3 (2)]. E3: The last day off in the week for a T 2 employee may be shifted right with compensatory leftward shift in the second day off for a T 3 , T 4 or T 2 employee [X 2 (2) shifted right with compensatory leftward shift of X 3 (2), X 4 (2), or X 2 (2)].…”

“…E5: The second day off in the week for a T 4 employee may be shifted left or right with a compensatory shift of the second day off for a T 2 , T 3 , or T 4 employee [X 4 (2) shifted left or right with a compensatory shift of X 2 (1), X 3 (2), or X 4 (2)]. Compensatory rightward shifts of the last day off for a T 2 employee [X 2 (2)] and leftward shifts of the first day off for a T 3 employee [X 3 (1)] may also be made without threatening the maximum work tour constraint.…”