Bounded flexibility in days-on and days-off scheduling

Abstract

This article presents a flexible days‐on and days‐off scheduling problem and develops an exact branch and price (B&P) algorithm to find solutions. The main objective is to minimize the size of the total workforce required to cover time‐varying demand over a planning horizon that may extend up to 12 weeks. A new aspect of the problem is the general restriction that the number of consecutive days on and the number of consecutive days off must each fall within a predefined range. Moreover, the total assignment of working days in the planning horizon cannot exceed some maximum value. In the B&P framework, the master problem is stated as a set covering‐type problem whose columns are generated iteratively by solving one of three different subproblems. The first is an implicit model, the second is a resource constrained shortest path problem, and the third is a dynamic program. Computational experiments using both real‐word and randomly generated data show that workforce reductions up to 66% are possible with highly flexible days‐on and days‐off patterns. When evaluating the performance of the three subproblems, it was found that each yielded equivalent solutions but the dynamic program proved to be significantly more efficient. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 60: 678–701, 2013

Nurse rostering: models and algorithms for theory, practice and integration with other problems

“…Brunner et al [18] proved that problem P 6 is NP-complete by showing that it has the circulant problem as a special case. Removing all constraints regarding consecutive assignments reduces the problem of finding a feasible solution for P 6 to the problem of finding a feasible flow in network G 1 .…”

“…Osogami and Imai [100] and Brunner et al [18] prove that rostering problems with constraints on the number of assignments of particular shifts, and with constraints on consecutive days worked and days-off are hard. Lau [80] describes a shift assignment problem closely related to rostering, and proves its NP-completeness.…”

Polynomially solvable personnel rostering problems

“…Constraints (32) require the decision variables to be either zero or one. Brunner et al (2013) proved that problem P 6 is NP-complete by showing that is has the circulant problem as a special case. Removing all constraints regarding consecutive assignments reduces the problem of finding a feasible solution for P 6 to the problem of finding a feasible flow in network G 1 .…”

“…There are only a few authors who have formally determined the hardness of a personnel rostering problem. Osogami and Imai (2000) and Brunner et al (2013) prove that rostering problems with constraints on the number of assignments of particular shifts, and with constraints on consecutive days worked and daysoff are hard. Lau (1996b) describes a shift assignment problem closely related to rostering, and proves its NP-completeness.…”

Designing an annual leave scheduling policy: Case of a financial center

“…Shift and daysoff scheduling problems are equivalent when there is a single shift on a work day. Consequently, related problems are classified under single-shift scheduling (see, e.g., [13,27,5,15,28,37,9]) and multiple-shift scheduling (see, e.g., [56,47,14,39,38]) of a single category or multiple categories of employees. There are other studies which consider employee preferences and hierarchy.…”