TY - JOUR T1 - A fuzzy inventory model with unit production cost, time depended holding cost, with-out shortages under a space constraint: a parametric geometric programming approach AU - Mandal, Wasim Akram AU - Islam, Sahidul PY - 2017 DA - October JF - New Trends in Mathematical Sciences PB - Mustafa BAYRAM WT - DergiPark SN - 2147-5520 SP - 40 EP - 51 VL - 5 IS - 4 LA - en AB - In thispaper, an Inventory model with unit production cost, time depended holdingcost, with-out shortages is formulated and solved. We have considered a singleobjective structural optimization model. In most real world situation, theobjective and constraint function of the decision makers are imprecise innature. Hence the coefficients, indices, the objective function and constraintgoals are imposed here in fuzzy environment. Geometric programming provides apowerful tool for solving a variety of imprecise optimization problems. Here weuse nearest interval approximation method to convert a triangular fuzzy numberto an interval number. In this paper, we transform this interval number to aparametric interval-valued functional form and then solve the parametricproblem by geometric programming technique. Numerical example is given toillustrate the model through this Parametric Geometric-Programming method. KW - Inventory model KW - fuzzy number KW - space constraint KW - geometric programming CR - Bellman, R.E, and Zadeh (1970), Decision making in a fuzzy environment, Management Science 17, B141-B164. CR - Carlsson, C. and P. Korhonen (1986), A parametric approach to fuzzy linear programming, Fuzzy sets and systems, 17-30. CR - Clark, A.J, (1992), An informal survey of multy-echelon inventory theory , naval research logistics Quarterly 19, 621-650. CR - 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. CR - 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. CR - Duffin,R.J., Peterson,E.L. & Zener,C.M. (1967).Geometric programming- theory and applications. Wiley, New York. CR - Hamacher, H.Leberling and H.J.Zimmermann (1978), Sensitivity Analysis in fuzzy linear Programming Fuzzy sets and systems 1, 269-281. CR - Hadley, G. and T.M. White (1963),Analysis of inventory system, Prentice-Hall, Englewood Cliffs, NJ. CR - 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. CR - 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. CR - Li,H.X. and Yen, V.C. (1995), Fuzzy Sets and Fuzzy decision making, CRC press, London. CR - M.K.Maity (2008), Fuzzy inventory model with two ware house under possibility measure in fuzzy goal, Euro.J.Oper. Res 188,746-774. CR - Raymond, F.E (1931), Quantity and Economic in manufacturing, McGraw-Hill, New York. CR - 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. CR - S. Islam, T.K. Roy (2010), Multi-Objective Geometric-Programming Problem and its Application. Yugoslav Journal of Operations Research,20,213-227. CR - S.T.Liu (2006), Posynomial Geometric-Programming with interval exponents and co-efficients, Europian Journal of Operations Research,168(2006), no.2, 345-353. CR - T.K. Roy and M. Maity (1995), A fuzzy inventory model with constraints, Opsearch, 32(4) (1995) 287-298. CR - 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. CR - Zadeh, L.A (1965), Fuzzy sets, Information and Control, 8, 338-353. CR - Zimmermann, H.J.(1985),Application of fuzzy set theory to mathematical programming, Information Science, 36, 29-58. CR - 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. UR - http://dergipark.org.tr/tr/pub/ntims/issue//547865 L1 - http://dergipark.org.tr/tr/download/article-file/685395 ER -