A Mathematical Programming Model for Scheduling Nursing Personnel in a Hospital

The Nursing Personnel Scheduling Problem is defined as the identification of that staffing pattern which (1) specifies the number of nursing personnel of each skill class to be scheduled among the wards and nursing shifts of a scheduling period, (2) satisfies total nursing personnel capacity, integral assignment, and other relevant constraints, and (3) minimizes a “shortage cost” of nursing care services provided for the scheduling period. The problem is posed as a mixed-integer quadratic programming problem, which is decomposed by a primal resource-directive approach into a multiple-choice programming master problem, with quadratic programming sub-problems. Initial results suggest that a linear programming formulation, with a post-optimal feasibility search scheme, may be substituted for the multiple-choice master problem. The model is tested on six wards of a 600-bed general hospital, and results are presented.