Approximate Dynamic Programming with Combined Policy Functions for Solving Multi-stage Nurse Rostering Problem

Abstract

An approximate dynamic programming that incorporates a combined policy, value function approximation and lookahead policy, is proposed. The algorithm is validated by applying it to solve a set of instances of the nurse rostering problem tackled as a multi-stage problem. In each stage of the problem, a weekly roster is constructed taking into consideration historical information about the nurse rosters in the previous week and assuming the future demand for the following weeks as unknown. The proposed method consists of three phases. First, a pre-process phase generates a set of valid shift patterns. Next, a local phase solves the weekly optimization problem using value function approximation policy. Finally, the global phase uses lookahead policy to evaluate the weekly rosters within a lookahead period. Experiments are conducted using instances from the Second International Nurse Rostering Competition and results indicate that the method is able to solve large instances of the problem which was not possible with a previous version of approximate dynamic programming.