Analyzing the product‐mix decision by using a fuzzy hierarchical model

The product‐mix decision has received considerable attention in management accounting and economics literatures. However, many studies in these literatures are contradicting, inconclusive and lack rigorous analysis of this complex decision. They seek to develop weights for the products in the product mix based on one objective, to maximize the firm’s profit ability. But before developing these weights, the studies must first rank these products, Ranking is a complex endeavor since it is often driven by a multitude of hierarchical financial and non‐financial goals and objectives. Ranking is also difficult due to the use of complex concepts such 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 the product mix decision. The model combines the powers of fuzzy‐set theory (Zadeh, 1965) and the analytic hierarchy process (Saaty, 1978). The fuzzy‐analytic‐hierarchical process (FAHP), developed by de Korvin and Kleyle (1999), is sufficiently powerful to account for the 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 non financial goals such as tradition and owners’ convictions and philosophies underlying the ranking of the products in the product mix. By way of example, the paper applies the FAHP model to rank order four products subject to these strategies and goals.