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In a series of publications coauthored by Anna Nagurney, Sten Thore and J. Pan,  a new goaling format has been developed, extending the well-known procedures of goal programming to the non-integrable case. The most recent paper is

 

A. Nagurney, S. Thore and J. Pan, ."Spatial Market Policy Modeling with Goal Targets," Operations Research, Vol. 44, No.2, 1996, pp. 393- 406. 

Excerpts from the Introduction:

"In this paper... we focus our attention on competitive economic markets with negative economic externalities and show how the generalization of goal programming through the use of variational inequality theory can address the formulation, qualitative analysis, and computation of economic equilibrium patterns in the presence of target goals... Our motivation ... stems from societal concerns with national energy policy, water and air pollution, global warming, the transportation of hazardous materials ... which is bringing the study of negative externalities to the fore..."

"In this paper we consider a competitive market economy involving the supply of some commodity (such as natural resource, energy, or agricultural produce) at several locations, the subsequent shipment of these supplies to several consumer locations, and the final deliveries at these locations to cover consumer demand. The shipment between a pair of supply and demand locations is charged a unit transaction cost ... This economy is subjected to a government goal mechanism in the following manner. A decision-maker establishes goals and the relative priorities of these goals for supplies, shipments, an consumer demand... Unit penalties are assessed for failure to comply. The ... unit penalty reflects the relative priority of the goal to the decision-maker. That is, the penalties are, in general, non-Archimedean transcendentals..."

"In what follows, we present for the first time non-integrable goal programming as a technique standing on its own, with its own motivation and economic interpretation, holding up whether the underlying supply and demand price functions are integrable or not."

 

The earlier publications on the same subject are

 

A. Nagurney, S. Thore and J. Pan, "The Modeling and Computation of Generalized Goal Programming Problems," in New Directions in Computational Economics, editors W. W. Cooper and A.B. Whinston, Kluwer Academic Publishers, Boston 1994, pp. 95-120.

 

A. Nagurney, S. Thore and J. Pan, "Generalized Goal Programming and Variational Inequalities," Operations Research Letters, Vol.12, No.4., 1992, pp. 217-226.