A two-echelon supply chain model with price and warranty dependent demand and pro-rata warranty policy under cost sharing contract
In this article, a two-echelon supply chain model with a single-vendor a single-buyer is considered. The vendor's production process is imperfect and the market demand is assumed to be dependent on the buyer's selling price and warranty period. The vendor consents to return a definite portion of the buyer's purchase value, if any product is found defective within the length of warranty. The refund value or the warranty cost is considered as a function of the warranty period and the buyer's selling price of the item. This warranty cost is assumed to be fully borne by the vendor in the first model (Model I) while in the second model (Model II), it is assumed that the buyer agrees to bear a portion of the warranty cost. The proposed models are solved under decentralized scenario. We also derive and optimize the average total profit of the supply chain in order to obtain the optimal decisions of the centralized model. We consider a Stackelberg game between the vendor and the buyer in the decentralized scenario, where the vendor is assumed to be the leader and the buyer as the pursuer. Through numerical study, it is observed that, with respect to all the key decisions of the models, Model II provides better outcomes than Model I. Sensitivity analysis is also carried out to examine the impacts of changes of parameter-values on the optimum decisions.
Blischke, W.R., & Murthy, D.N.P. (1992). Product warranty management: A taxonomy for warranty policies. European journal of operational research, 62(2), 127-148. DOI: https://doi.org/10.1016/0377-2217(92)90242-2
Chao, G.H., Iravani, S.M., & Savaskan, R.C. (2009). Quality improvement incentives and product recall cost sharing contracts. Management Science, 55(7), 1122-1138. DOI: https://doi.org/10.1287/mnsc.1090.1008
Chen, X., Li, L., & Zhou, M. (2012). Manufacturers pricing strategy for supply chain with warranty period-dependent demand. Omega, 40(6), 807-816. DOI: https://doi.org/10.1016/j.omega.2011.12.010
Cheng, T. (1991). An economic order quantity model with demand-dependent unit production cost and imperfect production processes. IIE transactions, 23(1), 23-28. DOI: https://doi.org/10.1080/07408179108963838
Cheng, Y., Wang, W., Wei, C., & Lee, K. (2018). An integrated lot-sizing model for imperfect production with multiple disposals of defective items. Scientia Iranica. Transaction E. Industrial Engineering, 25(2), 852-867.
Chu, L.Y., & Sappington, D.E. (2007). Simple cost-sharing contracts. American Economic Review, 97(1), 419-428. DOI: https://doi.org/10.1257/000282807780323433
De Giovanni, P., & Zaccour, G. (2013). Cost revenue sharing in a closed-loop supply chain. In Advances in Dynamic Games, Springer, 395-421. DOI: https://doi.org/10.1007/978-0-8176-8355-9_20
Despic, D., Bojovic, N., Kilibarda, M. & Kapetanović, M. (2019). Assessment of efficiency of military transport units using the DEA and SFA methods. Military Technical Courier, 67(1), 68–92.
Ertogral, K., Darwish, M., & Ben-Daya, M. (2007). Production and shipment lot sizing in a vendor-buyer supply chain with transportation cost. European Journal of Operational Research, 176(3),1592-1606. DOI: https://doi.org/10.1016/j.ejor.2005.10.036
Giri, B.C., Mondal, C., & Maiti, T. (2018). Analyzing 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. DOI: https://doi.org/10.1016/j.jclepro.2018.04.092
Goyal, S., & Szendrovits, A.Z. (1986). A constant lot size model with equal and unequal sized batch shipments between production stages. CSCW, 55(7), 1122-1138.
Goyal, S.K., & Cardenas-Barron, L.E. (2002). Note on: economic production quantity model for items with imperfect quality a practical approach. International Journal of Production Economics, 77(1), 85-87. DOI: https://doi.org/10.1016/S0925-5273(01)00203-1
Goyal, S.K., & Nebebe, F. (2000).Determination of economic production shipment policy for a single-vendor single-buyer system. European Journal of Operational Research, 121(1), 175-178. DOI: https://doi.org/10.1016/S0377-2217(99)00013-2
Heydari, J., & Asl-Naja_, J. (2016). Coordinating inventory decisions in a two-echelon supply chain through the target sales rebate contract. International Journal of Inventory Research, 3(1), 49-69. DOI: https://doi.org/10.1504/IJIR.2016.077454
Hill, R.M. (1999). The optimal production and shipment policy for the single-vendor single buyer integrated production-inventory problem. International Journal of Production Research, 37(11),2463-2475. DOI: https://doi.org/10.1080/002075499190617
Hill, R.M.(1997). The single-vendor single-buyer integrated production-inventory model with a generalised policy. European Journal of Operational Research, 97(3), 493-499. DOI: https://doi.org/10.1016/S0377-2217(96)00267-6
Hoque, M., & Goyal, S. (2000). An optimal policy for a single-vendor single-buyer integrated production inventory system with capacity constraint of the transport equipment. International Journal of Production Economics, 65(3), 305-315. DOI: https://doi.org/10.1016/S0925-5273(99)00082-1
Huang, C.K. (2004). An optimal policy for a single-vendor single-buyer integrated production inventory problem with process unreliability consideration. International Journal of Production Economics, 91(1), 91-98. DOI: https://doi.org/10.1016/S0925-5273(03)00220-2
Huang, Y.S., & Fang, C.C. (2008).A cost sharing warranty policy for products with deterioration. IEEE Transactions on Engineering Management, 55(4), 617-627. DOI: https://doi.org/10.1109/TEM.2008.927783
Jaber, M., Goyal, S., & Imran, M. (2008).Economic production quantity model for items with imperfect quality subject to learning effects. International Journal of Production Economics, 115(1), 143-150.
Jaber, M.Y., Goyal, S.K., & Imran, M. (2008).Economic production quantity model for items withimperfect quality subject to learning effects. International Journal of Production Economics, 115(1), 143-150. DOI: https://doi.org/10.1016/j.ijpe.2008.05.007
Jung, G.M., & Park, D.H. (2003).Optimal maintenance policies during the post-warranty period. Reliability Engineering & System Safety, 82(2), 173-185. DOI: https://doi.org/10.1016/S0951-8320(03)00144-3
Khan, M., Jaber, M., Gui_rida, A., & Zolfaghari, S. (2011). A review of the extensions of a modified eoq model for imperfect quality items. International Journal of Production Economics, 132(1), 1-12. DOI: https://doi.org/10.1016/j.ijpe.2011.03.009
Khorshidvand, B., Soleimani, H., Sibdari, S. & Esfahani, M.M.S. (2021).. Revenue management in a multi-level multi-channel supply chain considering pricing, greening, and advertising decisions. Journal of Retailing and Consumer Services, 59, 102425.
Lee, H.L., & Rosenblatt, M.J. (1987). Simultaneous determination of production cycle and inspection schedules in a production system. Management Science, 33(9), 1125-1136. DOI: https://doi.org/10.1287/mnsc.33.9.1125
Leng, M., & Parlar, M. (2010). Game-theoretic analyses of decentralized assembly supply chains: Non-cooperative equilibria vs. coordination with cost-sharing contracts. European Journal of Operational Research, 204(1), 96-104.
Maiti, T., & Giri, B.C. (2017). Two-period pricing and decision strategies in a two-echelon supply chain under price-dependent demand. Applied Mathematical Modelling, 42, 655-674. DOI: https://doi.org/10.1016/j.apm.2016.10.051
Mukhopadhyay, A., & Goswami, A. (2016).An EOQ model with shortages and selling price dependent time varying demand. International Journal of Supply Chain and Inventory Management, 1(2), 133-153. DOI: https://doi.org/10.1504/IJSCIM.2016.076411
Murthy, D., & Blischke, W. (1992). Product warranty management: an integrated framework for study. European Journal of Operational Research, 62(3), 261-281. DOI: https://doi.org/10.1016/0377-2217(92)90117-R
Murthy, D., & Blischke, W.R. (2000). Strategic warranty management: A life-cycle approach. IEEE Transactions on Engineering Management, 47(1), 40-54. DOI: https://doi.org/10.1109/17.820724
Murthy, D., & Djamaludin, I. (2002). New product warranty: A literature review. International Journal of Production Economics. International Journal of Production Economics, 79(3), 231-260. DOI: https://doi.org/10.1016/S0925-5273(02)00153-6
Naeij, J., & Shavandi, H. (2010). An optimal lot sizing and pricing in two echelon supply chain. International Journal of Industrial Engineering Computations, 1, 11-32. DOI: https://doi.org/10.5267/j.ijiec.2010.01.002
Pamucar, D.S. & Savin, L.M. (2020). Multiple-criteria model for optimal off-road vehicle selection for passenger transportation: BWM-COPRAS model. Military Technical Courier, 68(1), 28-64.
Park, M., Jung, K.M., & Park, D.H. (2013).Optimal post-warranty maintenance policy with repair time threshold for minimal repair. Reliability Engineering & System Safety, 111, 147-153. DOI: https://doi.org/10.1016/j.ress.2012.10.017
Polatoglu, H., & Sahin, I. (1998).Probability distributions of cost, revenue and profit over a warranty cycle. European Journal of Operational Research, 108(1), 170-183. DOI: https://doi.org/10.1016/S0377-2217(97)00094-5
Prez, F., & Torres, F. (2019).An integrated production-inventory model for deteriorating items to evaluate JIT purchasing alliances. International Journal of Industrial Engineering Computations, 10, 51-66.
Rogerson, W.P.(2003). Simple menus of contracts in cost-based procurement and regulation. American Economic Review, 93(3), 919-926. DOI: https://doi.org/10.1257/000282803322157160
Roy, A., Sana, S.S., & Chaudhuri, K. S. (2016).Joint decision on EOQ and pricing strategy of a dual channel of mixed retail and e-tail comprising of single manufacturer and retailer under stochastic demand. Computers & Industrial Engineering, 102, 423-434 DOI: https://doi.org/10.1016/j.cie.2016.05.002
Roy, A., Sana, S.S., & Chaudhuri, K. S. (2018).Optimal Pricing of competing retailers under uncertain demand-a two layer supply chain model. Annals of Operations Research 260 (1-2), 481-500 DOI: https://doi.org/10.1007/s10479-015-1996-0
Salameh, M., & Jaber, M. (2000).Economic production quantity model for items with imperfect quality. International Journal of Production Economics, 64(13), 59-64. DOI: https://doi.org/10.1016/S0925-5273(99)00044-4
Samanta, B., Giri, B.C., & Chaudhuri, K.S. (2018). A vendor-buyer supply chain model for deteriorating item with quadratic time-varying demand and pro-rata warranty policy. Springer, 371-383.
Sana, S.S. (2020). Price competition between green and non green products under corporate social responsible firm. Journal of Retailing and Consumer Services, 55, 102-118.
Shah, N.H., Chaudhari, U., & Jani, M.Y. (2016).An integrated production-inventory model with preservation technology investment for time-varying deteriorating item under time and price sensitive demand. International Journal of Inventory Research, 3(1), 81-98. DOI: https://doi.org/10.1504/IJIR.2016.077443
Taleizadeh, A., Crdenas-Barrn, L., Biabani, J., & Nikousokhan, R. (2012).Multi products single machine EPQ model with immediate rework process. International Journal of Industrial Engineering Computations, 3(2), 93-102. DOI: https://doi.org/10.5267/j.ijiec.2011.09.001
Thomas, M.U., & Rao, S.S. (1999). Warranty economic decision models: A summary and some suggested directions for future research. Operations Research, 47(6), 807-820. DOI: https://doi.org/10.1287/opre.47.6.807
Tsao, Y.C., & Sheen, G.J. (2012). Effects of promotion cost sharing policy with the sales learning curve on supply chain co ordination. Computers & Operations Research, 39(8), 1872-1878. DOI: https://doi.org/10.1016/j.cor.2011.07.009
Wei, J., Zhao, J., & Li, Y. (2015). Price and warranty period decisions for comple-mentary products with horizontal firms cooperation/noncooperation strategies. Journal of Cleaner Production, 105, 86-102. DOI: https://doi.org/10.1016/j.jclepro.2014.09.059
Wu, S. (2104).Warranty return policies for products with unknown claim causes and their optimisation. International Journal of Production Economics, 156, 52-61.
Xie, Y., Tai, A.H., Ching, W.K., & Siu, T.K. (2016).Pricing strategy for a two-echelon supply chain with optimized return effort level. International Journal of Production DOI: https://doi.org/10.1016/j.ijpe.2016.08.026
Yeh, R.H., Chen, M.Y., & Lin, C.Y. (2007).Optimal periodic replacement policy for repairable products under free-repair warranty. European Journal of Operational Research, 176(3), 1678-1686. DOI: https://doi.org/10.1016/j.ejor.2005.10.047
Yeh, R.H., Ho, W.T., & Tseng, S.T. (2000). Optimal production run length for products sold with warranty. European Journal of Operational Research, 120(3), 575-582. DOI: https://doi.org/10.1016/S0377-2217(99)00004-1
Zhao, H., Lin, B., Mao, W., & Ye, Y. (2014). Differential game analyses of logistics service supply chain coordination by cost sharing contract. Journal of Applied Mathematics, https://doi.org/10.1155/2014/842409. DOI: https://doi.org/10.1155/2014/842409