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Multi-objective geometric programming problem and its applications

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In this paper, we have discussed constrained posynomial Multi-Objective Geometric Programming Problem. Here we shall describe the fuzzy optimization technique (through Geometric Programming technique) In order to solve the above multiobjective problem. The solution procedure of the fuzzy technique is illustrated by a numerical example and real life applications. | Yugoslav Journal of Operations Research Volume 20 (2010), Number 2, 213-227 DOI:10.2298/YJOR1002213I MULTI-OBJECTIVE GEOMETRIC PROGRAMMING PROBLEM AND ITS APPLICATIONS Sahidul ISLAM Department of Mathematics, Guskara Mahavidyalaya, Guskara, Burdwan Received: May 2009 / Accepted: November 2010 Abstract: In this paper, we have discussed constrained posynomial Multi-Objective Geometric Programming Problem. Here we shall describe the fuzzy optimization technique (through Geometric Programming technique) In order to solve the above multiobjective problem. The solution procedure of the fuzzy technique is illustrated by a numerical example and real life applications. Keywords: Posynomial, geometric programming, MOGPP, max-min operator, gravel box problem. AMS Subject Classification: 90C29, 90C70. 1. INTRODUCTION GP method is an effective method used to solve a non-linear programming problem. It has certain advantages over the other optimization methods. Here, the advantage is that it is usually much simpler to work with the dual than the primal one. Solving a non-linear programming problem by GP method with degree of difficulty (DD) plays a significant role. (It is defined as DD = total number of terms in objective function and constraints – total number of decision variables – 1). Since late 1960’s, Geometric Programming (GP) has been known and used in various fields (like OR, Engineering sciences etc.). Duffin, Peterson and Zener [4] and Zener [11] discussed the basic theories on GP with engineering application in their books. Another famous book on GP and its application appeared in 1976 [2]. There are many references on applications and methods of GP in the survey paper by Ecker [5]. They described GP with positive or zero degree of difficulty. Today, most of the real-world decision-making problems in economic, environmental, social, and technical areas are multi-dimensional and multi-objectives ones. Multi-objective optimization problems differ from .