Fuzzy Economic Production Quantity Model for a Sustainable System via Geometric programming



Businesses strive to be Sustainable because of internal and external pressures .To examine sustainability, firms may use different methods of analysis. This paper develops a procedure to derive the fuzzy objective value of the fuzzy  geometric programming problem when the exponents of decision variables in the objective function, the cost and the constraint coefficients, and the right-hand sides are fuzzy numbers. Geometric programming provides a powerful tool for solving a variety of engineering optimization problems.. The idea is based on Zadeh’s extension principle to transform the fuzzy geometric programming problem into a pair of two-level of mathematical programs. Based on duality algorithm and a simple algorithm, the pair of two-level mathematical programs is transformed into a pair of conventional geometric programs. The upper bound and lower bound of the objective value are obtained by solving the pair of geometric programs. Using the new representation, the conventional geometric programming algorithm is modified to take into consideration the effect of the uncertainty (the fuzzy level). This modification is achieved by making the calculations of each step of the modified algorithm in pairs..Examples are used to illustrate that the whole idea proposed in this paper.

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[I] C.Glock,E.H.Grosse ,J.M.Ries,The lot sizing problem :A tertiary study ,Int.J.Prod.Econ.155(2014)39-51.

[II] M.Y.Jaber,A.M.El Saadany , M.A.Rosen,Simple price-driven Reverse Logistics System with entropy and Exergy costs,Int.J.Exergy 9(2011)486-502.

[III] Jung.Hoon,M.Klein Cerry.Optimal Inventory polices under decreasing cost Function via Geometric Programming.European Journal of Operational Research,132.628-648.

[IV] Shiang. Tai Liu., 2007. Geometric Programming with Fuzzy Parameters in Engineering Optimization, International Journal of approximate reasoning, 46, 484-498.

[V] Kordi, A., 2010. Optimal Fuzzy inventory policies via Fuzzy Geometric programming, Industrial Engineering and operations management, 1-4.

[VI] G.A. Kochen berger, Inventory models, optimization by Geometric programming, Decision Sciences, 2(1971), 193-205.

[VII] Sipkin, P.H., 2000. Foundations Inventory Management, Mc-graw-Hill Companies

[VIII] Nagarajan, M., Sosic, G., 2009. Conditions Stability in Assembly Models, 53, Operations Research, 57, 131-145.

[IX] Guardiola, L., Meca, A., Puertu, J., 2008. Production – Inventory Games PAMS – Games : Characterization of the owen point. Mathematical social sciences 56, 96-103.

[X] Bellman. R.E. Zadeh L.A., Decision-making in a fuzzy environment – Management science. 1970 17B141-13164.

[XI] Ding, H. Benyoucef, L., Xie, X., (2005) A Simulation Optimization methodology for supplier selection problem, International Journal of Computer Integrated Manufacturing, 18 (2-3), 210-224.


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