Determining Optimal Use of Resources among Regional Producers under Differing Levels of Cooperation

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Abstract
We determine optimal allocation of means of production between a principal and alternative commodities under varying degrees of cooperation among producers. Producers are grouped into subsets with stipulated efficiencies, costs of production and demand prices. These producers collectively control the production of the principal commodity whose price depends upon total supply. Optimal allocation is determined under conditions of (1) pure competition, (2) cooperation within subsets, and (3) cooperation among all producers. The latter problem is modeled as a nonconcave quadratic programming problem. A very efficient algorithm for solving this problem is presented. This algorithm has been used to determine the optimal distribution of cotton production among 300 regions.

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