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\textbf{A Fuzzy Max-Min Approach to Multi Objective, Multi Echelon Closed Loop Supply Chain}
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B. Ahlatcioglu Ozkok$^{1}$, \textbf{E. Budak}$^{1}$ and S. Ercan$^{2}$

$^{1}$Department of Mathematics, Yildiz Technical University, Istanbul, Turkey
$^{2}$Department of Mathematics, Firat University, Elazig, Turkey
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\textbf{Abstract}

In today's competitive markets, optimizing the process of delivering products from suppliers of raw materials to the customers for the firms formalizes an important problem in the literature. Increasingly contaminated world and limited sources of energy in recent years are regarded, it is inevitable for the mathematical models of any supply chain to have an environmentalist perspective. Hence, closed loop supply chain method has an increasing importance. In this study, a multi-objective linear model is given for the multi-echelon closed loop supply chain and the solution is obtained by utilizing Zimmermann's "min" operator with a fuzzy approach in which the minimum satisfactions of objectives are maximized. The model is to determine the locations of facilities and distribution quantity on the network regarding three objective functions, which are; minimizing time and cost, maximizing rating.  

\textbf{References}

[1] Wei, J., Zhao, J., “Pricing decisions with retail competition in a fuzzy closed-loop supply chain”, Expert Systems with Applications, Vol. 38, pp. 11209-11216, 2011. 

[2] Pishvaee. M.S., Razmi, J., “Environmental supply chain network design using multi-objective fuzzy mathematical programming”, In Press, Corrected Proof, Available online 20 October 2011.

[3] Zimmerman, H.J., Fuzzy Set Theory and its applications, Kluwer Academic Publishers, Boston/ Dordrecht/ London, 1992. \hrule

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