In this paper, we examine an optimal dynamic decision-making problem for a retailer’s inventory system of deteriorating items under two-level trade credit financing where the supplier, as well as the retailer, offers trade credit to the subsequent downstream member, the demand rate of which varies simultaneously with time and the length of credit period that is offered to the customers. The deterioration rate is non-decreasing over time. In addition, the risk of default increases with the credit period length. A generalized model is presented to determine the optimal trade credit and replenishment strategies that maximize the retailer’s annual total profit. We then demonstrate that the retailer’s optimal credit period and replenishment cycle time not only exist but also are unique. Thus, the search of the global optimal solution reduces to finding a local solution. Finally, we run several numerical examples to illustrate the problem and gain managerial insights.
Mots-clés : Inventory, two-level trade credit, deteriorating items, time-varying and credit-sensitive demand, default risk.
@article{RO_2018__52_4-5_1175_0,
author = {Mukherjee, Avik and Mahata, Gour Chandra},
title = {Optimal replenishment and credit policy in an inventory model for deteriorating items under two-levels of trade credit policy when demand depends on both time and credit period involving default risk},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {1175--1200},
publisher = {EDP-Sciences},
volume = {52},
number = {4-5},
year = {2018},
doi = {10.1051/ro/2018032},
zbl = {1411.90036},
mrnumber = {3880602},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ro/2018032/}
}
TY - JOUR AU - Mukherjee, Avik AU - Mahata, Gour Chandra TI - Optimal replenishment and credit policy in an inventory model for deteriorating items under two-levels of trade credit policy when demand depends on both time and credit period involving default risk JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2018 SP - 1175 EP - 1200 VL - 52 IS - 4-5 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ro/2018032/ DO - 10.1051/ro/2018032 LA - en ID - RO_2018__52_4-5_1175_0 ER -
%0 Journal Article %A Mukherjee, Avik %A Mahata, Gour Chandra %T Optimal replenishment and credit policy in an inventory model for deteriorating items under two-levels of trade credit policy when demand depends on both time and credit period involving default risk %J RAIRO - Operations Research - Recherche Opérationnelle %D 2018 %P 1175-1200 %V 52 %N 4-5 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ro/2018032/ %R 10.1051/ro/2018032 %G en %F RO_2018__52_4-5_1175_0
Mukherjee, Avik; Mahata, Gour Chandra. Optimal replenishment and credit policy in an inventory model for deteriorating items under two-levels of trade credit policy when demand depends on both time and credit period involving default risk. RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 4-5, pp. 1175-1200. doi : 10.1051/ro/2018032. http://archive.numdam.org/articles/10.1051/ro/2018032/
[1] and , A joint approach for setting unit price and the length of the credit period for a seller when end demand is price sensitive. Int. J. Prod. Econ. 83 (2003) 115–122. | DOI
[2] and , Ordering policies of deteriorating item under permissible delay in payments. J. Oper. Res. Soc. 46 (1995) 658–662. | DOI | Zbl
[3] , and , Retailer’s pricing, credit and inventory policies for deteriorating items in response to temporary price/credit incentives. Int. J. Prod. Econ. 81 (2003) 153–162. | DOI
[4] , and , Economic production quantity models for deteriorating items with up-stream full trade credit and down-stream partial trade credit. Int. J. Prod. Econ. 155 (2014) 302–309. | DOI
[5] , The simplified solution procedures for the optimal replenishment decisions under two levels of trade credit policy depending on the order quantity in a supply chain system. Expert Syst. Appl. 38 (2011) 13482–13486. | DOI
[6] and , The optimal retailer’s ordering policies for deteriorating items with limited storage capacity under trade credit financing. Int. J. Prod. Econ. 106 (2007) 127–145. | DOI
[7] and , The simplified solution algorithm for an integrated supplier buyer inventory model with two-part trade credit in a supply chain system. Eur. J. Oper. Res. 213 (2011) 156–165. | DOI | MR | Zbl
[8] and , Supply chain model with price- and trade credit-sensitive demand under two-level permissible delay in payments. Int. J. Syst. Sci. 44 (2013) 937–948. | DOI | MR | Zbl
[9] , Economic order quantity under conditions of permissible delay in payments. J. Oper. Res. Soc. 36 (1985) 335–338. | DOI | Zbl
[10] , and , Comment on an ordering policy for deteriorating items with allowable shortage and permissible delay in payment. J. Oper. Res. Soc. 59 (2008) 867–870. | DOI | Zbl
[11] , Optimal retailer’s ordering policies in the EOQ model under trade credit financing. J. Oper. Res. Soc. 54 (2003) 1011–1015. | DOI | Zbl
[12] , Optimal retailer’s replenishment decisions in the EPQ model under two levels of trade credit policy. Eur. J. Oper. Res. 176 (2007) 1577–1591. | DOI | Zbl
[13] and , Optimal replenishment and payment policies in the EOQ model under cash discount and trade credit. Asia Pac. J. Oper. Res. 20 (2003) 177–190. | MR | Zbl
[14] , and , Retailer’s optimal replenishment decisions with credit-linked demand under permissible delay in payments. Eur. J. Oper. Res. 190 (2008) 130–135. | DOI | Zbl
[15] , , and , Optimal replenishment and credit policy in EOQ model under two-levels of trade credit policy when demand is influenced by credit period. Int. J. Syst. Assur. Eng. Manag. 3 (2012) 352–359. | DOI
[16] , and , An ordering policy for deteriorating items with allowable shortage and permissible delay in payment. J. Oper. Res. Soc. 48 (1997) 826–833. | DOI | Zbl
[17] , and , An EOQ model for a deteriorating item with time dependent quadratic demand under permissible delay in payment. Appl. Math. Comput. 218 (2011) 1–9. | MR | Zbl
[18] , and , An inventory model with time dependent demand and shortages under trade credit policy. Econ. Model. 35 (2013) 349–355. | DOI
[19] and , The optimal replenishment decisions under two levels of trade credit policy depending on the order quantity. Expert Syst. Appl. 37 (2010) 5514–5522. | DOI
[20] , An EOQ model with non-instantaneous receipt and exponentially deteriorating items under two-level trade credit policy. Int. J. Prod. Econ. 113 (2008) 852–861. | DOI
[21] , and , An inventory model with deteriorating items under inflation when a delay in payment is permissible. Int. J. Prod. Econ. 63 (2000) 207–214. | DOI
[22] and , Optimal trade credit and order quantity when trade credit impacts on both demand rate and default risk. J. Oper. Res. Soc. 64 (2013) 1551–1556. | DOI
[23] , An EPQ-based inventory model for exponentially deteriorating items under retailer partial trade credit policy in supply chain. Expert Syst. Appl. 39 (2012) 3537–3550. | DOI
[24] , Partial trade credit policy of retailer in economic order quantity models for deteriorating items with expiration dates and price sensitive demand. J. Math. Model. Algorithms Oper. Res. 14 (2015) 363–392. | DOI | MR | Zbl
[25] , Retailer’s optimal credit period and cycle time in a supply chain for deteriorating items with up-stream and downstream trade credits. J. Ind. Eng. Int. 11 (2015) 353–366. | DOI
[26] , Optimal ordering policy with trade credit and variable deterioration for fixed lifetime products. Int. J. Oper. Res. 25 (2016) 307–326. | DOI | MR | Zbl
[27] and , Supply chain inventory model for deteriorating items with maximum lifetime and partial trade credit to credit-risk customers. Int. J. Manag. Sci. Eng. Manag. 12 (2017) 21–32.
[28] and , Production lot-size model with fuzzy production rate and fuzzy demand rate for deteriorating item under permissible delay in payments. Opsearch 43 (2006) 358–375. | DOI | Zbl
[29] and , An EOQ model for deteriorating items under trade credit financing in the fuzzy sense. Prod. Plan. Control 18 (2007) 681–692. | DOI
[30] and , Economic production quantity model with trade credit financing and price-discount offer for non decreasing time varying demand pattern. Int. J. Procure. Manag. 7 (2014) 563–581.
[31] , and , Optimal replenishment and credit policy in supply chain inventory model under two levels of trade credit with time- and credit-sensitive demand involving default risk. J. Ind. Eng. Int. 14 (2018) 31–42. | DOI
[32] , and , An inventory model for deteriorating items under stock-dependent demand and two-level trade credit. Appl. Math. Model. 34 (2010) 3273–3285. | DOI | MR | Zbl
[33] , and , An EPQ model for deteriorating items with inventory-level-dependent demand and permissible delay in payments. Int. J. Syst. Sci. 43 (2012) 1039–1053. | DOI | MR | Zbl
[34] , , and , An integrated inventory model with capacity constraint and order-size dependent trade credit. Comput. Ind. Eng. 84 (2015) 133–143. | DOI
[35] , , and , Continuous review inventory model with delay in payments. Int. J. Prod. Econ. 85 (2003) 91–95. | DOI
[36] and , A deterministic EOQ model with delays in payments and price-discount offers. Eur. J. Oper. Res. 184 (2008) 509–533. | DOI | MR | Zbl
[37] , An EOQ model with delay in payments and time varying deterioration rate. Math. Comput. Model. 55 (2012) 367–377. | DOI | MR | Zbl
[38] , Supply chain coordination with variable backorder, inspections, and discount policy for fixed lifetime products. Math. Probl. Eng. 14 (2016) 6318737. | MR | Zbl
[39] and , Variable deterioration and demand – an inventory model. Econ. Model. 31 (2013) 548–556. | DOI
[40] , and , An inventory model with trade-credit policy and variable deterioration for fixed lifetime products. Ann. Oper. Res. 229 (2015) 677–702. | DOI | MR | Zbl
[41] , and , Supply chain model for perishable products under inflation and permissible delay in payment. Comput. Oper. Res. 27 (2000) 59–75. | DOI | Zbl
[42] , , and , Optimal replenishment policy with variable deterioration for fixed lifetime products.Sci. Iran. 23 (2016) 2318–2329.
[43] , and , Optimal replenishment time for retailer under partial upstream prepayment and partial downstream overdue payment for quadratic demand. Math. Comput. Model. Dynam. Syst. 24 (2018) 1–11. | DOI | MR | Zbl
[44] , and , Effects of human errors and trade-credit financing in a two-echelon supply chain model. Eur. J. Ind. Eng. 12 (2018) 465–503. | DOI
[45] and , Optimal pricing and ordering policies for retailers under order-size-dependent delay in payments. Comput. Oper. Res. 30 (2003) 35–50. | DOI | Zbl
[46] , , and , Supply chain models for deteriorating products with ramp type demand rate under permissible delay in payments. Expert Syst. Appl. 38 (2011) 14861–14869. | DOI
[47] , On the economic order quantity under conditions of permissible delay in payments. J. Oper. Res. Soc. 53 (2002) 915–918. | DOI | Zbl
[48] , Optimal ordering policies for a retailer who offers distinct trade credits to its good and bad credit customers. Int. J. Prod. Econ. 119 (2009) 415–423. | DOI
[49] and , Optimal manufacturer’s replenishment policies in the EPQ model under two levels of trade credit policy. Eur. J. Oper. Res. 195 (2009) 358–363. | DOI | MR | Zbl
[50] and , Optimal ordering policy for a retailer in a supply chain with up-stream and down-stream trade credits. J. Oper. Res. Soc. 58 (2007) 1252–1255. | DOI
[51] and , Seller’s optimal credit period and replenishment time in a supply chain with up-stream and down-stream trade credits. J. Global Optim. 53 (2012) 417–430. | DOI | MR | Zbl
[52] , and , Optimal pricing and ordering policy under permissible delay in payments. Int. J. Prod. Econ. 97 (2005) 121–129. | DOI
[53] , and , Economic order quantity model with trade credit financing for non-decreasing demand. Omega 40 (2012) 328–335. | DOI
[54] , and , An inventory model for increasing demand under two levels of trade credit linked to order quantity. Appl. Math. Model. 37 (2013) 7624–7632. | DOI | MR | Zbl
[55] , and , Optimal trade credit and lot size policies in economic production quantity models with learning curve production costs. Int. J. Prod. Econ. 155 (2014) 318–323. | DOI
[56] and , Two-echelon trade credit financing for perishable items in a supply chain when demand depends on both selling price and credit period. Comput. Ind. Eng. 57 (2009) 773–786. | DOI
[57] , and , Seller’s optimal credit period and cycle time in a supply chain for deteriorating items with maximum lifetime. Eur. J. Oper. Res. 232 (2014) 315–321. | DOI | MR | Zbl
[58] and , Lot-sizing policies for deteriorating items with expiration dates and partial trade credit to credit-risk customers. Int. J. Prod. Econ. 155 (2014) 292–301. | DOI
[59] , , and , Optimal credit period and lot size for deteriorating items with expiration dates under two level trade credit financing. Eur. J. Oper. Res. 237 (2014) 898–908. | DOI | MR | Zbl
[60] and , Improving the supply chains performance through trade credit under inventory-dependent demand. Int. J. Prod. Econ. 143 (2013) 364–370. | DOI
Cité par Sources :
