Optimal manufacturer's cost sharing ratio, shipping policy and production rate – A two-echelon supply chain

Rau, 2003, Integrated inventory model for deteriorating items under a multi-echelon supply chain environment, Int J Prod Econ, 86, 155, 10.1016/S0925-5273(03)00048-3 Zhao, 2018, Stochastic customer order scheduling with setup times to minimize expected cycle time, Int J Prod Res, 7543, 1 Taifa, 2019, Cycle time reduction for productivity improvement in the manufacturing industry, J Ind Eng Manag Stud, 6, 147 Cachon, 1999, Competitive and cooperative inventory policies in a two-stage supply chain, Manag Sci, 45, 936, 10.1287/mnsc.45.7.936 AlDurgam, 2019, Economic production quantity model with variable machining rates and product quality, Int J Eng Bus Manag, 11, 1, 10.1177/1847979019872619 Chang, 2006, Integrated vendor–buyer cooperative inventory models with controllable lead time and ordering cost reduction, Eur J Oper Res, 170, 481, 10.1016/j.ejor.2004.06.029 Gharaei, 2021, An integrated stochastic EPQ model under quality and green policies: Generalised cross decomposition under the separability approach, Int J Syst Sci Oper Logist, 8, 119 Ghiami, 2015, A two-echelon production-inventory model for deteriorating items with multiple buyers, Int J Prod Econ, 159, 233, 10.1016/j.ijpe.2014.09.017 Jalbar, 2005, Integer-ratio policies for distribution/inventory systems, Int J Prod Econ, 93-94, 407, 10.1016/j.ijpe.2004.06.037 Ouyang, 2004, Integrated vendor–buyer cooperative models with stochastic demand in controllable lead time, Int J Prod Econ, 92, 255, 10.1016/j.ijpe.2003.10.016 Sarkar, 2013, A production-inventory model with probabilistic deterioration in two-echelon supply chain management, Appl Math Model, 37, 3138, 10.1016/j.apm.2012.07.026 Yan, 2011, An integrated production-distribution model for a deteriorating inventory item, Int J Prod Econ, 133, 228, 10.1016/j.ijpe.2010.04.025 Yang, 2000, Economic ordering policy of deteriorated item for vendor and buyer: an integrated approach, Prod Plan Control, 11, 474, 10.1080/09537280050051979 Yu, 2004, An integrated vendor-managed-inventory model for deteriorating item, Chin J Manag Sci, 12, 32 Utama, 2022, Integrated procurement-production inventory model in supply chain: a systematic review, Oper Res Perspect, 9 Kim, 1997, Implementation of JIT purchasing: an integrated approach, Prod Plan Control, 2, 152 Chou, 2000 Klein, 2007, Competitive and cooperative positioning in supply chain logistics relationships, Decis Sci, 38, 611, 10.1111/j.1540-5915.2007.00172.x Glock, 2012, The joint economic lot size problem: a review, Int J Prod Econ, 136, 671, 10.1016/j.ijpe.2011.10.026 Gharaei, 2022, An integrated lot-sizing policy for the inventory management of constrained multi-level supply chains: Null-space method, Int J Syst Sci Oper Logist Dolai, 2022, Analyzing an imperfect production inventory model for green products considering learning effect on screening process under advertisement dependent credit period, J Ind Manag Optim Panja, 2020, Exploring a two-layer green supply chain game theoretic model with credit linked demand and mark-up under revenue sharing contract, J Clean Prod, 250, 10.1016/j.jclepro.2019.119491 Khara, 2020, Sustainable recycling in an imperfect production system with acceptance quality level dependent development cost and demand, Comput Ind Eng, 142, 10.1016/j.cie.2020.106300 Glock, 2010, Batch sizing with controllable production rates, Int J Prod Econ, 48, 5925, 10.1080/00207540903170906 Khouja, 1994, The economic production lot size model under volume flexibility, Comput Oper Res, 22, 515, 10.1016/0305-0548(94)00032-4 Giri, 2005, Optimal design of unreliable production–inventory systems with variable production rate, Eur J Oper Res, 162, 372, 10.1016/j.ejor.2003.10.015 Larsen, 2005, The economic production lot size model extended to include more than one production rate, Int Trans Oper Res, 12, 339, 10.1111/j.1475-3995.2005.500_1.x Sana, 2010, An economic production lot size model in an imperfect production system, Eur J Oper Res, 201, 158, 10.1016/j.ejor.2009.02.027 Manna, 2018, An EPQ model with promotional demand in random planning horizon: Population varying genetic algorithm approach, J Intel Manuf, 29, 1515, 10.1007/s10845-016-1195-0 Dolai, 2021, Work performance dependent screening process under preservation technology in an imperfect production system, J Ind Prod Eng, 38, 414 Askari, 2021, A multi-product EPQ model for defective production and inspection with single machine, and operational constraints: Stochastic programming approach, 10.1007/978-3-030-89743-7_10 Hax, 1984 Silver, 1998 Glock, 2021, The impact of controllable production rates on the performance of inventory systems: a systematic review of the literature, Eur J Oper Res, 288, 703, 10.1016/j.ejor.2020.05.033 Glock, 2012, Lead time reduction strategies in a single-vendor–single-buyer integrated inventory model with lot size-dependent lead times and stochastic demand, Int J Prod Econ, 136, 37, 10.1016/j.ijpe.2011.09.007 Jauhari, 2014, Joint economic lot size (JELS) model for single-vendor single-buyer with variable production rate and partial backorder, Int J Oper Res, 20, 91, 10.1504/IJOR.2014.060517 AlDurgam, 2017, A single-vendor single-manufacturer integrated inventory model with stochastic demand and variable production rate, Int J Prod Econ, 191, 335, 10.1016/j.ijpe.2017.05.017 Kim, 2018, Production planning for a two-stage production system with multiple parallel machines and variable production rates, Int J Prod Econ, 196, 284, 10.1016/j.ijpe.2017.11.018 Jauhari, 2022, Low carbon inventory model for vendor‒buyer system with hybrid production and adjustable production rate under stochastic demand, Appl Math Model, 108, 840, 10.1016/j.apm.2022.04.012 Jauhari, 2022, Sustainable inventory management with hybrid production system and investment to reduce defects, Ann Oper Res Lu, 2016, Optimal buyer’s replenishment policy in the integrated inventory model for imperfect items, Math Problems Eng, 2016, 1 Popov, 2019, Mathematical approach for determining the optimal size of a logistic unit in case of high transport risk, 110018, 2172, 10.1063/1.5133621 Siajadi, 2006, Joint economic lot size in distribution system with multiple shipment policy, Int J Prod Econ, 102, 302, 10.1016/j.ijpe.2005.04.003 David, 2003, How far should JIT vendor-buyer relationship go?, Int J Prod Econ, 81-82, 361, 10.1016/S0925-5273(02)00274-8 Herbon, 2020, An approximated solution to the constrained integrated manufacturer-buyer supply problem, Oper Res Perspect, 7 Maimon, 1998 Roohnavazfar, 2019, Optimal paths in multi-stage stochastic decision networks, Oper Res Perspect, 6