Fuzzy Inventory Model for Time Dependent Deterioration with Quadratic Demand
Abstract
This paper investigates a fuzzy inventory model designed for deteriorating items with a time-dependent deterioration rate and a quadratic demand rate, while assuming no shortages. To address uncertainties inherent in inventory systems, the model utilizes fuzzy set theory, employing hexagonal fuzzy numbers as decision variables. The graded mean integration representation (GMIR) approach is applied to defuzzify these variables, enabling the determination of the optimal inventory strategy in a fuzzy environment. The primary objective is to minimize the total inventory cost per unit time by accounting for dynamic demand and deterioration rates. A numerical example is presented to demonstrate the methodology, and sensitivity analysis is performed to evaluate the impact of various parameters on cost and cycle time. Results indicate that the fuzzy model achieves a 2.6% cost reduction compared to a crisp model, showcasing its efficiency and adaptability. These findings underscore the model’s relevance for industries managing perishable goods, offering a robust framework for cost optimization under uncertain conditions.
References
1. A. Kalam; D. Samal; S.K. Sahu and M. Mishra; A Production Lot-size Inventory Model for Weibull Deteriorating Item with Quadratic Demand, Quadratic Production and Shortages. International Journal of Computer Science & Communication, 1(1), 259–262 (2010).
2. A. Limi; K. Rangarajan; P. Rajadurai; A. Akilbasha and K. Parameswari; Three Warehouse Inventory Model for Non-Instantaneous Deteriorating Items with Quadratic Demand, Time-Varying Holding Costs and Backlogging Over Finite Time Horizon. Ain Shams Engineering Journal, 15(7), p. 102826 (2024).
3. C.K. Sivashankari; Purchasing Inventory Models for Deteriorating Items with Quadratic Demand. Jurnal Teknik Industri, 20(2), 204–217 (2019).
4. D. Singh; M.G. Alharbi; A. Jayswal and A.A. Shaikh; Analysis of Inventory Model for Quadratic Demand with Three Levels of Production. Intelligent Automation & Soft Computing, 32(1), 167–182 (2022).
5. K. Singh and A.K. Saxena; 2023. Inventory Model for Quadratic Demand and Deteriorating Items Following Weibull Distribution with Trade Credit Policy. Ratio Mathematica 48, 497-515 (2023).
6. M.L. Malumfashi; M.T. Ismail and M.K.M. Ali; An EPQ Model for Delayed Deteriorating Items with Two-Phase Production Period, Exponential Demand Rate and Linear Holding Cost. Bulletin of the Malaysian Mathematical Sciences Society, 45 (Supp. 1), 395–424 (2022).
7. Md. A. Rahman and M.F. Uddin; Analysis of Inventory Model with Time Dependent Quadratic Demand Function Including Time Variable Deterioration Rate without Shortage. Asian Research Journal of Mathematics, 16(12), 97–109 (2021).
8. N.H. Shah; Three-layered Integrated Inventory Model for Deteriorating Items with Quadratic Demand and Two-level Trade Credit Financing. International Journal of Systems Science: Operations & Logistics, 4(2), 85–91 (2017).
9. P. Chaudhary and T. Kumar (2022); Intuitionistic Fuzzy Inventory Model with Quadratic Demand Rate, Time-Dependent Holding Cost and Shortages. Journal of Physics: Conference Series, International Conference on Innovation and Application in Science and Technology (ICIAST 2021), Greater Noida, India, Vol. 2223, p. 012003.
10.R. Begum; S.K. Sahu and R.R. Sahoo; An Inventory Model for Deteriorating Items with Quadratic Demand and Partial Backlogging. British Journal of Applied Science & Technology, 2(2), 112–131 (2012).
11. R. Patro; M. Acharya; M.M. Nayak; S. Patnaik; A Fuzzy Inventory Model with Time Dependent Weibull Deterioration, Quadratic Demand and Partial Backlogging. International Journal of Management and Decision Making, 16(3), 243–279 (2017).
12.R.I.P. Setiawan; J.D. Lesmono and T. Limansyah (2021); Inventory Control Problems with Exponential and Quadratic Demand considering Weibull Deterioration. Journal of Physics: Conference Series. Presented at the Journal of Physics Conference Series, p. 012057.
13. R.K. Yadav and A.K. Vats; A Deteriorating Inventory Model for Quadratic Demand and Constant Holding Cost with Partial Backlogging and Inflation. IOSR Journal of Mathematics 10(3), 47–52 (2014).
14.S. Gite; An EOQ Model for Deteriorating Item with Quadratic Time Demand Rate under Permissible Delay in Payment. International Journal of Statistika and Mathematika, 6(2), 51–55 (2013).
15.S. Khanra; S.K. Ghosh and K.S. Chaudhuri; An EOQ Model for a Deteriorating Item with Time Dependent Quadratic Demand under Permissible Delay in Payment. Applied Mathematics and Computation, 218(1), 1–9 (2011).
16.S.K. Ghosh and K.S. Chaudhuri; An EOQ Model with a Quadratic Demand, Time-Proportional Deterioration and Shortages in All Cycles. International Journal of Systems Science, 37(10), 663–672 (2006).
17. S.K. Ghosh and K.S. Chaudhuri; An Order-level Inventory Model for a Deteriorating Item with Weibull Distribution Deterioration, Time-Quadratic Demand and Shortages. Advanced Modelling and Optimization, 6(1), 21–35 (2004).
18.T. Sarkar; S.K. Ghosh and K.S. Chaudhuri; An Optimal Inventory Replenishment Policy for a Deteriorating Item with Time-Quadratic Demand and Time-dependent Partial Backlogging with Shortages in all cycles. Applied Mathematics and Computation, 218(18), 9147–9155 (2012).
19. U. Mishra; An EOQ Model with Time Dependent Weibull Deterioration, Quadratic Demand and Partial Backlogging. International Journal of Applied and Computational Mathematics, 2, 545–563 (2016).
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