
Accession Number : AD0762845
Title : An Operator Theory of Parametric Programming for the Generalized Transportation Problem. III. Weight Operators.
Descriptive Note : Research rept.,
Corporate Author : CARNEGIEMELLON UNIV PITTSBURGH PA MANAGEMENT SCIENCES RESEARCH GROUP
Personal Author(s) : Balachandran,V. ; Thompson,G. L.
Report Date : OCT 1972
Pagination or Media Count : 31
Abstract : The paper investigates the effect on the optimum solution of a capacitated generalized transportation problem when any coefficient of any row constraint is continuously varied as a linear function of a single parameter. The entire analysis is divided into three parts. Results are derived relative to the cases when the coefficient under consideration is associated to a cell where the optimal solution in that cell attains its lower bound or its upper bound. The discussion relative to the case when the coefficient under consideration is associated to a cell in the optimal basis is given in two parts. The first part deals with the primal changes of the optimal solution while the second part is concerned with the dual changes. It is shown that the optimal cost varies in a nonlinear fashion when the coefficient changes linearly in certain cases. The discussion in the paper is limited to basispreserving operators for which the changes in the data are such that the optimum bases are preserved. Relevant algorithms and illustrations are provided throughout the paper. (Author)
Descriptors : (*LINEAR PROGRAMMING, ALGORITHMS), (*TRANSPORTATION, MATHEMATICAL MODELS), CONVEX SETS, THEOREMS, OPTIMIZATION, OPERATORS(MATHEMATICS), THEOREMS
Subject Categories : Operations Research
Distribution Statement : APPROVED FOR PUBLIC RELEASE