An operator theory of parametric programming for the generalized transportation problem-IV-global operators, Naval Research Logistics Quarterly
This paper investigates the effect of the optimal solution of a (capacitated) generalized transportation problem when the data of the problem (the rim conditions - i.e., the available time of machine types and demands of product types, the per unit production costs, the per unit production time and the upper bounds) are continuously varied as a linear function of a single parameter. Operators that effect the transformation of optimal solution associated with such data changes, are shown to be a product of basis preserving operators (described in our earlier papers) that operate on a sequence of adjacent basis structures. Algorithms are furnished for the three types of operators - rim, cost, and weight. The paper concludes with a discussion of the production and managerial interpretations of the operators and a comment on the production paradox.
Balachandran, Bala. 1975. An operator theory of parametric programming for the generalized transportation problem-IV-global operators. Naval Research Logistics Quarterly. 22(2): 317-339.