Inventory Model for Quadratic Demand and Deteriorating Items Following Weibull Distribution with Trade Credit Policy

Khyati Singh, Ashendra Kumar Saxena


In this paper, an inventory model for deteriorating items following two parameter Weibull distribution with trade credit policy is developed, while demand is viewed as quadratic function of time. The supplier gives the retailer a trade credit period. Trade credit is a frequently used method of payment implemented by suppliers, and it generally leads to greater revenue and ultimately, higher income. The suggested inventory model seeks to calculate the ideal replenishment cycle duration in order to maximize the overall profit per unit of time.  Shortages are permitted and partially backlogged. Two categories are applied to the mathematical model. Case I: When the payment to settle the account is made on or before the positive inventory. Case II: When the payment to settle the ac-count is made after the inventory reaches to zero. The model is illustrated through numerical experiments, sensitivity analysis, and graphical depiction.


Inventory; Quadratic Demand; Deterioration; Weibull Distribution; Trade Credit.

Full Text:



Chowdhury, R. R., Ghosh, S. K., & Chaudhuri, K. S. (2015). An inventory model for deteriorating items with stock and price sensitive demand. International Journal of Applied and Computational Mathematics, 1, 187-201.

Karthikeyan, K., & Santhi, G. (2015). An inventory model for constant deteriorating items with cubic demand and salvage value. International Journal of Applied Engineering Research, 10(55), 0973-4562.

Lakshmidevi, P. K., & Maragatham, M. (2015). An inventory model with three rates of production and time dependent deterioration rate for quadratic demand rate. International Journal of Fuzzy Mathematical Archive, 6(1), 99-103.

Saha, S., & Sen, N. (2017). A study on inventory model with negative exponential demand and probabilistic deterioration under backlogging. Uncertain supply chain management, 5(2), 77-88.

Kumar, S., (2017). Development of an EOQ Inventory Model for Perishable Items with Exponentially Decaying Demand, Shortages and Partial Backlogging. International Journal for Research in Applied Science & Engineering Technology, ISSN: 2321-9653.

Aggrawal, P., & Singh, T. J. (2017). An EOQ model with ramp type demand rate, time dependent deterioration rate and shortages. Global Journal of Pure and Applied Mathematics, 13(7), 3381-3393.

Mahata, G. C., & De, S. K. (2017). Supply chain inventory model for deteriorating items with maximum lifetime and partial trade credit to credit-risk customers. International Journal of Management Science and Engineering Management, 12(1), 21-32.

Mishra, U., & Tripathy, C. K. (2015). An inventory model for Weibull deteriorating items with salvage value. International Journal of Logistics Systems and Management, 22(1), 67-76.

Udayakumar, R., & Geetha, K. V. (2018). An EOQ model for non-instantaneous deteriorating items with two levels of storage under trade credit policy. Journal of Industrial Engineering International, 14, 343-365.

Bishi, B., & Sahu, S. K. (2018). An inventory model for deteriorating items with quadratic demand and partial backlogging. Journal of computer and Mathematical Sciences, 9(12), 2188-2198.

Chitra, D. (2019). Replenishment Policy for Non instantaneous Deteriorating Items with Parabolic demand Pattern and partial backlogging for Queued Customers: Computational Approach. International Journal of Applied Engineering Research, 14(8), 1818-1827.

Mandal, B. (2020). An EOQ Inventory Model for Time-varying Deteriorating Items with Cubic Demand under Salvage Value and Shortages. International Journal of Systems Science and Applied Mathematics, 5(4), 36-42.

Khatri, P. D., & Gothi, U. B. (2020) An EPQ Model for Non-Instantaneous Weibully Decaying Items with Ramp Type Demand and Partially Backlogged Shortages.

Cárdenas-Barrón, L. E., Shaikh, A. A., Tiwari, S., & Treviño-Garza, G. (2020). An EOQ inventory model with nonlinear stock dependent holding cost, nonlinear stock dependent demand and trade credit. Computers & Industrial Engineering, 139, 105557.

Sharma, Ashish & Kaushik, Jitendra. (2021). Inventory model for deteriorating items with ramp type demand under permissible delay in payment. International Journal of Procurement Management. 14. 578. 10.1504/IJPM.2021.117292

Maryam Esmaeili & Mehri Nasrabadi (2021) An inventory model for single - vendor multi - retailer supply chain under inflationary conditions and trade credit, Journal of Industrial and Production Engineering, 38:2, 75-88, DOI: 10.1080/21681015.2020.1845248

Khyati and A. K. Saxena, Review on EOQ Models for Instanteneous and Non-Instanteneous Deteriorating Items, 2021 10th International Conference on System Modeling and Advancement in Research Trends (SMART), MORADABAD, India, 2021, pp. 312–315, doi:10.1109/SMART52563.2021.9676264.

Khyati and A. K. Saxena, "An EOQ Model for Deteriorating Items with Time Dependent Demand," 2022 11th International Conference on System Modeling & Advancement in Research Trends (SMART), Moradabad, India, 2022, pp. 926-930

Saxena, A. K., and Yadav, R. K. (2011, December). Ordering Policy For Non Instantaneous Decaying Items With Stock Dependent Demand and Shortages. In Proceedings of the International Conference on Soft Computing for Problem Solving (SocProS 2011) (pp. 497–513).

Shaikh, A. A., Panda, G. C., Khan, M. A. A., Mashud, A. H. M., & Biswas, A. (2020). An inventory model for deteriorating items with preservation facility of ramp type demand and trade credit. International Journal of Mathematics in Operational Research, 17(4), 514-551.

Khakzad, A., & Gholamian, M. R. (2020). The effect of inspection on deterioration rate: An inventory model for deteriorating items with advanced payment. Journal of cleaner production, 254, 120117,

Duary, A., Das, S., Arif, M. G., Abualnaja, K. M., Khan, M. A. A., Zakarya, M., & Shaikh, A. A. (2022). Advance and delay in payments with the price-discount inventory model for deteriorating items under capacity constraint and partially backlogged shortages. Alexandria Engineering Journal, 61(2), 1735-1745.

Kumari, M., Narang, P., & De, P. K. (2023). Optimization of an Inventory Model with Selling Price and Stock Sensitive Demand Along with Trade Credit Policy. In Soft Computing: Theories and Applications: Proceedings of SoCTA 2022 (pp. 47-57). Singapore: Springer Nature Singapore.



  • There are currently no refbacks.

Copyright (c) 2023 Khyati Singh, Ashendra Kumar Saxena

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.