Optimal Nursing Home Shift Scheduling: A Two-Stage Stochastic Programming Approach

Abstract

In this paper, we study a nursing home staff schedule optimization problem under resident demand uncertainty. We formulate a two-stage stochastic binary program accordingly, with objective to minimize the total labor cost (linearly related to work time) incurred by both regular registered nurses (RRNs) and part-time nurses (PTNs). As a significant constraint, we balance RRNs’ total amount of work time with residents’ total service need for every considered shift. Besides, we restrict feasible shift schedules based on common scheduling practice. We conduct a series of computational experiments to validate the proposed model. We discuss our optimal solutions under different compositions of residents in terms of their disabilities. In addition, we compare the total labor costs and an RRN scheduling flexibility index with the given optimal solution under different combinations of RRNs and PTNs. Our analysis offers an operational approach to set the minimum number of nurses on flexible shift schedules to cover uncertain the service needs while maintaining a minimum labor cost.