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MULTIPLE OBJECTIVE LINEAR PROGRAMMING IN OBJECTIVE SPACE
Abstract
The multiple objective linear programming (MOLP) problem is to maximize several linear objectives over a convex polyhedral set. The MOLP problem is max Cx, subject to x (ELEM) X = {x: Ax (LESSTHEQ) b, x (GREATERTHEQ) 0} where C is the k x n cost coefficient matrix and A is the m x n constraint matrix. x (ELEM) X is efficient and y = Cx (ELEM) Y = C(X) is nondominated if there does not exist an x* (ELEM) X such that y* = Cx* with (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) In most applications n > k so that C is not 1-1. As a result, it is possible for a subset of the feasible set X to have the same image, or same nondominated set, as X. Chapter 1 gives conditions when this is possible where the columns of the new constraint and cost coefficient matrices are a subset of the columns of A and C. This reduction in dimension is always possible if n < 2k + m. Also the image of an extreme point of X is not necessarily an extreme point of Y. Hence it is not always necessary to completely determine the set of efficient solutions in X in order to find the nondominated set in Y. In Chapter 2, an algorithm is developed which takes advantage of the simplification in structure of objective space to determine the nondominated set in Y. Chapter 3 considers post-optimal procedures. The problem of sensitivity of the nondominated set to changes in and parameterization of the cost coefficients is considered. Only the case where the changes can occur in a known fashion is considered.
Subject Area
Mathematics
Recommended Citation
SEBO, DONALD ELROY, "MULTIPLE OBJECTIVE LINEAR PROGRAMMING IN OBJECTIVE SPACE" (1981). ETD collection for University of Nebraska-Lincoln. AAI8208379.
https://digitalcommons.unl.edu/dissertations/AAI8208379