Using Fuzzy Set Theory to Help Resolve Governmental Hospitals’ Health Care Decision Conflicts

• In Event: Continental Breakfast and Research & Education Forum
  In Roundtable Session: Table 15: Auditing Pot Pourri

Abstract

While cost allocation decisions form considerable attention in the management accounting literatures, many such studies are contradicting, inconclusive and lack rigorous analysis of this complex decision. They often seek to develop product or service weights in order to make operating decisions and to with the sole objective of maximizing the firm's profitability. But before developing these weights, the studies must first rank these products—which is a complex endeavor that is often driven by many hierarchical financial and non-financial goals and objectives. Ranking is also difficult due to using such complex concepts as time, uncertainty, cost and interdependencies between accounting systems and manufacturing systems and among the products of the product mix. These concepts are inherently fuzzy and coextensively applied often with a confluence of variables operating simultaneously.

This paper applies an advanced mathematical model to account for a hospital cost allocation decision. The model combines the powers of fuzzy-set theory (Zadeh, 1965) and the analytic hierarchy process (Saaty, 1978). Korvin and Kleyle (1999)’s fuzzy-analytic-hierarchical process (FAHP) can help to optimize decisions involving ambiguous variables and the web of prioritized strategies and goals of cost leadership, product differentiation, financial objectives of earnings, cash flows and market share and nonfinancial goals such as tradition and owners’ convictions and philosophies underlying the ranking of the many complex cost allocation and similar decisions, such as products in the product mix.

We use data from seven Michigan spinal-cord injury facilities in applying the FAHP model to rank and otherwise develop more optimal strategies and goals.

Auditors can extend this methodology to test the underlying strength of such cost allocations in gather evidence for many other types of cost allocation methodologies.

Authors

• Alan Reinstein, Wayne State University

• Mohamed Bayou, University of Michigan-Dearborn

• Xinyu Du, Igate Patni Americas