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HIERARCHICAL PROGRAMMING AND APPLICA...

PARRAGA, FIDEL ABRAHAM.

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HIERARCHICAL PROGRAMMING AND APPLICATIONS TO ECONOMIC POLICY.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	HIERARCHICAL PROGRAMMING AND APPLICATIONS TO ECONOMIC POLICY./
Author:	PARRAGA, FIDEL ABRAHAM.
Description:	176 p.
Notes:	Source: Dissertation Abstracts International, Volume: 41-11, Section: B, page: 4237.
Contained By:	Dissertation Abstracts International41-11B.
Subject:	Engineering, System Science. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=8110119

HIERARCHICAL PROGRAMMING AND APPLICATIONS TO ECONOMIC POLICY.
PARRAGA, FIDEL ABRAHAM.

HIERARCHICAL PROGRAMMING AND APPLICATIONS TO ECONOMIC POLICY. - 176 p.

Source: Dissertation Abstracts International, Volume: 41-11, Section: B, page: 4237.

Thesis (Ph.D.)--The University of Arizona, 1981.

Outside the field of Mathematical Programming, conceptual models aimed at the hierarchical interactions of conflictive decision entities have appeared occasionally in the literature of Mathematical Economics and Game Theory. Thus, we have the monopolistic trading schemes authored by Shapley and Shubik, the leader-follower game proposed by Simaan and Cruz and the moral hazard problem in the Principal to Agent relationship. The novelty and value of the Mathematical Programming formulation of the hierarchical model lies in the fact that it is appropriate to carry out numerical experiments. Hierarchical Programming models can take on many forms, the objective functions and technical constraints can be linear or non-linear and the decision-making entities can have control over resource activities only, prices only or control over both. This dissertation focuses on the solution and economic policy applications of the two-level hierarchical model in which the objectives and technical constraints are linear and in which the decision making entities have control over resource activities only. The (linear-resource) two-level problem is a non-convex problem and can have many local optima. Existing solution methodologies rely heavily on branch and bound techniques and other less orthodox enumeration procedures. The "Algorithm of Interceptions" developed here is based on findings regarding the topological and geometric structure of the feasible domain of the problem. This structure is first established by a body of theorems that assert that the feasible domain is a connected collection of faces of the polyhedron formed by the upper and lower level technical constraints. Furthermore, if a local optimum is not the global optimum then the polyhedron formed by the technical constraints and the hyperplane given by setting the upper objective to a level slightly above the local optima have at least one vertex that belongs to the two-level feasible domain. It is also demonstrated that if a Candler-Townsley high point is not a local optima, then it is possible to identify an alternative optimal basis associated with the same high point but having a higher high point. Once the algorithm is completely developed it is applied to numerical examples of the literature and economic models developed in the chapter of applications. The solutions to these problems and the solutions obtained using the other methodologies are then used for a comparison exercise of the methodology of interceptions against the other methodologies.Subjects--Topical Terms:

1018128
Engineering, System Science.

HIERARCHICAL PROGRAMMING AND APPLICATIONS TO ECONOMIC POLICY.
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100 1 $a PARRAGA, FIDEL ABRAHAM. $3 1671849
245 1 0 $a HIERARCHICAL PROGRAMMING AND APPLICATIONS TO ECONOMIC POLICY.
300 $a 176 p.
500 $a Source: Dissertation Abstracts International, Volume: 41-11, Section: B, page: 4237.
502 $a Thesis (Ph.D.)--The University of Arizona, 1981.
520 $a Outside the field of Mathematical Programming, conceptual models aimed at the hierarchical interactions of conflictive decision entities have appeared occasionally in the literature of Mathematical Economics and Game Theory. Thus, we have the monopolistic trading schemes authored by Shapley and Shubik, the leader-follower game proposed by Simaan and Cruz and the moral hazard problem in the Principal to Agent relationship. The novelty and value of the Mathematical Programming formulation of the hierarchical model lies in the fact that it is appropriate to carry out numerical experiments. Hierarchical Programming models can take on many forms, the objective functions and technical constraints can be linear or non-linear and the decision-making entities can have control over resource activities only, prices only or control over both. This dissertation focuses on the solution and economic policy applications of the two-level hierarchical model in which the objectives and technical constraints are linear and in which the decision making entities have control over resource activities only. The (linear-resource) two-level problem is a non-convex problem and can have many local optima. Existing solution methodologies rely heavily on branch and bound techniques and other less orthodox enumeration procedures. The "Algorithm of Interceptions" developed here is based on findings regarding the topological and geometric structure of the feasible domain of the problem. This structure is first established by a body of theorems that assert that the feasible domain is a connected collection of faces of the polyhedron formed by the upper and lower level technical constraints. Furthermore, if a local optimum is not the global optimum then the polyhedron formed by the technical constraints and the hyperplane given by setting the upper objective to a level slightly above the local optima have at least one vertex that belongs to the two-level feasible domain. It is also demonstrated that if a Candler-Townsley high point is not a local optima, then it is possible to identify an alternative optimal basis associated with the same high point but having a higher high point. Once the algorithm is completely developed it is applied to numerical examples of the literature and economic models developed in the chapter of applications. The solutions to these problems and the solutions obtained using the other methodologies are then used for a comparison exercise of the methodology of interceptions against the other methodologies.
520 $a In the chapter of applications two existing linear programming models are recast as hierarchical models. In each case, policy instruments and a government concern are introduced in the upper level and the linear programming model is used as the corresponding lower level structure. The first model deals with the monetary policy exerted by the Federal Reserve System on the banking industry and the second with an agricultural policy problem.
590 $a School code: 0009.
650 4 $a Engineering, System Science. $3 1018128
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710 2 $a The University of Arizona. $3 1017508
773 0 $t Dissertation Abstracts International $g 41-11B.
790 $a 0009
791 $a Ph.D.
792 $a 1981
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=8110119