Optimizing the worst achievement rate in linear programming problems with an interval objective function

Optimizing the worst achievement rate in linear programming problems with an interval objective function

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Article ID: iaor1995331
Country: Japan
Volume: 6
Issue: 5
Start Page Number: 243
End Page Number: 251
Publication Date: May 1993
Journal: Transactions of the Institute of Electronics, Information and Communication Engineers
Authors: , ,
Keywords: programming: fractional, programming: parametric, optimization
Abstract:

In this paper, a new solution concept for linear programming problem with an interval objective function is proposed based on the worst achievement rate. First, given coefficients of the objective function, the achievement rate for each feasible solution is defined. Using the achievement rate, the interval linear programming problem is formulated as an optimization problem of the worst achievement rate among the objective coefficients within given intervals. The optimization problem of the worst achievement rate is reduced to min-max or max-min problem subject to separate constraints. It is shown that the solution optimizing the worst achievement rate has a desirable property. A solution algorithm based on the relaxation procedure and the simplex method is proposed to solve the optimization problem of the worst achievement rate. In order to illustrate the proposed solution algorithm, a numerical example is given. [In Japanese.]

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