Linear programming: methods and applications (5th ed.)
Linear programming: methods and applications (5th ed.)
Introduction to operations research, 4th ed.
Introduction to operations research, 4th ed.
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Techniques have been available for some time for determining optimum solutions to certain classes of resource allocation problems. These problems are characterized by a large number of solutions that may satisfy the basic conditions of the problem. The method most often employed to determine the optimum solution to such problems is linear programming. Unfortunately, linear programming techniques are generally not applicable to the type of problems where all constraints are not explicitly defined, e.g., where the demand is estimated or known only with a given probability. Problems of maximization of profits or social benefits in the allocation of available resources or facilities continuously arise in planning and architecture, where the amount of available or potential resources (utilities, housing units, social services, etc.) is explicitly known, but where the demand is not. This paper demonstrates how one may formulate problems with demands that are not precisely known, are projected, or are estimated with some given probability. In addition to the general statement of such problems, several specific applications of the method for both planning and architectural problems are presented. The examples and solutions given involve: 1) the distribution of municipal recreation equipment and facilities among several neighborhood parks each with different demands for the different facilities; 2) the allocation of city services to new communities with various estimated demands. The method presented in this paper also permits the formulation of such problems into the standard linear programming format for solution by computer.