An EPQ Model for Deteriorating Products with Delayed Payments and Shortage

Document Type : Research Paper

Authors

1 Faculty of Engineering, University of Kurdistan, Sananda, Iran

2 Department of Technology and Engineering, Payame Noor University, Tehran, Iran

10.22070/jqepo.2022.14964.1203

Abstract

Credit incentives are crucial tools in supply chain and inventory management. Using this strategy, the buyer could pay the purchase cost with a delay. Therefore, it will increase the order quantity and the buyer's satisfaction. This paper investigates the economic production model considering the incentive conditions for supplier credit, variable demand, deteriorating items, and shortages. It is assumed that the supplier sends the ordered items to the manufacturer on time; however, he receives the purchase price of the products after a permitted delay. Furthermore, the deterioration rate is a fixed percentage of the inventory level. Therefore, a nonlinear programming model is proposed for figuring out replenishment policy by minimizing the total inventory cost. The best replenishment policy is examined by employing Wolfram Mathematica. Moreover, a genetic algorithm is suggested due to the model's nonlinearity. Numerical analyses show that while the results do not significantly differ, the proposed GA reaches near-optimum solutions in less CPU time. 

Keywords

References

Abad, P. L., & Jaggi, C. (2003). A joint approach for setting the unit price and the length of the credit period for a seller when end demand is price sensitive. International Journal of Production Economics, 83(2), 115-122.  
Chapman, C. B., Ward, S. C., Cooper, D. F., & Page, M. (1984). Credit policy and inventory control. Journal of the Operational Research Society, 35(12), 1055-1065.
 Chaudhari, U., Shah, N. H., & Jani, M. Y. (2020). Inventory modeling of deteriorating items and preservation technology with advance payment scheme under quadratic demand. In Optimization and inventory management (pp. 69-79): Springer.
Chung, K.-J. (2009). A complete proof on the solution procedure for noninstantaneous deteriorating items with permissible delay in payment. Computers & Industrial Engineering, 56(1), 267-273.
 Chung, K.-J., & Huang, Y.-F. (2003). The optimal cycle time for EPQ inventory model under permissible delay in payments. International Journal of Production Economics, 84(3), 307-318.  
Chung, K.-J., & Huang, Y.-F. (2006). Retailer's optimal cycle times in the EOQ model with imperfect quality and a permissible credit period. Quality and Quantity, 40(1), 59-77.
 Dari, S., & Sani, B. (2019). An EPQ model for delayed deteriorating items with quadratic demand and linear holding cost. Operational Research Society of India 57, 46-72.
 Duary, A., Das, S., Arif, M. G., Abualnaja, K. M., Khan, M. A.-A., Zakarya, M., & Shaikh, A. A. (2021). Advance and delay in payments with the price-discount inventory model for deteriorating items under capacity constraint and partially backlogged shortages. Alexandria Engineering Journal.  
Goyal, S. K. (1985). Economic order quantity under conditions of permissible delay in payments. Journal of the Operational Research Society, 335-338.  
Haley, C. W., & Higgins, R. C. (1973). Inventory policy and trade credit financing. Management science, 20(4-part-i), 464-471.  
Hu, F., & Liu, D. (2010). Optimal replenishment policy for the EPQ model with permissible delay in payments and allowable shortages. Applied Mathematical Modelling, 34(10), 3108-3117.
 Khanra, S., Ghosh, S. K., & Chaudhuri, K. (2011). 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.
 Li, J., Feng, H., & Zeng, Y. (2014). Inventory games with permissible delay in payments. European Journal of Operational Research, 234(3), 694-700.
 Liao, J.-J. (2007). On an EPQ model for deteriorating items under permissible delay in payments. Applied Mathematical Modelling, 31(3), 393-403.  
Mahata, G. C. (2011). Optimal strategy for an EOQ model with noninstantaneous receipt and exponentially deteriorating items under permissible delay in payments. International Journal of Management Science and Engineering Management, 6(6), 450-458.  

Min, J., Zhou, Y.-W., Liu, G.-Q., & Wang, S.-D. (2012). An EPQ model for deteriorating items with inventory-level-dependent demand and permissible delay in payments. International Journal of Systems Science, 43(6), 1039-1053.
Ouyang, L.-Y., Teng, J.-T., Goyal, S. K., & Yang, C.-T. (2009). An economic order quantity model for deteriorating items with partially permissible delay in payments linked to order quantity. European Journal of Operational Research, 194(2), 418-431.
Palanivel, M., Priyan, S., & Uthayakumar, R. (2015). An inventory model with finite replenishment, probabilistic deterioration and permissible delay in payments. Journal of Management Analytics, 2(3), 254-279.  
Patoghi, A., & Setak, M. (2018). Coordinating replenishment and marketing policies for noninstantaneous deteriorating items with imprecise deterioration free time and general deterioration and holding cost rates. International Journal of Inventory Research, 5(1), 38-59.
 RezaMaiham, & Kamalabadi, i. (2012). Joint pricing and inventory control for noninstantaneous deteriorating items with partial backlogging and time and price dependent demand. International Journal of Production Economics, 136(1), 116-122.  
Sadeghi, H. (2019a). A forecasting system by considering product reliability, POQ policy, and periodic demand. Journal of Quality Engineering and Production Optimization, 4(2), 133-148.
 Sadeghi, H. (2019b). Optimal pricing and replenishment policy for production system with discrete demand. International Journal of Industrial Engineering and Management Science, 6(2), 37-50.  
Sadeghi, H., Golpîra, H., & Khan, S. A. R. (2021). Optimal integrated production-inventory system considering shortages and discrete delivery orders. Computers & Industrial Engineering, 156, 107233.
 Sadeghi, H., Makui, A., & Heydari, M. (2016). Multilevel production systems with dependent demand with uncertainty of lead times. Mathematical Problems in Engineering, 2016, 1-14. doi:https://doi.org/10.1155/2016/4967341
Sana, S. S., & Chaudhuri, K. S. (2008). A deterministic EOQ model with delays in payments and price-discount offers. European Journal of Operational Research, 148(2), 509–533.
Sarkar⸴ B. (2012). "An EOQ model with delay in payments and stock dependent demand in the presence of imperfect production. Applied Mathematics and Computation, 2018(17), 8295–8308.
 Singh, T., Muduly, M. M., Asmita, N., Mallick, C., & Pattanayak, H. (2020). A note on an economic order quantity model with timedependent demand, three-parameter Weibull distribution deterioration and permissible delay in payment. Journal of Statistics and Management Systems, 23(3), 643-662.
 Soni, H. N. (2013). Optimal replenishment policies for noninstantaneous deteriorating items with price and stock sensitive demand under permissible delay in payment. International Journal of Production Economics, 146(1), 259-268.
 Sundararajan, R., Vaithyasubramanian, S., & Nagarajan, A. (2021). Impact of delay in payment, shortage and inflation on an EOQ model with bivariate demand. Journal of Management Analytics, 8(2), 267-294.
 Supakar, P., & Mahato, S. K. (2020). An EPQ model with time proportion deterioration and ramp type demand under different payment schemes with fuzzy uncertainties. International Journal of Systems Science: Operations & Logistics, 1-15.
 Taleizadeh, A. A., Sarkar, B., & Hasani, M. (2020). Delayed payment policy in multi-product single-machine economic production quantity model with repair failure and partial backordering. Journal of Industrial & Management Optimization, 16(3), 1273.
 Tavakoli, S., & Taleizadeh, A. A. (2017). An EOQ model for decaying item with full advanced payment and conditional discount. Annals of Operations Research, 259(1), 415-436.  
Teng, J. (2002). On the economic order quantity under conditions of permissible delay in payments. Journal of the Operational Research Society, 53(8), 915-918. 
Journal of Quality Engineering and Production Optimization
Volume 7, Issue 1
May 2022
Pages 160-176

Files

Share

How to cite

Statistics