An Optimal Reordering Inventory Policy for Deteriorating Products in Fuzzy Set Terminology
Keywords:
Fuzzy, Inventory, Deterioration, Inflation, Time discountAbstract
This research paper provides a replenishment model for unpreserved products with consideration of the time value of money under the fuzzy situation. This mathematical model follows the discounted cash flow approach to provide inventory replenishment difficulty over a fixed planning horizon. In this model, the authors have shown that the total variable cost is minimized without backlogging under a fuzzy environment. Numerical examples are given to reveal the applicability of the model with respect to the different parameters of the system. This model is developed for uncertain business houses where the businessman is totally dependent on the arrival of the order and the customer both; hence, we provided a solution in this paper for those types of business houses.
References
1. A. Kumari, A. K. Goyal, K. Kumar, and S. Agrawal, “Optimal Inventory Policy with Price-Dependent Demand and Variable Deterioration Rate also Delt with Trade Credit,” Soch Mastnath Journal of Sciences and Technology, 17(1), pp. 47- 59, 2022.
2. A. K. Bhunia and M. Maiti, “An inventory model of deteriorating items with lot-size dependent replenishment cost and a linear trend in demand,” Applied Mathematical Modelling 23, pp. 301-308, 1999.
3. A. Goswami and K. S. Chaudhuri, “An EOQ model for deteriorating item with shortages and a linear trend in demand”, J. Oper. Res. Soc. 42, pp. 1105-1110, 1991.
4. A. K. Goyal, “A replenishment policy for deteriorating items with order size dependent replenishment cost and time dependent demand,” Brazilian Journal of Development, 10(1), pp. 895-905, 2024
5. A. K. Goyal and A. Chauhan, “An EOQ Model for Deteriorating Items with Selling Price Dependent Demand Rate with Learning Effect,” Nonlinear Studies, 23(4), pp. 541-550, 2016.
6. A. K. Goyal, A. Chauhan, and S. R. Singh, “An EPQ model with stock dependent demand and time varying deterioration with shortages under inflationary environment,” International Journal of Agricultural and Statistical Sciences, 9(1), pp. 173-182, 2013.
7. A. K. Goyal, A. Chauhan, and S. Saini, “A Mathematical Inventory Model for Deteriorating Items with Stock and Selling Price Dependent Demand and Partial Backlogging,” “International Journal of Applied Science and Technology, 9(1), pp. 86-89, 2017.
8. A. K. Goyal and S. Agrawal, “A Production Inventory Model for Deteriorating Items with Price Dependent Demand Incorporated with Partially Backlogged Shortages,” “International Journal of Pure and Applied Mathematics,” 118(22), pp. 1209-1214, 2018.
9. A. K. Goyal, S. Agrawal, and K. Kumar, “A Production Inventory Model with Selling Price and Stock Sensitive Demand and Partial Backlogging,” “Soch Mastnath Journal of Sciences and Technology,” 13(1-4), pp. 29-40, 2018.
10. A. K. Goyal, S. Gupta, and S. R. Singh, “An EOQ Model for Deteriorating Items with Stock Dependent Demand and Effect of Learning” International Transactions in Applied Sciences, 4(4), pp. 563-566, 2012.
11. A. K. Goyal, S. Agrawal, and K. Kumar, “An EOQ model with Stock Dependent Demand and Partial Backlogging Under Inflation,” Soch Mastnath Journal of Sciences and Technology”, 12(1-4), pp. 35-45, 2017.
12. A. K. Goyal, S. Agrawal, and K. Kumar, “Supply Chain Model with Ramp Type Demand Under Planning Horizon,” “Soch Mastnath Journal of Sciences and Technology,” 11(1-4), pp, 21-34, 2016.
13. A. K. Goyal, A. Chauhan, S. Singh, and N. Kumar, “An inventory model for deteriorated items with exponential demand under trade credit,” Proceedings of the International Conference on Innovative Trends in Computing Technology &Mathematic, pp 35-39, 2015.
14. A. K. Goyal, A. Chauhan, and S. Singh, “An EOQ inventory model with stock and selling price dependent demand rate, partial backlogging and variable ordering cost”, International Journal of Agricultural and Statistical Sciences, 11(2), pp. 441-447, 2015.
15. B. C. Giri, T. Chakrabarty and K. S. Chaudhari, “A note on a lot sizing heuristic for deteriorating items with time-varying demands and shortages,” comps. & O.R. 27, pp. 495-505, 2000.
16. H. Patel, H. Soni and A. Gor, “Time Proportional Non-Instantaneous Deterioration Decisions for Vendor Managed Inventory System”, Applications and Applied Mathematics: An International Journal, Volume 20(3), pp. 1-24, 2025.
17. K. Skouri and S. Papachristos, “A continuous review inventory model, with deteriorating items, time varying demand, linear replenishment cost, partially time-varying backlogging,” Applied Mathematical Modelling 26, pp. 603-617, 2002.
18. P. Singh, A. Chauhan, and A. K. Goyal, "A relative study of crisp and fuzzy optimal reordering policy for perishable items,” “International Journal of Agricultural and Statistical Sciences,” 16(1), pp. 137-145, 2020.
19. S. K. Ghosh and K. S. Chaudhary, “An order level inventory model for a deteriorating item with weibull distribution deterioration, time-quadratic demand and shortages”, Advanced Modeling and Optimization, 6(1), 2004.
20. S. Sana and K. S. Chaudhary, “On a volume flexible production policy for a deteriorating item with time dependent demand and shortages,” Advanced Modeling and Optimization, 6(1), 2004.
21. T. Chakraborty, B. C. Giri and K. S. Chaudhary, “Production lot sizing with process deterioration and machine breakdown under inspection schedule”, Omega the Int. Jour. Of Mang. Sc. 37, pp. 257-271, 2009.
22. T. K. Datta and A. K. Pal, “A note on a replenishment policy for an inventory model with linear trend in demand and shortages,” J. Oper. Res. Soc. 43, pp. 993-1001, 1999.
Downloads
Published
Data Availability Statement
Data is collected from the public domain, accessible for all.
