The Optimal Workforce Staffing Solutions With Random Patient Demand in Healthcare Settings

Background

The newsvendor model is the widely used analytic model in which the optimal inventory level is determined for a specified time period. Historically, it originates from the problem in which a newsvendor has to decide on the optimal stocking quantity of the newspaper (a single product) to be ordered from the publisher in some defined ahead time period; hence it is called the newsvendor problem. If too many issues are ordered there will be some financial loss due to unsold inventory. If not enough issues are ordered there will also be some financial loss due to unmet customer demand. The problem is determining the optimal quantity order that will minimize the total financial loss due to both over- and understock during some time period.

The newsvendor framework has been widely applied to problems in which decisions should be made on the fixed supply level with an uncertain (random) demand. Such problems are often occurring in supply chain management, retail, transportation, manufacturing, banking, and many other industries (Choi, 2012; Arikan, 2011; Porteus, 2002). Motivated by the importance of various practical applications of the newsvendor model, the entire special issue of the Decision Sciences journal (Chen et al., 2016), and the review paper (Qin et al., 2011) were dedicated to its novel advances and applications.

At the same time, the use of the newsvendor framework was rather limited in healthcare management for planning and budgeting the hospital units’ staffing while patient demand is uncertain.

For example, in the handbook of newsvendor problems, which is the first handbook dedicated exclusively to the state of the art in this area (Choi, 2012), the optimal nursing staffing problem with uncertain patient demand was not presented at all. However, this is a fruitful area of application of the newsvendor framework. The long-term nursing staffing plans should be developed on the annual basis. The medium-term staffing plans should usually be developed for a 4-6 weeks period, and be posted 1-2 weeks before the start of the planned period. Because of inevitable occurrences of unforeseen deviations from the planned staffing level, some short-term staffing adjustments should be made shortly before each shift to determine whether overtime, pooled or agency nurses are needed, or if the unit is overstaffed and some nurses are not currently needed. There is a cost associated with flexing staff up or down, along with issues of staff dissatisfaction with the erratic unpredictable schedules. There is an empirical evidence that the frequent staffing adjustments costs are accumulated to significant amounts that were not previously budgeted for. The optimal staffing level determined by the newsvendor model minimizes these accumulated costs, thus making nursing staffing plans and budgets more realistic.