A Simple Algorithm for the Mathematical Programming Approach to Joint Cost Allocation for Decision Making (Demand-Adjusted-Sales-Value Algorithm)*

This paper investigates the mathematical programming (MP) approach for decision making and cost allocation in the context of joint products. Through analysis of the MP approach to marginal-value-based cost allocations, an algorithm is developed to show that the allocations contain two elements: an element that is specific to individual joint products due to differences in demand elasticities, and an element based on relative adjusted sales values. If demand elasticities are identical for all joint products, then the traditional sales value method will generate the same cost allocation as the MP method. The new algorithm, the demand-adjusted-sales-value algorithm (DASV), is especially helpful for solving the MP model with linear demand functions. The DASV algorithm provides an easy way to generate costs that are useful for optimal decision making.