An Operator Theory of Parametric Programming for the Transportation Problem. II.
CARNEGIE-MELLON UNIV PITTSBURGH PA MANAGEMENT SCIENCES RESEARCH GROUP
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The paper investigates the effect on the optimum solution of a capacitated transportation problem when the data of the problem the rim conditions--i.e., the warehouse supplies and market demands--, the per unit transportation costs and the upper bounds are continuously varied as a linear function of a single parameter. Operators that effect the transformation of optimum solution associated with such data changes, are shown to be a product of basis preserving operators described in the earlier paper that operate on a sequence of adjacent basis structures. Algorithms are provided for both rim and cost operators. The paper concludes with a discussion of the economic and managerial interpretations of the operators. Author
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