Coordination of a single-manufacturer multi-retailer supply chain with price and green sensitive demand under stochastic lead time
DOI:
https://doi.org/10.31181/dmame0319102022dKeywords:
Two-level supply chain, multiple retailers, stochastic lead time, price and green sensitive demand, price discount mechanismAbstract
When dealing with uncertainties in the supply chain and ensuring customer satisfaction, efficient management of lead time plays a significant role. Likewise, besides managing inventory and pricing strategies adeptly in multi-retailer supply chains, it has become inevitable for firms to embrace green and sustainable business practices. In this context, this paper considers a two-level supply chain consisting of a single manufacturer and multiple retailers in which the manufacturer produces a single product and delivers it to the retailers in equal-sized batches. Each retailer faces a price and green-sensitive market demand. The lead time is assumed to be a random variable that follows a normal distribution. Shortages for retailer inventory are allowed to occur and are completely backlogged. The centralized model and a decentralized model based on the leader-follower Stackelberg gaming approach are developed. A price discount mechanism between the manufacturer and retailers is proposed. For the acceptance of this contract, the upper and lower limits of the price discount rate are established. Numerical outcomes exhibit that the price discount mechanism effectively coordinates the supply chain and enhances both environmental and economical performances. A sensitivity analysis with respect to some key parameters is performed, and certain managerial insights are emphasized.
Downloads
References
Agrawal, A.K., & Yadav, S. (2020). Price and profit structuring for single manufacturer multi-buyer integrated inventory supply chain under price-sensitive demand condition. Computers & Industrial Engineering, 139, 106208. https://doi.org/10.1016/j.cie.2019.106208
Alfares, H.K., & Ghaithan, A.M. (2016). Inventory and pricing model with price-dependent demand, time-varying holding cost, and quantity discounts. Computers & Industrial Engineering, 94, 170–177. https://doi.org/10.1016/j.cie.2016.02.009
Aljazzar, S.M., Jaber, M.Y., & Moussawi-Haidar, L. (2017). Coordination of a three-level supply chain (supplier–manufacturer–retailer) with permissible delay in payments and price discounts. Applied Mathematical Modelling, 48, 289–302. https://doi.org/10.1016/j.apm.2017.04.011
Atamer, B., Bakal, ˙I.S., & Bayındır, Z.P. (2013). Optimal pricing and production decisions in utilizing reusable containers. International Journal of Production Economics, 143(2), 222–232. https://doi.org/10.1016/j.ijpe.2011.08.007
Barman, A., Das, R., & De, P. K. (2021a). Optimal pricing, replenishment scheduling, and preservation technology investment policy for multi-item deteriorating inventory model under shortages. International Journal of Modeling, Simulation, and Scientific Computing, 12(05), 2150039. https://doi.org/10.1142/S1793962321500392
Barman, D., Mahata, G. C., & Das, B. (2021b). Advance payment based vendor–buyer production inventory model with stochastic lead time and continuous review policy. Opsearch, 58(4), 1217-1237. https://doi.org/10.1007/s12597-021-00521-9
Basiri, Z., & Heydari, J. (2017). A mathematical model for green supply chain coordination with substitutable products. Journal of cleaner production, 145, 232–249. https://doi.org/10.1016/j.jclepro.2017.01.060
Ben-Daya, M., As’ ad, R., & Nabi, K.A. (2019). A single-vendor multi-buyer production remanufacturing inventory system under a centralized consignment arrangement. Computers & Industrial Engineering, 135, 10–27. https://doi.org/10.1016/j.cie.2019.05.032
Chan, C.K., Fang, F., & Langevin, A. (2018). Single-vendor multi-buyer supply chain coordination with stochastic demand. International Journal of Production Economics, 206, 110–133. https://doi.org/10.1016/j.ijpe.2018.09.024
Chen, Z., & Sarker, B.R. (2017). Integrated production-inventory and pricing decisions for a single-manufacturer multi-retailer system of deteriorating items under jit delivery policy. The International Journal of Advanced Manufacturing Technology, 89( 5), 2099–2117. https://doi.org/10.1007/s00170-016-9169-0
Duary, A., Das, S., Arif, M. G., Abualnaja, K. M., Khan, M. A. A., Zakarya, M., & Shaikh, A. A. (2022). Advance and delay in payments with the price-discount inventory model for deteriorating items under capacity constraint and partially backlogged shortages. Alexandria Engineering Journal, 61(2), 1735-1745. https://doi.org/10.1016/j.aej.2021.06.070
Ebrahimi, S., Hosseini-Motlagh, S.M., & Nematollahi, M. (2019). Proposing a delay in payment contract for coordinating a two-echelon periodic review supply chain with stochastic promotional effort dependent demand. International Journal of Machine Learning and Cybernetics,10(5), 1037–1050. https://doi.org/10.1007/s13042-017-0781-6
Esmaeili, M., & Nasrabadi, M. (2021). An inventory model for single-vendor multi-retailer supply chain under inflationary conditions and trade credit. Journal of Industrial and Production Engineering, 38(2), 75-88. https://doi.org/10.1080/21681015.2020.1845248
Ghosh, D., & Shah, J. (2015). Supply chain analysis under green sensitive consumer demand and cost sharing contract. International Journal of Production Economics, 164, 319–329. https://doi.org/10.1016/j.ijpe.2014.11.005
Giri, B. C., & Dash, A. (2022). Optimal batch shipment policy for an imperfect production system under price-, advertisement-and green-sensitive demand. Journal of Management Analytics, 9(1), 86-119. https://doi.org/10.1080/23270012.2021.1931495
Giri, B., & Masanta, M. (2019). Optimal production policy for a closed-loop supply chain with stochastic lead time and learning in production. Scientia Iranica, 26(5), 2936–2951. 10.24200/SCI.2019.21537
Giri, B., & Masanta, M. (2020). Developing a closed-loop supply chain model with price and quality dependent demand and learning in production in a stochastic environment. International Journal of Systems Science: Operations & Logistics, 7(2), 147–163. https://doi.org/10.1080/23302674.2018.1542042
Giri, B., & Roy, B. (2016). Modelling supply chain inventory system with controllable lead time under price-dependent demand. The International Journal of Advanced Manufacturing Technology, 84(9), 1861–1871. https://doi.org/10.1007/s00170-015-7829-0
Giri, B., Dash, A., & Sarkar, A. (2020a). A single-vendor single-buyer supply chain model with price and green sensitive demand under batch shipment policy and planned backorder. International Journal of Procurement Management, 13(3), 299–321. https://doi.org/10.1504/IJPM.2020.107478
Giri, B., Mondal, C., & Maiti, T. (2018). Analysing a closed-loop supply chain with selling price, warranty period and green sensitive consumer demand under revenue sharing contract. Journal of cleaner production, 190, 822–837. https://doi.org/10.1016/j.jclepro.2018.04.092
Giri, B.C., Dash, A., & Sarkar, A. (2020b). A single- manufacturer multi-retailer integrated inventory model with price dependent demand and stochastic lead time. International Journal of Supply and Operations Management, 7(4), 384–409. 10.22034/IJSOM.2020.4.7
He, X.J., Kim, J.G., & Hayya, J.C. (2005). The cost of lead-time variability: The case of the exponential distribution. International Journal of Production Economics, 97(2), 130–142. https://doi.org/10.1016/j.ijpe.2004.05.007
Heydari, J., Govindan, K., & Aslani, A. (2019). Pricing and greening decisions in a three-tier dual channel supply chain. International Journal of Production Economics, 217, 185–196. https://doi.org/10.1016/j.ijpe.2018.11.01
Heydari, J., Govindan, K., & Basiri, Z. (2021). Balancing price and green quality in presence of consumer environmental awareness: a green supply chain coordination approach. International Journal of Production Research, 59(7), 1957-1975. https://doi.org/10.1080/00207543.2020.1771457
Ho, C.H., Ouyang, L.Y., & Su, C.H. (2008). Optimal pricing, shipment and payment policy for an integrated supplier–buyer inventory model with two-part trade credit. European Journal of Operational Research, 187(2), 496–510. https://doi.org/10.1016/j.ejor.2007.04.015
Hoque, M. (2013). A manufacturer–buyer integrated inventory model with stochastic lead times for delivering equal-and/or unequal-sized batches of a lot. Computers & operations research, 40(11), 2740–2751. https://doi.org/10.1016/j.cor.2013.05.008
Hoque, M. A. (2021). An optimal solution policy to an integrated manufacturer-retailers problem with normal distribution of lead times of delivering equal and unequal-sized batches. Opsearch, 58(2), 483-512. https://doi.org/10.1007/s12597-020-00485-2
Jaggi, C., Pareek, S., Khanna, A., & Sharma, R. (2015). Two-warehouse inventory model for deteriorating items with price-sensitive demand and partially backlogged shortages under inflationary conditions. International Journal of Industrial Engineering Computations, 6(1), 59-80. 10.5267/j.ijiec.2014.9.001
Li, B., Zhu, M., Jiang, Y., & Li, Z. (2016). Pricing policies of a competitive dual-channel green supply chain. Journal of Cleaner Production, 112, 2029–2042. https://doi.org/10.1016/j.jclepro.2015.05.017
Li, Y., Xu, X., & Ye, F. (2011). Supply chain coordination model with controllable lead time and service level constraint. Computers & Industrial Engineering, 61(3), 858–864. https://doi.org/10.1016/j.cie.2011.05.019
Lieckens, K., & Vandaele, N. (2007). Reverse logistics network design with stochastic lead times. Computers & Operations Research, 34(2), 395–416. https://doi.org/10.1016/j.cor.2005.03.006
Lin, H.J. (2016). Investing in lead-time variability reduction in a collaborative vendor–buyer supply chain model with stochastic lead time. Computers & Operations Research, 72, 43–49. https://doi.org/10.1016/j.cor.2016.02.002
Lin, Y.J., & Ho, C.H. (2011). Integrated inventory model with quantity discount and price-sensitive demand. Top, 19(1), 177–188. https://doi.org/10.1007/s11750-009-0132-1
Majumder, A., Jaggi, C.K., & Sarkar, B. (2018). A multi-retailer supply chain model with backorder and variable production cost. RAIRO-Operations Research, 52(3), 943–954. https://doi.org/10.1051/ro/2017013
Malleeswaran, B., & Uthayakumar, R. (2022). A single-manufacturer multi-retailer sustainable reworking model for green and environmental sensitive demand under discrete ordering cost reduction. Journal of Management Analytics, 1-20. https://doi.org/10.1080/23270012.2022.2030255
Mondal, C., & Giri, B. C. (2020). Retailers’ competition and cooperation in a closed-loop green supply chain under governmental intervention and cap-and-trade policy. Operational Research, 1-36. https://doi.org/10.1007/s12351-020-00596-0
Mondal, C., & Giri, B. C. (2021). Analyzing a manufacturer-retailer sustainable supply chain under cap-and-trade policy and revenue sharing contract. Operational Research, 1-36. https://doi.org/10.1007/s12351-021-00669-8
Najafnejhad, E., Tavassoli Roodsari, M., Sepahrom, S., & Jenabzadeh, M. (2021). A mathematical inventory model for a single-vendor multi-retailer supply chain based on the Vendor Management Inventory Policy. International Journal of System Assurance Engineering and Management, 12(3), 579-586. https://doi.org/10.1007/s13198-021-01120-z
Niksirat, M., & Nasseri, H. S. (2022). Knapsack problem in fuzzy nature: Different models based on credibility ranking method. Yugoslav Journal of Operations Research, 32(2), 203-218.
Nandra, R., Majumder, A., & Mishra, M. (2021a). A multi-retailer sustainable supply chain model with information sharing and quality deterioration. RAIRO-Operations Research, 55, S2773-S2794. https://doi.org/10.1051/ro/2020113
Nandra, R., Marak, K. R., Kaur, R., Dey, B. K., & Majumder, A. (2021b). Establishing relation between production rate and product quality in a single-vendor multi-buyer supply chain model. International Journal of Services Operations and Informatics, 11(2-3), 315-331. https://doi.org/10.1504/IJSOI.2021.117256
Nouri, M., Hosseini-Motlagh, S.M., Nematollahi, M., & Sarker, B.R. (2018). Coordinating manufacturer’s innovation and retailer’s promotion and replenishment using a compensation-based wholesale price contract. International Journal of Production Economics, 198, 11–24. https://doi.org/10.1016/j.ijpe.2018.01.023
Rad, M.A., Khoshalhan, F., & Glock, C.H. (2014). Optimizing inventory and sales decisions in a two-stage supply chain with imperfect production and backorders. Computers & Industrial Engineering, 74, 219–227. https://doi.org/10.1016/j.cie.2014.05.004
Shaikh, A., Mishra, P., & Talati, I. (2022). Optimal Ordering and Pricing Decision for Items Following Price Sensitive Quadratic Demand Under Combined Payment Scheme. Yugoslav Journal of Operations Research, 33(1), 41-58.
Safarnezhad, M., Aminnayeri, M., & Ghasemy Yaghin, R. (2021). Joint pricing and lot sizing model with statistical inspection and stochastic lead time. INFOR: Information Systems and Operational Research, 59(1), 111-144. https://doi.org/10.1080/03155986.2020.1794227
Saha, S., & Goyal, S. (2015). Supply chain coordination contracts with inventory level and retail price dependent demand. International Journal of Production Economics, 161, 140–152. https://doi.org/10.1016/j.ijpe.2014.12.025
Sajadieh, M.S., Jokar, M.R.A., & Modarres, M. (2009). Developing a coordinated vendor–buyer model in two-stage supply chains with stochastic lead-times. Computers & Operations Research, 36(8), 2484–2489. https://doi.org/10.1016/j.cor.2008.10.001
Sarkar, B., Dey, B. K., Sarkar, M., & AlArjani, A. (2021). A sustainable online-to-offline (O2O) retailing strategy for a supply chain management under controllable lead time and variable demand. Sustainability, 13(4), 1756. https://doi.org/10.3390/su13041756
Sarkar, B., Majumder, A., Sarkar, M., Dey, B. K., & Roy, G. (2017). Two-echelon supply chain model with manufacturing quality improvement and setup cost reduction. Journal of Industrial & Management Optimization, 13(2), 1085.
Sarkar, B., Majumder, A., Sarkar, M., Kim, N., & Ullah, M. (2018). Effects of variable production rate on quality of products in a single-vendor multi-buyer supply chain management. The International Journal of Advanced Manufacturing Technology, 99(1), 567-581. https://doi.org/10.1007/s00170-018-2527-3
Sarkar, S., Giri, B.C., & Sarkar, A.K. (2020a). A vendor–buyer inventory model with lot-size and production rate dependent lead time under time value of money. RAIRO-Operations Research, 54(4), 961–979. https://doi.org/10.1051/ro/2019030
Sarkar, S., Tiwari, S., Wee, H.M., & Giri, B. (2020b). Channel coordination with price discount mechanism under price-sensitive market demand. International Transactions in Operational Research, 27(5), 2509–2533. https://doi.org/10.1111/itor.12678
Sepehri, A., & Gholamian, M. R. (2022). A green inventory model with imperfect items considering inspection process and quality improvement under different shortages scenarios. Environment, Development and Sustainability, 1-29. https://doi.org/10.1007/s10668-022-02187-9
Swami, S., & Shah, J. (2013). Channel coordination in green supply chain management. Journal of the operational research society, 64(3), 336–351. https://doi.org/10.1057/jors.2012.44
Viswanathan, S., & Piplani, R. (2001). Coordinating supply chain inventories through common replenishment epochs. European Journal of Operational Research, 129(2), 277–286. https://doi.org/10.1016/S0377-2217(00)00225-3
Whitin, T.M. (1955). Inventory control and price theory. Management science, 2(1), 61–68. https://doi.org/10.1287/mnsc.2.1.61
Xu, J., Qi, Q., & Bai, Q. (2018). Coordinating a dual-channel supply chain with price discount contracts under carbon emission capacity regulation. Applied Mathematical Modelling, 56, 449–468. https://doi.org/10.1016/j.apm.2017.12.018
Yang, C.T., Ouyang, L.Y., & Wu, H. H. (2009). Retailer’s optimal pricing and ordering policies for non-instantaneous deteriorating items with price-dependent demand and partial backlogging. Mathematical Problems in Engineering, 2009, Article ID 198305. https://doi.org/10.1155/2009/198305.
Yang, S., Liu, H., Wang, G., & Hao, Y. (2021). Supplier’s cooperation strategy with two competing manufacturers under wholesale price discount contract considering technology investment. Soft Computing, 1-18. https://doi.org/10.1007/s00500-021-05904-0
Zanoni, S., Mazzoldi, L., Zavanella, L.E., & Jaber, M.Y. (2014). A joint economic lot size model with price and environmentally sensitive demand. Production & Manufacturing Research, 2(1), 341–354. https://doi.org/10.1080/21693277.2014.913125
Zhang, K., & Feng, S. (2014). Research on revenue sharing coordination contract in automobile closed-loop supply chain. In Proceedings of 2014 IEEE International Conference on Service Operations and Logistics, and Informatics, IEEE, 298–302. https://doi.org/10.1108/IMDS-05-2017-0181
Zhang, R., Liu, J., & Qian, Y. (2022). Wholesale-price vs cost-sharing contracts in a green supply chain with reference price effect under different power structures. Kybernetes, https://doi.org/10.1108/K-11-2021-1096.
Zhu, Q., Li, X., & Zhao, S. (2018). Cost-sharing models for green product production and marketing in a food supply chain. Industrial Management & Data Systems, 118, 654-682. https://doi.org/10.1108/IMDS-05-2017-0181
Zu, Y., Deng, D., & Chen, L. (2021). Optimal control of carbon emission reduction strategies in supply chain with wholesale price and consignment contract. Environmental Science and Pollution Research, 28(43), 61707-61722. https://doi.org/10.1007/s11356-021-15080-1
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Decision Making: Applications in Management and Engineering
This work is licensed under a Creative Commons Attribution 4.0 International License.
