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