In this paper, we develop an integrated two-echelon supply chain inventory model with a single-manufacturer and multi-retailers in which each retailer’s demand is dependent on selling price of the product. The manufacturer produces a single product and dispatched the order quantities of the retailers in some equal batches. The production process is imperfect and produces imperfect quality of products with a defective percentage which is random in nature and follows binomial distribution. Inspection process is performed by the retailers to classify the defective items in each lot delivered from the manufacturer. The defective items that were found by the retailer will be returned to the manufacturer at the next delivery. Lead time is random and it follows an exponential distribution. We also assume that shortages are allowed and are completely backlogged at each retailer’s end. A closed form solution to maximize the expected average profit for both the centralized and the decentralized scenarios are obtained. The developed models are illustrated with the help of some numerical examples using stochastic search genetic algorithm (GA). It is found that integration of the supply chain players results an impressive increment in the profit of the whole supply chain. Sensitivity analysis is also performed to explore the impacts of key-model parameters on the expected average profit of the supply chain.
Keywords: Two-echelon supply chain, Single-manufacturer, Multi-retailers, Imperfect quality items, Price dependent demand, Stochastic lead time, Genetic algorithm
@article{RO_2021__55_6_3459_0,
author = {Barman, Dipak and Mahata, Gour Chandra},
title = {A single-manufacturer multi-retailer integrated inventory model for items with imperfect quality, price sensitive demand and planned back orders},
journal = {RAIRO. Operations Research},
pages = {3459--3491},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {6},
doi = {10.1051/ro/2021156},
mrnumber = {4344867},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2021156/}
}
TY - JOUR AU - Barman, Dipak AU - Mahata, Gour Chandra TI - A single-manufacturer multi-retailer integrated inventory model for items with imperfect quality, price sensitive demand and planned back orders JO - RAIRO. Operations Research PY - 2021 SP - 3459 EP - 3491 VL - 55 IS - 6 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2021156/ DO - 10.1051/ro/2021156 LA - en ID - RO_2021__55_6_3459_0 ER -
%0 Journal Article %A Barman, Dipak %A Mahata, Gour Chandra %T A single-manufacturer multi-retailer integrated inventory model for items with imperfect quality, price sensitive demand and planned back orders %J RAIRO. Operations Research %D 2021 %P 3459-3491 %V 55 %N 6 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ro/2021156/ %R 10.1051/ro/2021156 %G en %F RO_2021__55_6_3459_0
Barman, Dipak; Mahata, Gour Chandra. A single-manufacturer multi-retailer integrated inventory model for items with imperfect quality, price sensitive demand and planned back orders. RAIRO. Operations Research, Tome 55 (2021) no. 6, pp. 3459-3491. doi: 10.1051/ro/2021156
[1] and , Inventory and pricing model with price-dependent demand, time-varying holding cost, and quantity discounts. Comput. Ind. Eng. 94 (2016) 170–177. | DOI
[2] , A joint economic-lot-size model for purchaser and vendor. Decision Sci. 17 (1986) 292–311. | DOI
[3] and , An imprecise-inventory model with PEND and SEND policy. Int. J. Math. Oper. Res. 13 (2018) 243–268. | MR | DOI
[4] and , Two-echelon supply chain inventory model with variable lead time and ramp-type demand for deterioration item under bi-level credit period. IJIR 6 (2021) 14–46. | DOI
[5] , and , Advance payment based vendor-buyer production inventory model with stochastic lead time and continuous review policy. Opsearch 58 (2021) 1217–1237. | MR | DOI
[6] , , and , Back-ordered inventory model with inflation in a Cloudy-Fuzzy environment. J. Ind. Manag. Optim. 17 (2021) 1913–1941. | MR | DOI
[7] and , Integrated single vendor single buyer model with stochastic demand and variable lead time. Int. J. Prod. Econ. 92 (2004) 75–80. | DOI
[8] and , Optimal inventory policies for imperfect inventor with price dependent stochastic demand and partially backlogged shortages. Yugosl. J. Oper. Res. 22 (2012) 199–223. | MR | Zbl | DOI
[9] , Economic production quantity with rework process at a single-stage manufacturing system with planned back-orders. Comput. Ind. Eng. 57 (2009) 1105–1113. | DOI
[10] , , and , An integrated inventory model involving discrete setup cost reduction, variable safety factor, selling price dependent demand, and investment. RAIRO-Oper. Res. 53 (2019) 39–57. | MR | DOI
[11] and , An inventory model with controllable lead time and ordering cost, log-normal-distributed demand, and gamma-distributed available capacity. Cogent Bus. Manag. 5 (2018) 1469182. | DOI
[12] and , Optimal production policy for a closed-loop supply chain with stochastic lead time and learning in production. Scientia Iranica 26 (2019) 2936–2951.
[13] and , Developing a closed-loop supply chain model with price and quality dependent demand and learning in production in a stochastic environment. Int. J. Syst. Sci. Oper. Logist. 7 (2020) 147–163.
[14] , Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, Reading, MA (1989). | Zbl
[15] , An integrated inventory model for a single supplier-single customer problem. Int. J. Prod. Res. 15 (1976) 107–111. | DOI
[16] , How many parts to make at once. Mag. Manage. 10(2) (1913) 135–136, 152. [Reprinted in Oper. Res. 38 (1990) 947–950.
[17] , A manufacturer-buyer integrated inventory model with stochastic lead times for delivering equal-and/or unequal-sized batches of a lot. Comput. Oper. Res. 40 (2013) 2740–2751. | MR | DOI
[18] and , An integrated vendor-buyer inventory model with imperfect items and planned back orders. Int. J. Adv. Manuf. Technol. 68 (2013) 2121–2132. | DOI
[19] , and , Replenishment policies for imperfect inventory system under natural idle time and shortages. Yugosl. J. Oper. Res. 30 (2020) 251–270. | MR | DOI
[20] and , Single-vendor multi-buyer integrated production-inventory model with controllable lead time and service level constraints. Appl. Math. Model. 37 (2013) 1753–1767. | MR | DOI
[21] and , Integrated vendor-buyer inventory models with inflation and time value of money in controllable lead time. Decision Sci. Lett. 5 (2016) 81–94. | DOI
[22] , , , and , Economic order quantity models for items with imperfect quality and emission considerations. Int. J. Syst. Sci. Oper. Logist. 5 (2018) 99–115.
[23] , , and , Inventory and pricing decisions for imperfect quality items with inspection errors, sales returns, and partial back-orders under inflation. RAIRO-Oper. Res. 54 (2020) 287–306. | MR | Zbl | Numdam | DOI
[24] and , An elasticity approach to the newsvendor with price-sensitive demand. Oper. Res. 59 (2011) 301–312. | MR | Zbl | DOI
[25] , and , Supply chain coordination model with controllable lead time and service level constraint. Comput. Indus. Eng. 61 (2011) 858–864. | DOI
[26] , An integrated supply chain inventory model with imperfect-quality items, controllable lead time and distribution free demand. Yugosl. J. Oper. Res. 23 (2013) 87–109. | MR | Zbl | DOI
[27] , Investing in lead-time variability reduction in a collaborative vendor-buyer supply chain model with stochastic lead time. Comput. Oper. Res. 72 (2016) 43–49. | MR | DOI
[28] , and , Joint pricing and inventory management for growing items in a supply chain under trade credit. Soft. Comput. 25 (2021) 7271–7295. | DOI
[29] , A fuzzy genetic algorithm with varying population size to solve an inventory model with credit-linked promotional demand in an imprecise planning horizon. Eur. J. Oper. Res. 213 (2011) 96–106. | MR | Zbl | DOI
[30] and , A single-vendor multi-buyer integrated model with controllable lead time and quality improvement through reduction in defective items. Int. J. Syst. Sci. Oper. Logist. 2 (2015) 1–14.
[31] , and , Integrated vendor-buyer cooperative models with stochastic demand in controllable lead time. Int. J. Prod. Econ. 92 (2004) 255–266. | DOI
[32] , , , and , Effect of price-sensitive demand and default risk on optimal credit period and cycle time for a deteriorating inventory model. RAIRO-Oper. Res. 55 (2021) S2575–S2592. | MR | DOI
[33] , and , Deteriorating inventory with preservation technology under price- and stock-sensitive demand. J. Indus. Manage. Optim. 16 (2020) 1585–1612. | MR | DOI
[34] , and , An integrated vendor-buyer model with quadratic demand under inspection policy and preservation technology. Hacettepe J. Math. Stat. 49 (2020) 1168–1189. | MR | DOI
[35] and , Vendor Managed inventory of a single-vendor multiple-retailer single-warehouse Supply Chain under stochastic Demands. Int. J. Supply Oper. Manage. 1 (2014) 297–313.
[36] , Optimal lot sizing, process quality improvement and setup cost reduction. Oper. Res. 34 (1986) 37–144. | Zbl | DOI
[37] and , Customer lead time management when both demand and price are lead time sensitive. Eur. J. Oper. Res. 153 (2004) 769–781. | MR | Zbl | DOI
[38] and , Multiple-buyer single-vendor in a continuous review inventory model with ordering cost reduction dependent on lead time. Int. J. Recent Innov. Trends Comput. Communi. 6 (2018) 154–160.
[39] and , Economic production cycles with imperfect production processes. IIE Trans. 18 (1986) 48–55. | DOI
[40] and , Economic production quantity model for items with imperfect quality. Int. J. Prod. Econ. 64 (2000) 59–64. | DOI
[41] , , and , Channel coordination with price discount mechanism under price-sensitive market demand. Int. Trans. Oper. Res. 27 (2019) 1–25. | MR
[42] , , and , Supplier selection in three echelon supply chain and vendor managed inventory model under price dependent demand condition. Int. J. Supply Oper. Manage. 2 (2016) 1079–1101.
[43] , and , An integrated inventory model for multi-echelon supply chains with deteriorating items: a price-dependent demand approach. J. Indus. Prod. Eng. 37 (2020) 87–96.
[44] , A constrained integrated imperfect manufacturing-inventory system with preventive maintenance and partial backordering. Ann. Oper. Res. 261 (2018) 303–337. | MR | DOI
[45] , and , An EOQ inventory model with partial backordering and reparation of imperfect products. Int. J. Prod. Econ. 182 (2016) 418–434. | DOI
[46] , and , Multiproduct multiple-buyer single-vendor supply chain problem with stochastic demand, variable lead-time, and multi-chance constraint. Expert Syst. Appl. 39 (2012) 5338–5348. | DOI
[47] and , Single-vendor multi-buyer integrated inventory system for multi-item. Int. J. Math. Oper. Res 14 (2019) 359–376. | MR | DOI
[48] and , A vendor-buyer inventory model for defective items with errors in inspections, stochastic lead time and freight cost. INFOR 57 (2019) 597–622. | MR
[49] , Inventory control and price theory. Manage. Sci. 2 (1955) 61–68. | DOI
[50] , , , and , Collaboration for a closed-loop deteriorating inventory supply chain with multi-retailer and price-sensitive demand. Int. J. Prod. Econ. 143 (2013) 557–566. | DOI
[51] and , Inventory and lead time planning with lead-time sensitive demand. IIE Trans. 39 (2007) 439–452. | DOI
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