Solving Rostering Tasks as Constraint Optimization

Based on experiences with the ORBIS Dienstplan-system [Mey97] — a nurse rostering system that is currently used in about 30 German hospitals — this paper describes how to use constraint processing for automatic rostering. In practice, nurse rostering problems have many varying parameters: Working time accounts, demands on crew attendance, set of used shifts, working time models, etc. Hence, rostering requires a flexible formalism for representing the variants of the problem as well as a robust search procedure that is able to cope with all problem instances. The described approach differs in mainly two points from other constraint-based approaches [AS99,WH95] to rostering. On the one hand, the used constraint formalism allows the integration of finegrained optimization tasks by fuzzy constraints, which a roster may partially satisfy and partially violate. Such constraints have been used to optimize the amount of working time and the presence on the ward. In contrast, traditional frameworks for constraint processing consider only crisp constraints which are either completely violated or satisfied. On the other hand, the described system uses an any-time algorithm to search for good rosters. The traditional constraint-based approach for solving optimization tasks is to use extensions of the branch&bound. Unfortunately, performance of tree search algorithms is very sensitive to even minor changes in the problem representation. ORBIS Dienstplan integrates the branch&bound into local search. The branch&bound is used to enable the optimization of more than one variable assignment within one improvement step. This search algorithm converges quickly on good rosters and, additionally, enables a more natural integration of user interaction.