The objective is to develop a model considering demand dependent on selling price and deterioration occurs after a certain period of time, which follows two-parameter Weibull distribution. Shortages are allowed and fully backlogged. Fuzzy optimal solution is obtained by considering hexagonal fuzzy numbers and for defuzzification Graded Mean Integration Representation Method. A numerical example is provided for the illustration of crisp and fuzzy, both models. To observe the effect of changes in parameters, sensitivity analysis is carried out.
References
[1]
Whitin, T.M. (1957) Theory of Inventory Management. Princeton University Press, Princeton.
[2]
Ghare, P.M. and Scharder, G.P. (1963) A Model for an Exponentially Decaying Inventory. Journal of Industrial Engineering, 14, 238-243.
[3]
Covert, R.P. and Philip, G.C. (1973) An EOQ Model for Items with Weibull Distribution Deterioration. AIIE Transactions, 5, 323-326. https://doi.org/10.1080/05695557308974918
[4]
Datta, T.K. and Pal, A.K. (1988) Order Level Inventory System with Power Demand Pattern for Items with Variable Rate of Deterioration. Indian Journal of Pure and Applied Mathematics, 19, 1043-1053.
[5]
Giri, B.C. and Chaudhuri, K.S. (1998) Deterministic Models of Perishable Inventory with Stock-Dependent Demand Rate and Nonlinear Holding Cost. European Journal of Operational Research, 105, 467-474. https://doi.org/10.1016/S0377-2217(97)00086-6
[6]
Ouyang, L.Y., Hsieh, T.P., Dye, C.Y. and Chang, H.C. (2003) An Inventory Model for Deteriorating Items with Stock-Dependent Demand under the Conditions of Inflation and Time-Value of Money. The Engineering Economist, 48, 52-68. https://doi.org/10.1080/00137910308965051
[7]
Mishra, V.K. (2013) An Inventory Model of Instantaneous Deteriorating Items with Controllable Deterioration Rate for Time Dependent Demand and Holding Cost. Journal of Industrial Engineering and Management, 6, 495-506. https://doi.org/10.3926/jiem.530
[8]
Sharma, V. and Chaudhary, R.R. (2013) An Inventory Model for Deteriorating Items with Weibull Deterioration with Time Dependent Demand and Shortages. Research Journal of Management Sciences, 2, 28-30.
[9]
Zhao, L. (2014) An Inventory Model under Trapezoidal Type Demand, Weibull-Distributed Deterioration, and Partial Backlogging. Journal of Applied Mathematics, 2014, Article ID: 747419. https://doi.org/10.1155/2014/747419
[10]
Uthayakumar, R. and Karuppasamy, S.K. (2019) An EOQ Model for Deteriorating Items with Different Types of Time-Varying Demand in Healthcare Industries. The Journal of Analysis, 27, 3-18. https://doi.org/10.1007/s41478-018-0100-y
[11]
Zadeh, L.A. (1965) Fuzzy Sets. Information and Control, 8, 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
[12]
Shekarian, E., Kazemi, N., Abdul-Rashid, S.H. and Olugu, E.U. (2017) Fuzzy Inventory Models: A Comprehensive Review. Applied Soft Computing, 55, 588-621. https://doi.org/10.1016/j.asoc.2017.01.013
[13]
Jaggi, C., Sharma, A. and Mandeep, M. (2012) A Fuzzy Inventory Model for Deteriorating Items with Initial Inspection and Allowable Shortage under the Condition of Permissible Delay in Payment. International Journal of Inventory Control and Management, 2, 167-200. https://doi.org/10.58517/IJICM.2012.2202
[14]
Kumar, S. and Rajput, U.S. (2015) Fuzzy Inventory Model for Deteriorating Items with Time Dependent Demand and Partial Backlogging. Applied Mathematics, 6, 496-509. https://doi.org/10.4236/am.2015.63047
[15]
Mandal, W.A. and Islam, S. (2016) Fuzzy E.O.Q. Model for Deteriorating Items, with Constant Demand, Shortages, and Fully Backlogging. Oxford Journal of Intelligent Decision and Data Science, 2016, 29-45.
[16]
Mohanty, B. and Tripathy, P.K. (2017) Fuzzy Inventory Model for Deteriorating Items with Exponentially Decreasing Demand under Fuzzified Cost and Partial Backlogging. International Journal of Mathematics Trends and Technology, 51, 182-189. https://doi.org/10.14445/22315373/IJMTT-V51P524
[17]
Sahoo, S., Acharya, M. and Nayak, M.M. (2019) A Three Rates of EOQ/EPQ Model for Instantaneous Deteriorating Items Involving Fuzzy Parameter under Shortages. International Journal of Innovative Technology and Exploring Engineering, 8, 405-418.
[18]
Biswas, A.K. and Islam, S. (2019) A Fuzzy EPQ Model for Non-Instantaneous Deteriorating Items Where Production Depends on Demand Which Is Proportional to Population, Selling Price as Well as Advertisement. Independent Journal of Management & Production, 10, 1679-1703. https://doi.org/10.14807/ijmp.v10i5.897
[19]
Indrajitsingha, S.K., Raula, P., Samanta, P., Misra, U. and Raju, L. (2021) An EOQ Model of Selling-Price-Dependent Demand for Non-Instantaneous Deteriorating Items during the Pandemic COVID-19. Walailak Journal of Science and Technology, 18, Article 13398. https://doi.org/10.48048/wjst.2021.13398
