Multi-objective fuzzy inventory model with three constraints: a geometric programming approach

A multi-item multi-objective inventory model with shortages and demand dependent unit cost has been formulated along with storage space, number of orders and production cost restrictions. In most of the real world situations, the cost parameters, the objective functions and constraints of the decision makers are imprecise in nature. Hence the cost parameters, the objective functions and constraints are imposed here in fuzzy environment. This model has been solved by geometric programming method. The results for the model without shortages are obtained as a particular case. The sensitivity analysis has been discussed for the change of the cost parameters. The models are illustrated with numerical examples.

[1]  Cheng-Kang Chen,et al.  Optimal determination of quality level, selling quantity and purchasing price for intermediate firms , 2000 .

[2]  H. Zimmermann.  DESCRIPTION AND OPTIMIZATION OF FUZZY SYSTEMS , 1975 .

[3]  Adrijit Goswami,et al.  A Replenishment Policy for Items with Finite Production Rate and Fuzzy Deterioration Rate , 2001 .

[4]  B. Werners.  Interactive multiple objective programming subject to flexible constraints , 1987 .

[5]  Arthur F. Veinott,et al.  Analysis of Inventory Systems , 1963 .

[6]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[7]  Madan M. Gupta,et al.  Fuzzy mathematical models in engineering and management science , 1988 .

[8]  M. A. Hall,et al.  The analysis of an inventory control model using posynomial geometric programming , 1982 .

[9]  Cerry M. Klein,et al.  Optimal inventory policies under decreasing cost functions via geometric programming , 2001, Eur. J. Oper. Res..

[10]  Ronald R. Yager,et al.  A procedure for ordering fuzzy subsets of the unit interval , 1981, Inf. Sci..

[11]  Manoranjan Maiti,et al.  A fuzzy EOQ model with demand-dependent unit cost under limited storage capacity , 1997 .

[12]  Richard Bellman,et al.  Decision-making in fuzzy environment , 2012 .

[13]  M. Abou-El-Ata,et al.  Multi-item EOQ inventory model with varying holding cost under two restrictions: A geometric programming approach , 1997 .

[14]  Nicholas R. Jennings,et al.  Prioritised fuzzy constraint satisfaction problems: axioms, instantiation and validation , 2003, Fuzzy Sets Syst..

[15]  Hideo Tanaka,et al.  On Fuzzy-Mathematical Programming , 1973 .

[16]  G. Bortolan,et al.  A review of some methods for ranking fuzzy subsets , 1985 .

[17]  Mao-Jiun J. Wang,et al.  Ranking fuzzy numbers with integral value , 1992 .

[18]  Manoranjan Maiti,et al.  Multi-item inventory model with quantity-dependent inventory costs and demand-dependent unit cost under imprecise objective and restrictions: A geometric programming approach , 2000 .

[19]  Mona F. El-Wakeel,et al.  Probabilistic multi-item inventory model with varying order cost under two restrictions: A geometric programming approach , 2003 .

[20]  T.C.E. Cheng.  An economic order quantity model with demand-dependent unit cost , 1989 .

[21]  K. S. Park,et al.  Fuzzy-set theoretic interpretation of economic order quantity , 1987, IEEE Transactions on Systems, Man, and Cybernetics.

[22]  Graham K. Rand,et al.  Decision Systems for Inventory Management and Production Planning , 1979 .

[23]  R. Tiwari,et al.  Fuzzy goal programming- an additive model , 1987 .

[24]  A. Hariri,et al.  Multi-item production lot-size inventory model with varying order cost under a restriction: A geometric programming approach , 1997 .

[25]  J. J. Saade,et al.  Ordering fuzzy sets over the real line: an approach based on decision making under uncertainty , 1992 .

[26]  Clarence Zener,et al.  Geometric Programming : Theory and Application , 1967 .

[27]  D. Dubois,et al.  A unified view of ranking techniques for fuzzy numbers , 1999, FUZZ-IEEE'99. 1999 IEEE International Fuzzy Systems. Conference Proceedings (Cat. No.99CH36315).

[28]  R JenningsNicholas,et al.  Prioritised fuzzy constraint satisfaction problems , 2003 .