ANNUAL REPORT. MANAGEMENT SCIENCE. NOTES ON OPTIMIZATION AND DECISION PROBLEMS .
CALIFORNIA UNIV BERKELEY CENTER FOR RESEARCH IN MANAGEMENT SCIENCE
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A class of problems of optimal resource allocation over time was studied using the techniques of dynamic programming. Sufficient conditions were found for the state valuation function to be the unique solution of the usual functional equation of dynamic programming. Exact solutions were found for the case of linear-loga rithmic production and criterion functions. This exact solution was used to form the basis of an algorithm designed to handle any problem in which the production functions are differentiable and the criterion function is differentiable, and separable in time. Numerical computations were performed to compare two algorithms for the solution of systems of linear inequalities, the standard artificial variables method, and the new characteristic function method of Debreu.