Implications of Resource Directive Allocation Models for Organizational Design

This paper develops theoretical results, for a class of coordination mechanisms for resource allocation in decentralized firms, using as a model the decomposition of linear programs. Of the two pure decentralized allocation mechanisms (price-directive and resource-directive), resource-directive mechanisms, based in concept upon rationing or budgeting procedures, have received less attention in the literature. This paper focuses on these mechanisms and reports that under rather mild conditions the use of the plausible and economically appealing rule of allocating a global resource so as to equalize its marginal value over alternate uses is almost surely doomed to failure. In particular it is found that (1) resource-directive decompositions induce a kind of structural degeneracy in the decentralized divisions; (2) the amount of degeneracy increases with the number of divisions and the number of scarce global resources; and (3) degeneracy "seeks its own level" in that degeneracies spread over the divisions. The implication of these results for those interested in organizational design is that caution should be observed in utilizing such a rule as equalizing marginal values, and that more complicated and costly procedures for effecting resource allocation may be required. Finally, some symmetries between price-directive and resource-directive mechanisms are summarized.