A Benders decomposition-based matheuristic for the Cardinality Constrained Shift Design Problem

Abstract

The Shift Design Problem is an important optimization problem which arises when scheduling personnel in industries that require continuous operation. Based on the forecast, required staffing levels for a set of time periods, a set of shift types that best covers the demand must be determined. A shift type is a consecutive sequence of time periods that adheres to legal and union rules and can be assigned to an employee on any day. In this paper we introduce the Cardinality Constrained Shift Design Problem; a variant of the Shift Design Problem in which the number of permitted shift types is bounded by an upper limit. We present an Integer Programming model for this problem and show that it's structure lends itself very naturally to Benders decomposition. Due to convergence issues with a conventional implementation, we propose a matheuristic based on Benders decomposition for solving the problem. Furthermore, we argue that an important step in this approach is finding dual alternative optimal solutions to the Benders subproblems and describe an approach to obtain a diverse set of these. Numerical tests show that the described methodology significantly outperforms a commercial Mixed Integer Programming solver on instances with 1241 different shift types and remains competitive for larger cases with 2145 shift types. On all classes of problems the heuristic is able to quickly find good solutions.

Refueling Station Location Model to Support Evacuation of Alternative Fuel Vehicles

“…Specifically, our model is structured as a path-based location-routing problem. Benders decomposition has been used to provide both exact and heuristic solutions to the location-routing problem (33)(34)(35)(36) and multi-stage problem (relevant to our problem) (37)(38)(39)(40) with side constraints.…”

Multi-period green reverse logistics network design: An improved Benders-decomposition-based heuristic approach

“…Lai, Sohn, Tseng and Chiang (2010) and Poojari and Beasley (2009) used a genetic algorithm to obtain a (sub-optimal) solution for the master problem in the BD approach. Furthermore, to address the convergence issue, Lusby, Range and Larsen (2016) and Boschetti and Maniezzo (2009) developed a BD-based heuristic to solve the problem with a good-quality solution. Üster and Hwang (2016) and Easwaran and Üster (2010) strengthened Benders' cuts using algorithms such as the two-phase method and the Tabu approach.…”

Demand smoothing in shift design

“…These models typically have multiple objectives such as, for example, minimizing the deviation from the demand, minimizing the number of shifts used or balancing workload (Musliu et al, 2004;Di Gaspero et al, 2007). Lusby et al (2016) include additional hard constraints on the maximum number of shifts and the number of available employees on each day. Even without considering breaks or skills, these optimization problems are already very challenging from a computational point of view and have lead to the development of a wide range of heuristics.…”

“…Third, the number of shifts is not minimized. Instead, constraints are included which limit the number of shifts, as proposed by Lusby et al (2016). As in the canonical shift design problem, the aim in the present paper is to determine the set of shifts that best matches the demand requirements for a single day.…”