The setting of weights in linear goal-programming problems

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Abstract

It is the author's view that preemptive linear-goal programming and its associated simplex-based allgorithm is too restrictive in its ability to search out an acceptable solution and imposes an unrealistic burden on the decision maker by requiring a statement of strict preemptive priorities. Also, the question of goal norming is one that has little relevance in terms of what the basic problem really is: i.e. finding a suitable set of objective function weights that can be applied to the over- and under-achievement deviation variables. This paper describes why the author has reached these conclusions, and his approach for solving large-scale goal programs.

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    The authors have stressed that the preemptive priority approach presents computational superiority over existing methods (Chen & Tsai, 2001). However, Akoz and Petrovic (2007) have emphasized the possibility of the results giving high achievements value for only the higher priority level goals while Gass (1987) has highlighted the difficulty in determining definite objective hierarchy. Hannan (1985) has also indicated that the approach is time consuming and determining the weights is hard.

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    In fact, the deviations from the zero target level of space utilization goal may only be positive values. Gass (1987) argues that a hard pre-emptive multi-objective model may be unrealistic because this assumes infinite trade-offs between different levels, and also the sequential solution technique may cut-off some interesting parts of the solution space. So, we apply the flexible pre-emptive goal hierarchy proposed by Akoz and Petrovic (2007) because it takes simultaneously the achievement degrees of fuzzy goals and constraints, as well as the satisfaction degrees of fuzzy goals priorities into consideration through modeling fuzzy binary relations between each pair of goals belonging to different priority levels.

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Saul I. Gass received his U.S. in Education and M.A. in Mathematics from Boston University, and his Ph.D. in Engineering Science/Operations Research from the University of California, Berkeley. He is currently Professor in Management Science and Statistics, College of Business and Management, University of Maryland, College Park. Dr Gass began his career in operations research with the USAF Directorate of Management Analysis, and was Manager of Federal Civil Programs for IBM's Federal Systems Division, Senior Vice-President of World Systems Laboratories, and Vice-President of Mathematica, Inc. He is a past President of the Operations Research Society of America, and is currently President of Omega Rho, the international honor society in operations research. His books include Linear Programming (McGraw-Hill, fifth edition) and Decision Making, Models and Algorithms (Wiley-Interscience). Dr Gass has jogged over 10, 000 miles in the major cities of the world, including Potomac, Maryland.

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