A systematic two phase approach for the nurse rostering problem

Nurse Rostering is a combinatorial problem hard to solve due to its size and complexity. Several real world details that arise in practice make computerized approaches to the problem indispensable. The specifications of the problem that we solve are those defined in the Nurse Rostering Competition INRC2010. In this contribution, we solve the Nurse Rostering Problem by partitioning the original problem into sub-problems. Each sub-problem has size that is computationally manageable and is solved using Mathematical Programming. We implemented a two phase strategy, where in the first phase an assignment of nurses to working days occurs while in the second phase nurses assigned to each day are scheduled to certain shifts of the day. The problem is scanned several times from start to end and an extensive number of partial schedule exchanges between nurses are tried. The two phases are presented below. Phase 1: Assignment of nurses to working days At the first phase the working and resting days of all nurses for the specified planning horizon are defined. Then an Integer Programming problem is defined and solved for the first week (7 consecutive days) of the planning horizon. The formulation of the IP model ensures the satisfaction of the hard constraints imposed by the problem. For this reason the total number of nurses that work in each day should equal the work demand of the day and each nurse should work no more than one shift in each day. In this phase the only soft constraints that are considered are those that depend on work or rest assignment. These constraints are used at the cost function. All the possible combinations of work/rest for a week period are examined for all nurses (128 possible values for each nurse). In this way a feasible schedule of all nurses are produced, that covers the daily