Impact of productivity on cross-training configurations and optimal staffing decisions in hospitals

• Published in: European journal of operational research 2014-10, Vol.238 (1), p.254-269
• Main Authors: Gnanlet, Adelina, Gilland, Wendell G.
• Format: Article
• Language: English
• Subjects: Chaining; Cost control; Cost engineering; Cost reduction; Cross-training; Decision making; Decision making models; Demand; Flexibility; Healthcare; Mathematical analysis; Nurses; Occupational training; Optimization; Productivity; Stochastic programming; Studies; Workforce planning
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2014.03.033

•Optimal cross-training decision under stochastic demand and productivity changes.•Centralized and decentralized decision making analyzed for three configurations.•Beyond threshold productivity fewer nurses provide benefit.•Chaining policy on average provides 1.20% cost savings over partial flexibility.•Productivity moderates demand increase and optimal cross-training decisions. Cross-training of nursing staff has been used in hospitals to reduce labor cost, provide scheduling flexibility, and meet patient demand effectively. However, cross-trained nurses may not be as productive as regular nurses in carrying out their tasks because of a new work environment and unfamiliar protocols in the new unit. This leads to the research question: What is the impact of productivity on optimal staffing decisions (both regular and cross-trained) in a two-unit and multi-unit system. We investigate the effect of mean demand, cross-training cost, contract nurse cost, and productivity, on a two-unit, full-flexibility configuration and a three-unit, partial flexibility and chaining (minimal complete chain) configurations under centralized and decentralized decision making. Under centralized decision making, the optimal staffing and cross-training levels are determined simultaneously, while under decentralized decision making, the optimal staffing levels are determined without any knowledge of future cross-training programs. We use two-stage stochastic programming to derive closed form equations and determine the optimal number of cross-trained nurses for two units facing stochastic demand following general, continuous distributions. We find that there exists a productivity level (threshold) beyond which the optimal number of cross-trained nurses declines, as fewer cross-trained nurses are sufficient to obtain the benefit of staffing flexibility. When we account for productivity variations, chaining configuration provides on average 1.20% cost savings over partial flexibility configuration, while centralized decision making averages 1.13% cost savings over decentralized decision making.