The present study presents a fuzzy inventory model for non-instantaneous deteriorating items under conditions of permissible delay in payments. In the current paper, we incorporate the condition in which, the supplier accepts the partial payment at the end of the credit period and the reaming amount after that period under the term and condition. Here, the demand rate is a function of the selling price. Also, it is assumed that shortages are allowed and are fully backlogged. The present paper also considers that the interest earned (I$$) on the fixed deposit amount, i.e., revenue generated by fulfilling the shortage, balance amount, after settling the account is higher than that of usual interest rate (I$$). Hence, the objective of this study is to determine the retailer’s optimal policies that maximize the total profit. Also, some theoretical results are obtained, which shows that the optimal solution not only exists, it is unique also. The impact of the new proposed credit policy is investigated on the optimality of the solution for the non-instantaneous deteriorating products. The validation of the proposed model and its solution method is demonstrated through the numerical example. The results indicate that the inventory model, along with the solution method, provides a powerful tool to the retail managers under real-world situations. Results demonstrate that it is essential for the managers to consider the inclusion of new proposed credit policy significantly increases the net annual profit.
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DOI : 10.1051/ro/2019104
Mots-clés : Inventory, trade credit, pricing, non-instantaneous deterioration, shortages, triangular fuzzy number, function principle and signed distance method
@article{RO_2020__54_6_1793_0,
author = {Sharma, Anuj Kumar and Tiwari, Sunil and Yadavalli, V.S.S. and Jaggi, Chandra K.},
title = {Optimal trade credit and replenishment policies for non-instantaneous deteriorating items},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {1793--1826},
publisher = {EDP-Sciences},
volume = {54},
number = {6},
year = {2020},
doi = {10.1051/ro/2019104},
mrnumber = {4150236},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ro/2019104/}
}
TY - JOUR AU - Sharma, Anuj Kumar AU - Tiwari, Sunil AU - Yadavalli, V.S.S. AU - Jaggi, Chandra K. TI - Optimal trade credit and replenishment policies for non-instantaneous deteriorating items JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2020 SP - 1793 EP - 1826 VL - 54 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2019104/ DO - 10.1051/ro/2019104 LA - en ID - RO_2020__54_6_1793_0 ER -
%0 Journal Article %A Sharma, Anuj Kumar %A Tiwari, Sunil %A Yadavalli, V.S.S. %A Jaggi, Chandra K. %T Optimal trade credit and replenishment policies for non-instantaneous deteriorating items %J RAIRO - Operations Research - Recherche Opérationnelle %D 2020 %P 1793-1826 %V 54 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2019104/ %R 10.1051/ro/2019104 %G en %F RO_2020__54_6_1793_0
Sharma, Anuj Kumar; Tiwari, Sunil; Yadavalli, V.S.S.; Jaggi, Chandra K. Optimal trade credit and replenishment policies for non-instantaneous deteriorating items. RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 6, pp. 1793-1826. doi : 10.1051/ro/2019104. http://www.numdam.org/articles/10.1051/ro/2019104/
[1] and , Ordering policies of deteriorating items under permissible delay in payments, J. Oper. Res. Soc. 46 (1995) 658–662. | DOI | Zbl
[2] , and , Review of inventory systems with deterioration since 2001, Eur. J. Oper. Res. 221 (2012) 275–284. | DOI | MR | Zbl
[3] and , Generalized Convexity and Optimization: Theory and Applications, Springer Science & Business Media 616 (2008). | MR | Zbl
[4] , and , Fuzzy mixture inventory model with variable lead-time based on probabilistic fuzzy set and triangular fuzzy number, Math. Comput. Modell. 39 (2004) 287–304. | DOI | MR | Zbl
[5] , and , Optimal replenishment policies for non-instantaneous deteriorating items with stock-dependent demand, Int. J. Prod. Econ. 123 (2010) 62–68. | DOI
[6] and , Fuzzy inventory model for deteriorating items with permissible delay in payment, Appl. Math. Comput. 182 (2006) 711–726. | MR | Zbl
[7] , and , Retailer’s economic order quantity when the supplier offers conditionally permissible delay in payments link to order quantity, Int. J. Prod. Econ. 155 (2014) 284–291. | DOI
[8] , , and , Inventory and shelf-space optimization for fresh produce with expiration date under freshness-and-stock-dependent demand rate, J. Oper. Res. Soc. 67 (2016) 884–896. | DOI
[9] , and , The retailer’s optimal ordering policy with trade credit in different financial environments, Appl. Math. Comput. 218 (2012) 9623–9634. | MR | Zbl
[10] and , An EOQ model for items with Weibull distribution deterioration, Am. Inst. Ind. Eng. Trans. 5 (1973) 323–326.
[11] , and , Multi-item stochastic and fuzzy-stochastic inventory models under two restrictions, Comput. Oper. Res. 31 (2004) 1793–1806. | DOI | Zbl
[12] , and , An economic production quantity inventory model involving fuzzy demand rate and fuzzy deterioration rate, J. Appl. Math. Comput. 12 (2003) 251. | DOI | MR | Zbl
[13] , The effect of preservation technology investment on a non-instantaneous deteriorating inventory model, Omega. Int. J. Manage. Sci. 41 (2013) 872–880. | DOI
[14] and , Economic design of an inventory policy for non-instantaneous deteriorating items under permissible delay in payments, J. Comput. Appl. Math. 233 (2010) 2492–2505. | DOI | MR | Zbl
[15] and , A model for exponentially decaying inventories, J. Ind. Eng. 14 (1963) 238–243.
[16] , Economic order quantity under conditions of permissible delay in payments, J. Oper. Res. Soc. 36 (1985) 335–338. | DOI | Zbl
[17] and , Recent trends in modelling of deteriorating inventory, Eur. J. Oper. Res. 134 (2001) 1–16. | DOI | MR | Zbl
[18] , Operations and cost. Factory Management Series. A.W. Shaw Co., Chicago, 1915 48–52.
[19] and , Optimal replenishment policy for the EPQ model with permissible delay in payments and allowable shortages, Appl. Math. Model. 34 (2010) 3108–3117. | DOI | MR | Zbl
[20] , Optimal retailers ordering policies in the EOQ model under trade credit financing, J. Oper. Res. Soc. 54 (2003) 1011–1015. | DOI | Zbl
[21] and , An optimal replenishment policy for non-instantaneous deteriorating items with two storage facilities, Int. J. Serv. Oper. Inform. 5 (2010) 209–230.
[22] , and , Credit financing in economic ordering policies for non-instantaneous deteriorating items with price dependent demand and two storage facilities, Ann. Oper. Res. 248 (2017) 253–280. | DOI | MR
[23] , 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
[24] , On an EPQ model for deteriorating items under permissible delay in payments, Appl. Math. Model. 31 (2007) 393–403. | DOI | Zbl
[25] and , A comprehensive extension of an integrated inventory model with ordering cost reduction and permissible delay in payments, Appl. Math. Model. 37 (2013) 4709–4716. | DOI | MR
[26] and , Joint pricing and inventory control for non-instantaneous deteriorating items with partial backlogging and time and price dependent demands, Int. J. Prod. Econ. 136 (2012) 116–122. | DOI
[27] and , Joint control of inventory and its pricing for non-instantaneously deteriorating items under permissible delay in payments and partial backlogging, Math. Comput. Model. 55 (2012) 1722–1733. | DOI | MR | Zbl
[28] , , and , Reviewing the literature of inventory models under trade credit contact, Discrete Dyn. Nat. Soc. 2014 (2014) 975425. | DOI
[29] , Perishable inventory theory: a review, Oper. Res. 30 (1982) 680–708. | DOI | Zbl
[30] , and , A study on an inventory model for non-instantaneous deteriorating items with permissible delay in payments, Comput. Ind. Eng. 51 (2006) 637–651. | DOI
[31] , and , Optimal ordering policy for deteriorating items with partial backlogging under permissible delay in payments, J. Global. Optim. 34 (2006) 245–271. | DOI | MR | Zbl
[32] , and , Retailer’s ordering policy for non-instantaneous deteriorating items with quantity discount, stock dependent demand and stochastic backorder rate, J. Chin. Inst. Indust. Eng. 25 (2008) 62–72.
[33] , , and , A comprehensive extension of the optimal replenishment decisions under two levels of trade credit policy depending on the order quantity, Appl. Math. Comput. 224 (2013) 268–277. | MR
[34] , Survey of literature on continuously deteriorating inventory models, J. Oper. Res. Soc. 42 (1991) 27–37. | DOI | Zbl
[35] , , and , Two storage inventory model with fuzzy deterioration over a random planning horizon, Math. Comput. Modell. 46 (2007) 1419–1433. | DOI | MR | Zbl
[36] , 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
[37] , and , A review of trade credit literature: opportunities for research in operations, Eur. J. Oper. Res. 231 (2013) 245–256. | DOI
[38] , and , Optimizing inventory and marketing policy for non-instantaneous deteriorating items with generalized type deterioration and holding cost rates, Omega. Int. J. Manage. Sci. 41 (2013) 421–430. | DOI
[39] and , Retailer’s decision for ordering and credit policies for deteriorating items when a supplier offers order-linked credit period or cash discount, Appl. Math. Comput. 259 (2015) 569–578. | MR
[40] and , Optimal pricing and inventory policies for non-instantaneous deteriorating items with permissible delay in payment: fuzzy expected value model, Int. J. Indust. Eng. Comput. 3 (2012) 281–300.
[41] , and , A lot sizing model with advance payment and planned backordering, Ann. Oper. Res. 271 (2018) 1001–1022. | DOI | MR
[42] and , An EOQ model for decaying item with full advanced payment and conditional discount, Ann. Oper. Res. 259 (2017) 415–436. | DOI | MR | Zbl
[43] , On the economic order quantity under conditions of permissible delay in payments, J. Oper. Res. Soc. 53 (2002) 915–918. | DOI | Zbl
[44] , 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
[45] , , and , A comprehensive extension of optimal ordering policy for stock-dependent demand under progressive payment scheme, Eur. J. Oper. Res. 215 (2011) 97–104. | DOI | MR | Zbl
[46] , and , Economic order quantity model with trade credit financing for non-decreasing demand, Omega. Int. J. Manage. Sci. 40 (2012) 328–335. | DOI
[47] , , and , Impact of trade credit and inflation on retailer’s ordering policies for non-instantaneous deteriorating items in a two-warehouse environment, Int. J. Prod. Econ. 176 (2016) 154–169. | DOI
[48] , Joint location, inventory, and preservation decisions for non-instantaneous deterioration items under delay in payments, Int. J. Syst. Sci. 47 (2016) 572–585. | DOI | MR | Zbl
[49] , , and , Inventory models for deteriorating items with maximum lifetime under downstream partial trade credits to credit-risk customers by discounted cash-flow analysis, Int. J. Prod. Econ. 171 (2016) 105–115. | DOI
[50] , and , An optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand and partial backlogging, Int. J. Prod. Econ. 101 (2006) 369–384. | DOI
[51] , and , Coordinating replenishment and pricing policies for non-instantaneous deteriorating items with price-sensitive demand, Int. J. Syst. Sci. 40 (2009) 1273–1281. | DOI | MR | Zbl
[52] and , Fuzzy inventory with backorder for fuzzy order quantity, Inf. Sci. 93 (1996) 283–319. | DOI | Zbl
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