Multiple Objective Linear Programming with Parametric Criteria Coefficients

Article Abstract:

In this paper we study the multiple objective linear programming problem with parametric criteria coefficients. This problem is of interest since in many situations the coefficients of the objective functions of a multiple objective linear program either represent estimates of the true data or are subject to systematic variations. Properties of this problem are developed, and an algorithm for generating the set of all weakly-efficient extreme points of this problem is described. To implement this algorithm, a nonconvex subproblem must be solved for each candidate extreme point encountered. This is accomplished by applying the Generalized Benders Decomposition method. Computational results concerning the solution of these subproblems are presented. (Reprinted by Permission of Publisher.)

Algorithms, Algorithm, Decision theory

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Finding Certain Weakly-Efficient Vertices in Multiple Objective Linear Fractional Programming

Article Abstract:

Recently Kornbluth and Steuer have developed a simplex-based algorithm for finding all weakly-efficient vertices of an augmented feasible region of a multiple objective linear fractional programming problem. As part of this algorithm, they presented a method for detecting certain weakly-efficient vertices called break points. In this note we show that the procedure used by Kornbluth and Steuer in this method for computing the numbers needed to find these break points may sometimes fail. We also propose a fail-safe method for computing these numbers and give some computational results with this method. (Reprinted by Permission of Publisher)

Criteria, Decision Making, Methods

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Finding certain weakly-efficient vertices in multiple objective linear fractional programming

Article Abstract:

A recently developed algorithm for finding 'break points' (or weakly efficient vertices) in an augmented feasible region of a multiple objective linear fractional programming problem is criticized for being incapable of finding all break points for all circumstances. An alternative method for identifying these break points is also developed and shown to be 'fail-safe'.

Research, Case studies, Optimization theory, Nonlinear programming, Mathematical programming

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