Abstract
Employee scheduling is a well known problem that appears in a wide range of different areas including health care, air lines, transportation services, and basically any organization that has to deal with workforces. In this paper we model a collection of challenging staff scheduling instances as a weighted partial Boolean maximum satisfiability (maxSAT) problem. Using our formulation we conduct a comparison of four different cardinality constraint encodings and analyze their applicability on this problem. Additionally, we measure the performance of two leading solvers from the maxSAT evaluation 2015 in a series of benchmark experiments and compare their results to state of the art solutions. In the process we also generate a number of challenging maxSAT instances that are publicly available and can be used as benchmarks for the development and verification of modern SAT solvers.
Highlights
Staff scheduling problems arise whenever there is the need for efficient management and distribution of workforce over periods of time
Currently the state of the art solvers that are based on integer programming produce better results for many of the considered instances, the results show that maximum Boolean satisfiability problem (maxSAT) as an exact method gives promising results for employee scheduling problems
In this paper we have introduced, to the best of our knowledge, for the first time a partial weighted Boolean maximum satisfiability model for variants of the employee scheduling problem and the nurse rostering problem
Summary
Staff scheduling problems arise whenever there is the need for efficient management and distribution of workforce over periods of time. To show that the applicability of maxSAT is not restricted to the instances from Curtois and Qu (2014), we will describe how the maxSAT formulation introduced in this paper can be adapted to model the well known problem instances from the second international nurse rostering competition (INRC2) (Ceschia et al 2015). – We provide the first maxSAT formulation for the variant of the employee scheduling problem introduced by Curtois and Qu (2014). We chose to focus on this specific problem formulation as it provides a number of instances that include challenging and realistic scheduling problems, while still being intuitive and straightforward to use. For example a hard constraint in our problem could restrict the minimum and maximum amount of time that an employee has to work in total over the whole scheduling horizon. We have a deeper look on all of the constraints
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