International Journal of Science and Engineering

International Journal of Science and EngineeringJuly-Dec 2023 Vol:2 Issue:2

Effect of Multivariate Demand on an Inventory Model for Deteriorating Items with Trade Credit


Businesses that want to strike a balance between financial efficiency and customer happiness face the complex and crucial challenge of effective inventory management in the face of items that are deteriorating and susceptible to time- and price-dependent demand. This paper investigates an innovative financial method that uses trade credit to address this problem. The goal is to identify the ideal order quantity and replenishment intervals that balance meeting client demand with reducing overall costs. The model takes into consideration seasonality and price fluctuations when considering degrading goods subject to fluctuating demand patterns. Generally, we study inventory models with constant demand. In this model, we assume that demand is a function of time and selling price, allows for shortages, and assumes a constant deterioration rate of inventory items. Demand is affected by selling price if the price varies significantly with time. The objective of the model is to minimize the overall costs when demand is affected by the selling price with time. The paper presents a methodology to determine the optimal solution. The research introduces an efficient algorithm to obtain the optimal solution. The proposed model is validated through a numerical example. Conducting sensitivity analysis allows us to investigate the impact of different parameters on the optimal solution.


Sanjeev Kumar, Jaivindra Tomar  ( Pages 65-84 )
Affiliation:Department of Mathematics, DAV College, Bulandshahr, Uttar Pradesh, India      DOI:


Trade Credit; Multivariate demand; Shortage


1.     Chakravarty, A. K., & Martin, G. E. (1988). An optimal joint buyer-seller discount pricing model. Computers & operations research15(3), 271-281.

2.     Covert, R. P., & Philip, G. C. (1973). An EOQ model for items with Weibull distribution deterioration. AIIE transactions5(4), 323-326.

3.     Ghare, P. M. (1963). A model for an exponentially decaying inventory. J. ind. Engng14, 238-243.

4.     Goyal, S. K. (1985). Economic order quantity under conditions of permissible delay in payments. Journal of the operational research society, 335-338.

5.     Jawla, P., & Singh, S. R. (2016). Multi-item economic production quantity model for imperfect items with multiple production setups and rework under the effect of Preservation Technology and learning environment. International Journal of Industrial Engineering Computations, 703–716.

6.     Prakash, O., & Biswas, N. (2023). Manufacturing inventory model with random demand and finite production rate under two levels of Trade Credit Finance. International Journal of Inventory Research, 6(2), 164.

7.     Rana, K., Singh, S. R., Saxena, N., & Sana, S. S. (2021). Growing items inventory model for carbon emission under the permissible delay in payment with partially backlogging. Green Finance, 3(2), 153–174.

8.     Sarkar, B., & Sarkar, S. (2013). Variable deterioration and demand—An inventory model. Economic Modelling31, 548-556.

9.     Singh, S. R., & Rana, K. (2023). A sustainable production inventory model for growing items with trade credit policy under partial backlogging. International Journal of Advanced Operations Management15(1), 64-81.

10.  Tayal, S., Singh, S. R., & Sharma, R. (2014). A multi item inventory model for deteriorating items with expiration date and allowable shortages. Indian Journal of Science and Technology, 7(4), 463–471.

11.  Tayal, S., Singh, S. R., Sharma, R., & Chauhan, A. (2014). Two echelon supply chain model for deteriorating items with effective investment in preservation technology. International Journal of Mathematics in Operational Research, 6(1), 84.

12.  Tiwari, S., Cárdenas-Barrón, L. E., Iqbal Malik, A., & Jaggi, C. K. (2022). Retailer’s credit and inventory decisions for imperfect quality and deteriorating items under two-level trade credit. Computers & Operations Research, 138, 105617.

13.  Vandana, Singh, S. R., Yadav, D., Sarkar, B., & Sarkar, M. (2021). Impact of energy and carbon emission of a supply chain management with two-level trade-credit policy. Energies, 14(6), 1569.

14.  Wee, H. M., & Law, S. T. (2001). Replenishment and pricing policy for deteriorating items taking into account the time-value of money. International Journal of Production Economics71(1-3), 213-220.

15.  Yang, C. T., Dye, C. Y., & Ding, J. F. (2015). Optimal dynamic trade credit and preservation technology allocation for a deteriorating inventory model. Computers & Industrial Engineering87, 356-369.

Subscription content Buy the paper to read

AACS Journals

Copyright © 2020 AACS All rights reserved