A fuzzy inventory model with unit production cost, time depended holding cost, with-out shortages under a space constraint: a parametric geometric programming approach

Abstract

In this paper, an Inventory model with unit production cost, time depended holding cost, with-out shortages is formulated and solved. We have considered a single objective structural optimization model. In most real world situation, the objective and constraint function of the decision makers are imprecise in nature. Hence the coefficients, indices, the objective function and constraint goals are imposed here in fuzzy environment. Geometric programming provides a powerful tool for solving a variety of imprecise optimization problems. Here we use nearest interval approximation method to convert a triangular fuzzy number to an interval number. In this paper, we transform this interval number to a parametric interval-valued functional form and then solve the parametric problem by geometric programming technique. Numerical example is given to illustrate the model through this Parametric Geometric-Programming method.

Keywords

• Inventory model,fuzzy number,space constraint,geometric programming

References

1. Bellman, R.E, and Zadeh (1970), Decision making in a fuzzy environment, Management Science 17, B141-B164.
2. Carlsson, C. and P. Korhonen (1986), A parametric approach to fuzzy linear programming, Fuzzy sets and systems, 17-30.
3. Clark, A.J, (1992), An informal survey of multy-echelon inventory theory , naval research logistics Quarterly 19, 621-650.
4. D.Dutta and Pavan Kumar (2012), Fuzzy inventory without shortages using trapezoidal fuzzy number with sensitivity analysis IOSR Journal of mathematics , Vol. 4(3), 32-37.
5. Dutta, D.J.R. Rao, and R.N Tiwary (1993), Effect of tolerance in fuzzy linear fractional programming, fuzzy sets and systems 55, 133-142.
6. Duffin,R.J., Peterson,E.L. & Zener,C.M. (1967).Geometric programming- theory and applications. Wiley, New York.
7. Hamacher, H.Leberling and H.J.Zimmermann (1978), Sensitivity Analysis in fuzzy linear Programming Fuzzy sets and systems 1, 269-281.
8. Hadley, G. and T.M. White (1963),Analysis of inventory system, Prentice-Hall, Englewood Cliffs, NJ.

9. Kotb A.M Kotb, Hala A.Fergancy (2011), Multi-item EOQ model with both demand-depended unit cost and varying Leadtime via Geometric Programming, Applied mathematics, 2011, 2, 551-555.
10. Khun, H.W and A.W. Tucker (1951), Non-linear programming, proceeding second Berkeley symposium Mathematical Statistic and probability (ed) Nyman ,J.University of California press 481-492.
11. Li,H.X. and Yen, V.C. (1995), Fuzzy Sets and Fuzzy decision making, CRC press, London.
12. M.K.Maity (2008), Fuzzy inventory model with two ware house under possibility measure in fuzzy goal, Euro.J.Oper. Res 188,746-774.
13. Raymond, F.E (1931), Quantity and Economic in manufacturing, McGraw-Hill, New York.
14. S. Islam, T.K. Roy (2006), A fuzzy EPQ model with flexibility and reliability consideration and demand depended unit Production cost under a space constraint: A fuzzy geometric programming approach, Applied Mathematics and Computation vol. 176(2), 531-544.
15. S. Islam, T.K. Roy (2010), Multi-Objective Geometric-Programming Problem and its Application. Yugoslav Journal of Operations Research,20,213-227.
16. S.T.Liu (2006), Posynomial Geometric-Programming with interval exponents and co-efficients, Europian Journal of Operations Research,168(2006), no.2, 345-353.
17. T.K. Roy and M. Maity (1995), A fuzzy inventory model with constraints, Opsearch, 32(4) (1995) 287-298.
18. Y.Liang, F.Zhou (2011), A two warehouse inventory model for deteriorating items under conditionally permissible delay in Payment, Appl. Math. Model.35, 2221-2231.
19. Zadeh, L.A (1965), Fuzzy sets, Information and Control, 8, 338-353.
20. Zimmermann, H.J.(1985),Application of fuzzy set theory to mathematical programming, Information Science, 36, 29-58.
21. Zimmermann, H.J.(1992), "Methods and applications of Fuzzy Mathematical programming", in An introduction to Fuzzy Logic Application in Intelligent Systems (R.R. Yager and L.A.Zadeh, eds), pp.97- 120, Kluwer publishers, Boston.