*Periodicity.:*

**May - June 2020***e-ISSN......:*

**2236-269X**### Multi objective fuzzy inventory model with deterioration, price and time dependent demand and time dependent holding cost

#### Abstract

In this paper, we have formulated an inventory model with time dependent holding cost, selling price as well as time dependent demand. Multi-item inventory model has been considered under limitation on storage space. Due to uncertainty all the require cost parameters are taken as generalized trapezoidal fuzzy number. Our proposed multi-objective inventory model has been solved by using fuzzy programming techniques which are FNLP, FAGP, WFNLP and WFAGP methods. A numerical example is provided to demonstrate the application of the model. Finally to illustrate the model and sensitivity analysis and graphical representation have been shown.

#### Keywords

#### References

ALFARES, H. K.; GHAITHAN, A. M. (2016) Inventory and Pricing Model with Price-Dependent Demand, Time-Varying Holding Cost, and Quantity Discounts, Computers & Industrial Engineering, doi: http://dx.doi.org/10.1016/j.cie.2016.02.009

BHUNIA, A. K.; SHAIKH, A. A. (2014) A deterministic inventory model for deteriorating items with selling price dependent demand and three-parameter Weibull distributed deterioration, International Journal of Industrial Engineering Computations, n. 5, p. 497–510

BORTOLAN, G.; DEGANI R. (1985) A review of some methods for ranking fuzzy numbers, Fuzzy Sets and Systems, n. 15, p. 1–19.

COVERT, R. P.; PHILIP, G. C. (1973) An EOQ model for items with Weibull distribution deterioration. AIIE Transaction, n. 5, p. 323–326.

GHARE, P. M.; SCHRADER, G. H. (1963) A model for exponentially decaying inventory system. International Journal of Production Research, n. 21, p. 449–460.

GHOSH, S. K.; SARKAR , T.; CHAUDHURI, K. (2015) A Multi-Item Inventory Model for Deteriorating Items in Limited Storage Space with Stock-Dependent Demand, American Journal of Mathematical and Management Sciences, v. 34, n. 2, p. 147-161, DOI: 10.1080/01966324.2014.980870.

HARRI, F. W. (1913) How many parts to make at once factory, Mag. Mannage., n. 10, p.135-136.

ISLAMM, S.; ROY, T. K. (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, v. 176, n. 2, p. 531-544.

ISLAMM, S.; MANDAL, W. A. (2017) A Fuzzy Inventory Model (EOQ Model) with Unit Production Cost, Time Depended Holding Cost, Without Shortages Under a Space Constrain: A Fuzzy Parametric Geometric Programming (FPGP) Approach, Independent Journal of Management Production, v. 8, n. 2, p. 299–318. DOI: dx.doi.org/10.14807/ijmp.v8i2.535.

ISLAMM, S.; MONDAL, W. A. (2017) Fuzzy E.O.Q Model with Constant Demand and Shortages: A Fuzzy Signomial Geometric Programming (FSGP) Apprach, Independent Journal Of Management & Production, v. 8, n. 4, p. 1191-1209.

KUMAR, S.; SINGH, A. K.; PATEL, M. K. (2016) Optimization of Weibull deteriorating items inventory model under the effect of price and time dependent demand with partial backlogging, Sadhana, v. 41, DOI 10.1007/s12046-016-0533-4

LIANG, Y.; ZHOU, F. (2011) A two warehouse inventory model for deteriorating items under conditionally permissible delay in Payment, Appl. Math. Model, n. 35, p. 2221-2231.

LIOU T. S.; WANG, M. J. (1992) Ranking fuzzy numbers with integral value, Fuzzy Sets and Systems, n. 50, p. 247–255.

MAITY, M. K. (2008) Fuzzy inventory model with two ware house under possibility measure in fuzzy goal, Euro. J Oper. Res, n. 188, p. 746-774.

MOMDAL, B.; BHUNIA, A. K.; MAITI, M. (2003) An inventory system of ameliorating items for price dependent demand rate. Computers and Industrial Engineering, n. 45, p. 443–456.

ROY, A. (2014) Fuzzy inventory model for deteriorating items with price dependent demand, International Journal of Management Science and Engineering Management, DOI: 10.1080/17509653.2014.959086.

ROY, T. K.; MAITY, M. (1995) A fuzzy inventory model with constraints, Operation research, v. 32, n. 4, p.287- 298.

SHAH, N. H.; SHAH, B. J.; WEE, H. M. (2009) A lot size inventory model for the Weibull distributed deterioration rate with discounted selling price and stock-dependent demand, Int. J. Data Analysis Techniques and Strategies, v. 1, n. 4, p. 355–363.

SRIDEVI, G.; NIRUPAMA DEVI, K.; SRINIVASA RAO, K. (2010) Inventory model for deteriorating items with Weibull rate of replenishment and selling price dependent demand, Int. J. Operational Research, v. 9, n. 3, p. 329–349.

YANG, H. L. (2016) Two Warehouse Partial Backlogging inventory model for deteriorating items under inflation, International Journal of Production Economics, n. 103, p. 362-370.

YU-CHUNG TSAO, GWO-JI-SHEEN (2008) Dynamic pricing promotion and replenishment policies for a deteriorating item under permissible delay in payments, Computer & operation research, n. 35, p. 3562-3580.

ZADEH, L. A. (1965) Fuzzy sets, Information and Control, n. 8, p. 338-353.

ZIMMERMANN, H. J. (1985) Application of fuzzy set theory to mathematical programming, Information Science, n. 36, p. 29-58.

ZIMMERMANN, H. J. (1992) Methods and applications of Fuzzy Mathematical programming, in An introduction to Fuzzy Logic Application in Intelligent Systems, p. 97- 120, Kluwer publishers, Boston.

DOI: http://dx.doi.org/10.14807/ijmp.v11i3.1083

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