A UNIQUE SOLUTION FOR THE NUCLEOLUS IN ACCOUNTING ALLOCATIONS

The nucleolus method has been suggested in the literature as a means for accounting decision makers to allocate joint costs in situations where entities share a common resource. The nucleolus has the advantage, vis-a-vis other methods, of maximizing the benefit to the least-well-off entity or groups of entities, and therefore reducing the possibility that one or more entities may desire to withdraw from the sharing arrangement. The nucleolus is basically a linear programming model. Because of its formulation, the nucleolus may yield multiple optimal solutions. No reformulation of the nucleolus seems to exist to overcome this problem The minimum total propensity to disrupt (MTPD) is suggested as an extension of the nucleolus to identify unique values for allocations with multiple solutions. The MTPD, while exhibiting deficiencies as a stand-alone method, is similar in overall objective to the nucleolus and its mathematical function possesses a unique minimum. It is therefore the logical method for identifying a unique nucleolus solution. The use of the MTPD extension is critically examined through a representative application.