The determination of a subset of efficient solutions via goal programming

doi:10.1016/0305-0548(81)90027-7

Computers & Operations Research

Volume 8, Issue 1, 1981, Pages 9-16

https://doi.org/10.1016/0305-0548(81)90027-7 Get rights and content

Abstract

A wide variety of models and methods have been proposed to solve the vectormaximum problem. Many of these approaches center their attention on linear programming with several objective functions and seek to obtain the set of efficient (Pareto optimal) solutions. Another approach to the same problem is to rank the objectives according to a priority structure and seek the lexicographic minimum of an ordered function of goal deviations. This latter approach, known as goal programming with preemptive priorities, has, in the literature, usually been treated as a separate topic. In this paper we show that the solution to the linear goal programming problem can be made to always be an efficient solution from which we may conduct a practical investigation of a subset of efficient solutions which form a useful compromise set. While perhaps lacking the elegance of the more esoteric approaches, this technique nonetheless has worked well in practice on actual problems.

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^∗: Dr. James P. Ignizio received a B.S.E.E. from the University of Akron, a M.S.E. from the University of Alabama and a Ph.D. in Operations Research and Industrial Engineering from Virginia Polytechnic Institute. He is now a member of the faculty of the Department of Industrial and Management Systems Engineering at the Pennsylvania State University. Dr. Ignizio is the author of three textbooks in the Operations Research area and of numerous technical publications. His primary areas of research interests are in Multiobjective Optimization and Large-Scale Systems.

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The determination of a subset of efficient solutions via goal programming

Abstract

Comput. & Ops Res.

Fuzzy Sets and Systems

Management Models and Industrial Applications of Linear Programming

Goal Programming and Extensions

A review of goal programming: A tool for multi-objective analysis

J. Opl. Res. Soc.