Multi-objective geometric programming problem with ?-constraint method |
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Authors: | AK Ojha KK Biswal |
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Institution: | 1. School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Bhubaneswar 751 013, Orissa, India;2. Department of Mathematics, NIIS Institute of Business Administration, Bhubaneswar 752 054, Orissa, India |
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Abstract: | In multi-objective geometric programming problem there are more than one objective functions. There is no single optimal solution which simultaneously optimizes all the objective functions. Under these conditions the decision makers always search for the most “preferred” solution, in contrast to the optimal solution. A few mathematical programming methods namely fuzzy programming, goal programming and weighting methods have been applied in the recent past to find the compromise solution. In this paper ?-constraint method has been applied to find the non-inferior solution. A brief solution procedure of ?-constraint method has been presented to find the non-inferior solution of the multi-objective programming problems. Further, the multi-objective programming problems is solved by the fuzzy programming technique to find the optimal compromise solution. Finally, two numerical examples are solved by both the methods and compared with their obtained solutions. |
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Keywords: | Geometric programming Vector minimization ?-Constraint method Fuzzy programming Duality theory Pareto optimal solution |
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