A Deterministic Inventory Model for Deteriorating 
Items with Biquadratic Demand, Constant Deterioration 
Rate and Salvage Value

M. Pradeepa; S. Sobia; M. Valliathal

doi:https://doi.org/10.14445/22315373/IJMTT-V71I9P103

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 71 | Issue 9 | Year 2025 | Article Id. IJMTT-V71I9P103 | DOI : https://doi.org/10.14445/22315373/IJMTT-V71I9P103

A Deterministic Inventory Model for Deteriorating Items with Biquadratic Demand, Constant Deterioration Rate and Salvage Value

M. Pradeepa, S. Sobia, M. Valliathal

Received	Revised	Accepted	Published
14 Jul 2025	16 Aug 2025	04 Sep 2025	18 Sep 2025

Citation :

M. Pradeepa, S. Sobia, M. Valliathal, "A Deterministic Inventory Model for Deteriorating Items with Biquadratic Demand, Constant Deterioration Rate and Salvage Value," International Journal of Mathematics Trends and Technology (IJMTT), vol. 71, no. 9, pp. 17-31, 2025. Crossref, https://doi.org/10.14445/22315373/IJMTT-V71I9P103

Abstract

A deterministic inventory model is designed for the study to focus on deteriorating items with biquadratic demand, constant deterioration rate, and salvage value. The model works towards optimizing inventory levels to maximize Profit by efficiently managing perishable products. The study provides analytical solutions and numerical examples to showcase the practical application of the model in inventory management. In addition, the sensitivity analysis further explores the impact of the essential parameters in inventory management, highlighting the real-world applicability of the model.

Keywords

Inventory, Deterioration, Demand, Profit, Salvage Value.

References

[1] P.M. Ghare, and G.F. Schrader, “A Model for an Exponentially Decaying Inventory,” Journal of Industrial Engineering, vol. 14, no. 5, pp. 238-243, 1963.
[Google Scholar]
[2] Richard P. Covert, and George C. Philip, “An EOQ Model for Items with Weibull Distribution Deterioration,” AIIE Transactions, vol. 5, no. 4, pp. 323-326, 1973.
[CrossRef] [Google Scholar] [Publisher Link]
[3] Y.K. Shah, and M.C. Jaiswal, “An Order-level Inventory Model for a System with Constant Rate of Deterioration,” Opsearch, vol. 14, no. 3, pp. 174-184, 1977.
[Google Scholar]
[4] Upendra Dave, and L.K. Patel, “(T,Si) Policy Inventory Model for Deteriorating Items with Time Proportional Demand,” Journal of the Operational Research Society, vol. 32, no. 2, pp. 137-142, 1981.
[CrossRef] [Google Scholar] [Publisher Link]
[5] R.H. Hollier, and K.L. Mak, “Inventory Replenishment Policies for Deteriorating Items in a Declining Market,” International Journal of Production Research, vol. 21, no. 6, pp. 813-836, 1983.
[CrossRef] [Google Scholar] [Publisher Link]
[6] Adrijit Goswami, and K. S. Chaudhuri, “An EOQ Model for Deteriorating Items with Shortages and a Linear Trend in Demand,” The Journal of the Operational Research Society, vol. 42, no. 12, pp. 1105-1110, 1991.
[CrossRef] [Google Scholar] [Publisher Link]
[7] S.K. Goyal, and B.C. Giri, “Recent Trends in Modeling of Deteriorating Inventory,” European Journal of Operational Research, vol. 134, no. 1, pp. 1-16, 2001.
[CrossRef] [Google Scholar] [Publisher Link]
[8] Poonam Mishra, and Nita H. Shah “Inventory Management of Time Dependent Deteriorating Items with Salvage Value,” Applied Mathematical Sciences, vol. 2, no. 16, pp. 793-798, 2008.
[Google Scholar] [Publisher Link]
[9] R. Venkateswarlu, and R. Mohan, “An Inventory Model with Quadratic Demand, Constant Deterioration and Salvage Value,” Research Journal of Mathematical and Statistical Sciences, vol. 2, no. 1, pp. 1-5, 2014.
[Google Scholar] [Publisher Link]
[10] Mishra Vinod Kumar, “Controllable Deterioration Rate for Time-Dependent Demand and Time-Varying Holding Cost,” Yugoslav Journal of Operations Research, vol. 24, no. 1, pp. 87-98, 2014.
[CrossRef] [Google Scholar] [Publisher Link]
[11] Parmar Kirtan, and U.B. Gothi, “EOQ Model with Constant Deterioration Rate and Time Dependent Demand and IHC,” Pacific Business Review International, vol. 7, no. 12, pp. 1-11, 2015.
[Google Scholar] [Publisher Link]
[12] K. Karthikeyan, and G. Shanthi, “An Inventory Model for Constant Deteriorating Items with Cubic Demand and Salvage Value,” International Journal of Applied Engineering Research, vol. 10, no. 55, pp. 3723-3728, 2015.
[Google Scholar]
[13] R.P. Tripathi, and Shweta Singh Tomar, “Establishment of EOQ Model with Quadratic Time-sensitive Demand and Parabolic-time Linked Holding Cost with Salvage Value,” International Journal of Operations Research, vol. 15, no. 3, pp. 135-144, 2018.
[CrossRef] [Google Scholar] [Publisher Link]
[14] Pavan Kumar, “An Inventory Planning Problem for Time-varying Linear Demand and Parabolic Holding Cost with Salvage Value,” Croatian Operational Research Review, vol. 10, no. 2, pp. 187-199, 2019.
[Google Scholar] [Publisher Link]
[15] Atiqur Rahman, and Mohammed Forhad Uddin, “Analysis of Inventory Model with Time Dependent Quadratic Demand Function Including Time Variable Deterioration Rate without Shortage,” Asian Research Journal of Mathematics, vol. 16, no. 12, pp. 97 109, 2020.
[CrossRef] [Google Scholar] [Publisher Link]
[16] I. Aliyu, and B. Sani, “An Inventory Model for Deteriorating Items with a Generalised Exponential Increasing Demand, Constant Holding Cost and Constant Deterioration Rate,” Applied Mathematical Sciences, vol. 14, no. 15, pp. 725-736, 2020.
[CrossRef] [Google Scholar] [Publisher Link]
[17] Suman, and Vinod Kumar, “Analytical Study of Deterministic Inventory Model with Consideration of Biquadratic Demand Rate and Weibull Distribution as Deterioration Rate,” International Journal of Innovative Research in Technology, vol. 9, no. 4, pp. 642 651, 2022.
[Publisher Link]
[18] Pooja Soni, and Rajender Kumar, “A Deterministic Inventory Model with Biquadratic Demand Variable Deterioration Rate and Carrying Cost,” Turkish Online Journal of Qualitative Inquiry, vol. 13, no. 1, pp. 1530-1538, 2022.
[Google Scholar]
[19] Karan Pathak, Ajay Singh Yadav, and Priyanka Agarwal, “Optimizing Two-warehouse Inventory for Shelf- Life Stock with Time varying Biquadratic Demand under Shortages and Inflation,” Mathematical Modelling of Engineering Problems, vol. 11, no. 2, pp. 446-456, 2024.
[CrossRef] [Google Scholar] [Publisher Link]