Partial backordering inventory model with limited storage capacity under order-size dependent trade credit
Abstract
This study formulates an inventory model with limited storage capacity under the condition of order-size dependent trade credit. Shortages are allowed and partially backlogged. The objective of this study is to determine the optimal replenishment cycle length, the optimal fraction of no shortage, and whether retailers should choose to rent an extra warehouse to store more items, such that retailers’ total annual profit is maximized. We prove the global optimally of objective functions and derive the closed-form optimal solution. Some numerical examples are presented to illustrate the applicability of the proposed model. Sensitivity analysis is carried out and managerial insights are obtained. We find that if retailers’ own warehouse capacity is relatively small, they always benefit from enlarging order quantity and renting an extra warehouse; meanwhile, suppliers further prolong the credit period is beneficial for both parties. On the contrary, as retailers’ own warehouse capacity increases and exceeds the optimal order quantity under that of without capacity constraints, adopting the same replenishment strategy as that without capacity constraints is profitable for retailers. Our results also reveal that other model parameters (e.g., ordering cost, inventory holding cost, shortages cost, backordering rate, etc.) have a significant impact on retailers’ optimal decisions.
First published online 17 November 2021
Keyword : inventory, order-size dependent trade credit, limited storage capacity, partial backordering
How to Cite
Jiang, W.-H., Xu, L., Chen, Z.-S., Pedrycz, W., & Chin, K.-S. (2022). Partial backordering inventory model with limited storage capacity under order-size dependent trade credit. Technological and Economic Development of Economy, 28(1), 131–162. https://doi.org/10.3846/tede.2021.15704
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Chang, C. T., Cheng, M. C., & Ouyang, L. Y. (2015). Optimal pricing and ordering policies for non-instantaneously deteriorating items under order-size-dependent delay in payments. Applied Mathematical Modelling, 39(2), 747–763. https://doi.org/10.1016/j.apm.2014.07.002
Chang, C. T., Ouyang, L. Y., & Teng, J. T. (2003). An EOQ model for deteriorating items under supplier credits linked to ordering quantity. Ap-plied Mathematical Modelling, 27(12), 983–996. https://doi.org/10.1016/S0307-904X(03)00131-8
Chen, S. C., & Teng, J. T. (2015). Inventory and credit decisions for time-varying deteriorating items with up-stream and down-stream trade credit financing by discounted cash flow analysis. European Journal of Operational Research, 243(2), 566–575. https://doi.org/10.1016/j.ejor.2014.12.007
Chen, S. C., Cárdenas-Barrón, L. E., & Teng, J. T. (2014). Retailer’s economic order quantity when the supplier offers conditionally permissible delay in payments link to order quantity. International Journal of Production Economics, 155, 284–291. https://doi.org/10.1016/j.ijpe.2013.05.032
Chung, K. J., & Liao, J. J. (2009). The optimal ordering policy of the EOQ model under trade credit depending on the ordering quantity from the DCF approach. European Journal of Operational Research, 196(2), 563–568. https://doi.org/10.1016/j.ejor.2008.04.018
Chung, K. J., Lin, S. D., & Srivastava, H. M. (2013). The inventory models under conditional trade credit in a supply chain system. Applied Mathematical Modelling, 37(24), 10036–10052. https://doi.org/10.1016/j.apm.2013.05.044
Diabat, A., Taleizadeh, A. A., & Lashgari, M. (2017). A lot sizing model with partial downstream delayed payment, partial upstream advance pay-ment, and partial backordering for deteriorating items. Journal of Manufacturing Systems, 45, 322–342. https://doi.org/10.1016/j.jmsy.2017.04.005
Feng, L., & Chan, Y. L. (2019). Joint pricing and production decisions for new products with learning curve effects under upstream and down-stream trade credits. European Journal of Operational Research, 272(3), 905–913. https://doi.org/10.1016/j.ejor.2018.07.003
Feng, L., Wang, W. C., Teng, J. T., & Cárdenas-Barrón, L. E. (2021). Pricing and lot-sizing decision for fresh goods when demand depends on unit price, displaying stocks and product age under generalized payments. European Journal of Operational Research, 296(3), 940–952. https://doi.org/10.1016/j.ejor.2021.04.023
Ghiami, Y., & Beullens, P. (2020). The continuous resupply policy for deteriorating items with stock-dependent observable demand in a two-warehouse and two-echelon supply chain. Applied Mathematical Modelling, 82, 271–292. https://doi.org/10.1016/j.apm.2020.01.046
Ghiami, Y., Williams, T., & Wu, Y., (2013). A two-echelon inventory model for a deteriorating item with stock-dependent demand, partial back-logging and capacity constraints. European Journal of Operational Research, 231(3), 587–597. https://doi.org/10.1016/j.ejor.2013.06.015
Goyal, S. K. (1985). Economic order quantity under conditions of permissible delay in payments. Journal of the Operational Research Society, 36(4), 335–338. https://doi.org/10.1057/jors.1985.56
Gupta, M., Tiwari, S., & Jaggi, C. K. (2020). Retailer’s ordering policies for time-varying deteriorating items with partial backlogging and permis-sible delay in payments in a two-warehouse environment. Annals of Operations Research, 295(1), 139–161. https://doi.org/10.1007/s10479-020-03673-x
Hartley, R. V. (1976). Operations research: A managerial emphasis (pp. 315–317). Good Year, Santa Monica.
Huang, Y. F. (2006). An inventory model under two levels of trade credit and limited storage space derived without derivatives. Applied Mathe-matical Modelling, 30(5), 418–436. https://doi.org/10.1016/j.apm.2005.05.009
Huang, Y. F. (2007). Economic order quantity under conditionally permissible delay in payments. European Journal of Operational Research, 176(2), 911–924. https://doi.org/10.1016/j.ejor.2005.08.017
Jaggi, C. K., Gautam, P., & Khanna, A, (2018a). Credit policies for deteriorating imperfect quality items with exponentially increasing demand and partial backlogging. In N. Shah & M. Mittal (Eds.), Handbook of research on promoting business process improvement through inventory control techniques (pp. 90–106). IGI Global. https://doi.org/10.4018/978-1-5225-3232-3.ch006
Jaggi, C. K., Gautam, P., Khanna, A. (2018b). Inventory decisions for imperfect quality deteriorating items with exponential declining demand under trade credit and partially backlogged shortages. In P. Kapur, U. Kumar, & A. Verma (Eds.), Springer proceedings in business and eco-nomics. Quality, IT and business operations (pp. 213–229). Springer. https://doi.org/10.1007/978-981-10-5577-5_18
Jaggi, C. K., Pareek, S., Khanna, A., & Sharma, R. (2014). Credit financing in a two-warehouse environment for deteriorating items with price-sensitive demand and fully backlogged shortages. Applied Mathematical Modelling, 38(21–22), 5315–5333. https://doi.org/10.1016/j.apm.2014.04.025
Jaggi, C. K., Tiwari, S., & Goel, S. K. (2017). Credit financing in economic ordering policies for non-instantaneous deteriorating items with price dependent demand and two storage facilities. Annals of Operations Research, 248(1–2), 253–280. https://doi.org/10.1007/s10479-016-2179-3
Jain, D., & Aggarwal, K. K. (2012). The effect of inflation-induced demand and trade credit on ordering policy of exponentially deteriorating and imperfect quality items. International Transactions in Operational Research, 19(6), 863–889. https://doi.org/10.1111/j.1475-3995.2012.00849.x
Jamal, A. M. M., Sarker, B. R., & Wang, S. (1997). An ordering policy for deteriorating items with allowable shortage and permissible delay in payment. Journal of the Operational Research Society, 48(8), 826–833. https://doi.org/10.1057/palgrave.jors.2600428
Jonas, C. P. (2019). Optimizing a two-warehouse system under shortage backordering, trade credit, and decreasing rental conditions. International Journal of Production Economics, 209, 147–155. https://doi.org/10.1016/j.ijpe.2018.06.003
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