Entropy-based Demand Splits in a Hospital-Warehouse Profit Center

Abstract

Financial pressures on healthcare industry in the United States and elsewhere have forced the industry to address their supply costs, their fastest growing cost sector currently comprising over 40 % of their total spend. In the USA, the healthcare supplies market is dominated by a few large distributors and significant barriers to entry. Cost reducing measures to date have relied on Group Purchasing Organizations to leverage economies of scale in negotiating price reductions. Recently, the healthcare industry has been deemphasizing this practice. In doing so, healthcare organizations have merged to form large Integrated Delivery Networks, leveraging their collective purchasing capacity to negotiate price reductions. These organizations have essentially created their own internal Group Purchasing Organizations to compete with external suppliers. Although these ventures have been publicized to be “successful”, their overall success cannot be independently validated. Furthermore, the operational details of creating these ventures, financial analyses, and operations are not publically available. Our ultimate objective is to model the creation of ventures in which healthcare organizations enter price competitions with their external vendors using the currently prevalent market parameters and practices. Specifically, the models would identify and quantitate the parameters that determine venture success, here referred to as Venture Success Metrics. Such models would comprise multiple external suppliers of different products that belong to different categories. This thesis is our first step towards that objective. It represents a simplified venture in which the hospital runs its own warehouse as a profit center that competes with one external vendor on a single supply item. The model is based on currently prevalent healthcare industry practices. In particular, it incorporates discount schedules that accurately account for the unique healthcare industry practice of offering year-2 volume-based discounts based on year-1 volumes, restricted only to the contract period. Modeling a simplified venture enabled us to identify and quantitate the parameters that determine venture success. These parameters comprise the vendor and warehouse year-1 profit objectives as well as the bias of the hospital’s purchases from its own warehouse. Pursuing the models of the thesis induced the development of healthcare-relevant sigmoidal discount schedules. These functions accurately represent the tabular step-function discount schedules while averting the infinite and discontinuous derivatives of the latter. Their “continuous derivatives” advantage renders the sigmoidal discounts readily useable in computing price equilibria, a feat that was not easily achievable with the rigid step-function discounts. The thesis also introduces novel demand split functions in which a customer’s total demand can be equitably apportioned across all suppliers subject to diverse business objectives such as price constraints or biasing purchases in favor of one or more suppliers while retaining equitability. The ultimate economic goal for achieving equitability is to conserve supply source. The demand split methodology introduced in this thesis can be characterized as “achieving equitability under business constraints”. A series of examples are provided to illustrate the methods developed in this research. Finally, the thesis concludes with a synopsis of the findings and future extensions.