Unequal shipment policy in a sustainable production inventory system considering defective items and multi-level price breaks

References

• Ali, H., & Zhang, J. (2023). A fuzzy multi-objective decision-making model for global green supplier selection and order allocation under quantity discounts. Expert Systems with Applications, 225, 120119. https://doi.org/10.1016/j.eswa.2023.120119
   Web of Science ®Google Scholar
• Battini, D., Persona, A., & Sgarbossa, F. (2014). A sustainable EOQ model: Theoretical formulation and applications. International Journal of Production Economics, 149, 145–153. https://doi.org/10.1016/j.ijpe.2013.06.026
   Web of Science ®Google Scholar
• Beck, F. G., Glock, C. H., & Kim, T. (2017). Coordination of a production network with a single buyer and multiple vendors with geometrically increasing batch shipments. International Journal of Production Economics, 193, 633–646. https://doi.org/10.1016/j.ijpe.2017.07.015
   Web of Science ®Google Scholar
• Bonney, M., & Jaber, M. Y. (2011). Environmentally responsible inventory models: Non-classical models for a non-classical era. International Journal of Production Economics, 133(1), 43–53. https://doi.org/10.1016/j.ijpe.2009.10.033
   Web of Science ®Google Scholar
• Bouchery, Y., Ghaffari, A., Jemai, Z., & Dallery, Y. (2012). Including sustainability criteria into inventory models. European Journal of Operational Research, 222(2), 229–240. https://doi.org/10.1016/j.ejor.2012.05.004
   Web of Science ®Google Scholar
• Castellano, D., Gabbrielli, R., Gallo, M., Giri, B. C., & Sarkar, S. (2023). Optimizing production-inventory replenishment and lead time decisions under a fill rate constraint in a two-echelon sustainable supply chain with quality issues. International Journal of Systems Science: Operations & Logistics, 10(1), 2173540.
   Web of Science ®Google Scholar
• Chaharmahali, G., Molla-Alizadeh-Zavardehi, D., Jasemi, M., & Ghandalipour, S. (2022). Modified metaheuristic algorithms to design a closed-loop supply chain network considering quantity discount and fixed-charge transportation. Expert Systems with Applications, 202, 117364. https://doi.org/10.1016/j.eswa.2022.117364
   Web of Science ®Google Scholar
• Daryanto, Y., Wee, H. M., & Astanti, R. D. (2019). Three-echelon supply chain model considering carbon emission and item deterioration. Transportation Research Part E: Logistics and Transportation Review, 122, 368–383. https://doi.org/10.1016/j.tre.2018.12.014
   Web of Science ®Google Scholar
• Das, R., Barman, A., Roy, B., & De, P. K. (2022). Pricing and greening strategies in a dual-channel supply chain with cost and profit sharing contracts. Environment, Development and Sustainability, 25(6), 5053–5086. https://doi.org/10.1007/s10668-022-02255-0
   Web of Science ®Google Scholar
• Dash, A., Giri, B. C., & Sarkar, A. K. (2022). Coordination and defect management strategy for a two-level supply chain under price and sales effort-sensitive demand. International Journal of Systems Science: Operations & Logistics, 10(1), 2103198.
   Google Scholar
• Gautam, P., Kishore, A., Khanna, A., & Jaggi, C. K. (2019). Strategic defect management for a sustainable green supply chain. Journal of Cleaner Production, 233, 226–241. https://doi.org/10.1016/j.jclepro.2019.06.005
   Web of Science ®Google Scholar
• Gautam, P., Maheshwari, S., & Jaggi, C. K. (2022). Sustainable production inventory model with greening degree and dual determinants of defective items. Journal of Cleaner Production, 367, 132879. https://doi.org/10.1016/j.jclepro.2022.132879
   Web of Science ®Google Scholar
• Giri, B. C., & Dash, A. (2021). 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
   Web of Science ®Google Scholar
• Giri, B. C., & Roy, B. (2013). A vendor–buyer integrated production–inventory model with quantity discount and unequal sized shipments. International Journal of Operational Research, 16(1), 1–13. https://doi.org/10.1504/IJOR.2013.050537
   Google Scholar
• Giri, B. C., & Sharma, S. (2014). Lot sizing and unequal-sized shipment policy for an integrated production–inventory system. International Journal of Systems Science, 45(5), 888–901. https://doi.org/10.1080/00207721.2012.742595
   Web of Science ®Google Scholar
• Giri, B. C., & Sharma, S. (2017). Integrated model for an imperfect production–inventory system with a generalised shipment policy, errors in quality inspection and ordering cost reduction. International Journal of Systems Science: Operations & Logistics, 4(3), 260–274.
   Google Scholar
• Glock, C. H. (2012). A comparison of alternative delivery structures in a dual sourcing environment. International Journal of Production Research, 50(11), 3095–3114. https://doi.org/10.1080/00207543.2011.592160
   Web of Science ®Google Scholar
• Goyal, S. K. (1995). A one-vendor multi-buyer integrated inventory model: A comment. European Journal of Operational Research, 82(1), 209–210. https://doi.org/10.1016/0377-2217(93)E0357-4
   Web of Science ®Google Scholar
• 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. https://doi.org/10.1016/S0377-2217(99)00013-2
   Web of Science ®Google Scholar
• Guchhait, R., Dey, B. K., Bhuniya, S., Ganguly, B., Mandal, B., Bachar, R. K., Sarkar, B., Wee, H. M., & Chaudhuri, K. (2020). Investment for process quality improvement and setup cost reduction in an imperfect production process with warranty policy and shortages. RAIRO Operations Research, 54(1), 251–266. https://doi.org/10.1051/ro/2018101
   Web of Science ®Google Scholar
• Guchhait, R., & Sarkar, B. (2021). Economic and environmental assessment of an unreliable supply chain management. RAIRO Operations Research, 55(5), 3153–3170. https://doi.org/10.1051/ro/2021128
   Web of Science ®Google Scholar
• Hariga, M., As'ad, R., & Shamayleh, A. (2017). Integrated economic and environmental models for a multi stage cold supply chain under carbon tax regulation. Journal of Cleaner Production, 166, 1357–1371. https://doi.org/10.1016/j.jclepro.2017.08.105
   Web of Science ®Google Scholar
• Harris, F. W. (1913). How many parts to make at once. Factory, The Magazine of Management, 10(2), 135–136.
   Google Scholar
• He, P., Chen, L., Zou, X., Li, S., Shen, H., & Jian, J. (2019). Energy taxes, carbon dioxide emissions, energy consumption and economic consequences: A comparative study of nordic and G7 countries. Sustainability, 11(21), 6100. https://doi.org/10.3390/su11216100
   Web of Science ®Google Scholar
• 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. https://doi.org/10.1016/S0377-2217(96)00267-6
   Web of Science ®Google Scholar
• Hoque, M. A. (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
   Web of Science ®Google Scholar
• Hoque, M. A., & Bhattacharya, A. (2020). A manufacturer-buyers integrated inventory model with generic distribution of lead times to deliver equal and/or unequal batch sizes. Computers & Operations Research, 124, 105047. https://doi.org/10.1016/j.cor.2020.105047
   Web of Science ®Google Scholar
• Hota, S. K., Ghosh, S. K., & Sarkar, B. (2022). A solution to the transportation hazard problem in a supply chain with an unreliable manufacturer. AIMS Environmental Science, 9(3), 354–380. https://doi.org/10.3934/environsci.2022023
   Web of Science ®Google Scholar
• Huang, C. K. (2002). An integrated vendor-buyer cooperative inventory model for items with imperfect quality. Production Planning and Control, 13(4), 355–361. https://doi.org/10.1080/09537280110112424
   Web of Science ®Google Scholar
• 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. https://doi.org/10.1016/S0925-5273(03)00220-2
   Web of Science ®Google Scholar
• Huang, Y. S., Ho, J. W., Jian, H. J., & Tseng, T. L. (2021). Quantity discount coordination for supply chains with deteriorating inventory. Computers & Industrial Engineering, 152, 106987. https://doi.org/10.1016/j.cie.2020.106987
   Web of Science ®Google Scholar
• Jaber, M. Y., Glock, C. H., & El Saadany, A. M. A. (2013). Supply chain coordination with emissions reduction incentives. International Journal of Production Research, 51(1), 69–82. https://doi.org/10.1080/00207543.2011.651656
   Web of Science ®Google Scholar
• Jain, M., Sharma, N., & Singh, P. (2023). Sustainable inventory prediction with random defect and rework using Bat algorithm. RAIRO-Operations Research, 57(2), 481–501. https://doi.org/10.1051/ro/2023011
   Web of Science ®Google Scholar
• Jauhari, W. A., Pamuji, A. S., & Rosyidi, C. N. (2014). Cooperative inventory model for vendor–buyer system with unequal-sized shipment, defective items and carbon emission cost. International Journal of Logistics Systems and Management, 19(2), 163–186. https://doi.org/10.1504/IJLSM.2014.064657
   Google Scholar
• Juman, Z. A. M. S., M'Hallah, R., Lokuhetti, R., & Battaïa, O. (2022). A multi-vendor multi-buyer integrated production-inventory model with synchronised unequal-sized batch delivery. International Journal of Production Research, 61(2), 462–484. https://doi.org/10.1080/00207543.2021.2009586
   Web of Science ®Google Scholar
• Karimpoor, M., Nasiri, G. R., & Monabbati, S. E. (2023). Production, distribution, and capacity planning for an integrated buyer-vendor system incorporating different production and shipping scenarios. Computers & Industrial Engineering, 184, 109545.. https://doi.org/10.1016/j.cie.2023.109545
   Web of Science ®Google Scholar
• Kazemi, N., Abdul-Rashid, S. H., Ghazilla, R. A. R., Shekarian, E., & Zanoni, S. (2016). Economic order quantity models for items with imperfect quality and emission considerations. International Journal of Systems Science: Operations & Logistics, 5(2), 99–115.
   Google Scholar
• Khan, M. A. A., Ahmed, S., Babu, M. S., & Sultana, N. (2020). Optimal lot-size decision for deteriorating items with price-sensitive demand, linearly time-dependent holding cost under all-units discount environment. International Journal of Systems Science: Operations & Logistics, 9(1), 61–74.
   Google Scholar
• Khanna, A., Gautam, P., Sarkar, B., & Jaggi, C. K. (2020). Integrated vendor–buyer strategies for imperfect production systems with maintenance and warranty policy. RAIRO-Operations Research, 54(2), 435–450. https://doi.org/10.1051/ro/2019029
   Web of Science ®Google Scholar
• Krichen, S., Laabidi, A., & Abdelaziz, F. B. (2011). Single supplier multiple cooperative retailers inventory model with quantity discount and permissible delay in payments. Computers & Industrial Engineering, 60(1), 164–172. https://doi.org/10.1016/j.cie.2010.10.014
   Web of Science ®Google Scholar
• Kwon, Y. W., Sheu, J. B., & Yoo, S. H. (2022). Quadratic quantity discount contract under price-dependent demand and consumer returns. Transportation Research Part E: Logistics and Transportation Review, 164, 102756. https://doi.org/10.1016/j.tre.2022.102756
   Web of Science ®Google Scholar
• Li, J., Ou, J., & Cao, B. (2023). The roles of cooperative advertising and endogenous online price discount in a dual-channel supply chain. Computers & Industrial Engineering, 176, 108980. https://doi.org/10.1016/j.cie.2023.108980
   Web of Science ®Google Scholar
• Mahato, F., Choudhury, M., & Mahata, G. C. (2023). Inventory models for deteriorating items with fixed lifetime, partial backordering and carbon emissions policies. Journal of Management Analytics, 10(1), 129–190. https://doi.org/10.1080/23270012.2023.2179431
   Web of Science ®Google Scholar
• Mandal, P., & Giri, B. C. (2017). A two-warehouse integrated inventory model with imperfect production process under stock-dependent demand and quantity discount offer. International Journal of Systems Science: Operations & Logistics, 6(1), 15–26.
   Google Scholar
• Manna, A. K., Das, B., & Tiwari, S. (2020). Impact of carbon emission on imperfect production inventory system with advance payment base free transportation. RAIRO-Operations Research, 54(4), 1103–1117. https://doi.org/10.1051/ro/2019015
   Web of Science ®Google Scholar
• Marchi, B., Zanoni, S., & Jaber, M. Y. (2019). Economic production quantity model with learning in production, quality, reliability and energy efficiency. Computers & Industrial Engineering, 129, 502–511. https://doi.org/10.1016/j.cie.2019.02.009
   Web of Science ®Google Scholar
• Mashud, A. H. M., Pervin, M., Mishra, U., Daryanto, Y., Tseng, M. -L., & M. K. Lim (2021). A sustainable inventory model with controllable carbon emissions in green-warehouse farms. Journal of Cleaner Production, 298, 126777. https://doi.org/10.1016/j.jclepro.2021.126777
   Web of Science ®Google Scholar
• Mashud, A. H. M., Roy, D., Daryanto, Y., Mishra, U., & Tseng, M.-L. (2022). Sustainable production lot sizing problem: A sensitivity analysis on controlling carbon emissions through green investment. Computers & Industrial Engineering, 169, 108143. https://doi.org/10.1016/j.cie.2022.108143
   Web of Science ®Google Scholar
• Nobil, A. H., & Sedigh, A. H. A. (2017). An economic production quantity inventory model with a defective production system and uncertain uptime. International Journal of Inventory Research, 4(2/3), 132–147. https://doi.org/10.1504/IJIR.2017.088756
   Google Scholar
• Nobil, A. H., Sedigh, A. H. A., & Afshar-Nadjafi, B. (2019). Lot-sizing problem for a defective processing system with categorized items, backordering and pricing policy. Journal of Revenue and Pricing Management, 19(4), 255–265. https://doi.org/10.1057/s41272-019-00208-3
   Web of Science ®Google Scholar
• Nobil, A. H., Seifbarghy, M., Sedigh, A. H. A., & Pishva, D. (2016). Considering discrete delivery ordering and shipment consolidation in a three-echelon supply chain with failure. International Journal of Advanced Operations Management, 8(4), 247–275. https://doi.org/10.1504/IJAOM.2016.084148
   Google Scholar
• Nobil, E., Cárdenas-Barrón, L. E., Loera-Hernández, I. d. J., Smith, N. R., Treviño-Garza, G., Céspedes-Mota, A., & Nobil, A. H. (2023). Sustainability economic production quantity with warm-up function for a defective production system. Sustainability, 15(2), 1397. https://doi.org/10.3390/su15021397
   Web of Science ®Google Scholar
• Porteus, E. L. (1986). Optimal lot sizing, process quality improvement and setup cost reduction. Operations Research, 34(1), 137–144. https://doi.org/10.1287/opre.34.1.137
   Web of Science ®Google Scholar
• Rosenblatt, M. J., & Lee, H. L. (1986). Economic production cycles with imperfect production processes. IIE Transactions, 18(1), 48–55. https://doi.org/10.1080/07408178608975329
   Web of Science ®Google Scholar
• Sana, S. S. (2011). A production-inventory model of imperfect quality products in a three-layer supply chain. Decision Support Systems, 50(2), 539–547. https://doi.org/10.1016/j.dss.2010.11.012
   Web of Science ®Google Scholar
• Sarkar, B., Ganguly, B., Pareek, S., & Cárdenas-Barrón, L. E. (2022). A three-echelon green supply chain management for biodegradable products with three transportation modes. Computers & Industrial Engineering, 174, 108727. https://doi.org/10.1016/j.cie.2022.108727
   Web of Science ®Google Scholar
• Sarkar, S., & Giri, B. C. (2018). Stochastic supply chain model with imperfect production and controllable defective rate. International Journal of Systems Science: Operations & Logistics, 7(2), 133–146.
   Google Scholar
• Selvaraj, H., & Ramasamy, U. (2021). Imperfect production supply chain model considering price-sensitive demand and quantity discounts under free distribution approach. RAIRO-Operations Research, 55, S1833–S1848. https://doi.org/10.1051/ro/2020070
   Web of Science ®Google Scholar
• 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, 25(4), 3269–3297. https://doi.org/10.1007/s10668-022-02187-9
   Web of Science ®Google Scholar
• Shah, N. H., Rabari, K., & Patel, E. (2022). Greening efforts and deteriorating inventory policies for price-sensitive stock-dependent demand. International Journal of Systems Science: Operations & Logistics, 10(1), 2022808.
   Google Scholar
• Sustainable Development Goals -- the United Nations. Retrieved August 27, 2023, from https://sdgs.un.org/goals.
   Google Scholar
• Taleizadeh, A. A., Cárdenas-Barrón, L. E., 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. https://doi.org/10.5267/j.ijiec.2011.09.001
   Google Scholar
• Taleizadeh, A. A., Khanbaglo, M. P. S., & Cárdenas-Barrón, L. E. (2016). An EOQ inventory model with partial backordering and reparation of imperfect products. International Journal of Production Economics, 182, 418–434. https://doi.org/10.1016/j.ijpe.2016.09.013
   Web of Science ®Google Scholar
• The Guardian. Nearly $2tn of damage inflicted on other countries by US emissions. retrieved July 20, 2022, from https://www.theguardian.com/environment/2022/jul/12/us-carbon-emissions-greenhouse-gases-climate-crisis.
   Google Scholar
• Tiwari, S., Daryanto, Y., & Wee, H. M. (2018). Sustainable inventory management with deteriorating and imperfect quality items considering carbon emission. Journal of Cleaner Production, 192, 281–292. https://doi.org/10.1016/j.jclepro.2018.04.261
   Web of Science ®Google Scholar
• United States Environmental Protection Agency. Sources of greenhouse gas emissions. Retrieved August 27, 2023, from https://www.epa.gov/ghgemissions/sources-greenhouse-gas-emissions.
   Google Scholar
• Utama, D. M., Santoso, I., Hendrawan, Y., & Dania, W. A. P. (2022). Integrated procurement-production inventory model in supply chain: A systematic review. Operations Research Perspectives, 9, 100221. https://doi.org/10.1016/j.orp.2022.100221
   Google Scholar
• Wahab, M. I. M., Mamun, S. M. H., & Ongkunaruk, P. (2011). EOQ models for a coordinated two-level international supply chain considering imperfect items and environmental impact. International Journal of Production Economics, 134(1), 151–158. https://doi.org/10.1016/j.ijpe.2011.06.008
   Web of Science ®Google Scholar
• Wangsa, I. D. (2017). Greenhouse gas penalty and incentive policies for a joint economic lot size model with industrial and transport emissions. International Journal of Industrial Engineering Computations, 8(4), 453–480. http://dx.doi.org/10.5267/j.ijiec.2017.3.003
   Web of Science ®Google Scholar
• Wangsa, I. D., Tiwari, S., Wee, H. M., & Reong, S. (2020). A sustainable vendor–buyer inventory system considering transportation, loading and unloading activities. Journal of Cleaner Production, 271, 122120. https://doi.org/10.1016/j.jclepro.2020.122120
   Web of Science ®Google Scholar
• Wu, K. S., Ouyang, L. Y., & Ho, C. H. (2007). Integrated vendor–buyer inventory system with sublot sampling inspection policy and controllable lead time. International Journal of Systems Science, 38(4), 339–350. https://doi.org/10.1080/00207720601160389
   Web of Science ®Google Scholar
• Yadav, D., Kumari, R., Kumar, N., & Sarkar, B. (2021). Reduction of waste and carbon emission through the selection of items with cross-price elasticity of demand to form a sustainable supply chain with preservation technology. Journal of Cleaner Production, 297, 126298. https://doi.org/10.1016/j.jclepro.2021.126298
   Web of Science ®Google Scholar
• Yu, C., Qu, Z., Archibald, T. W., & Luan, Z. (2020). An inventory model of a deteriorating product considering carbon emissions. Computers & Industrial Engineering, 148, 106694. https://doi.org/10.1016/j.cie.2020.106694
   Web of Science ®Google Scholar
• Yu, H. F., & Hsu, W. K. (2016). An integrated inventory model with immediate return for defective items under unequal-sized shipments. Journal of Industrial and Production Engineering, 34(1), 70–77. https://doi.org/10.1080/21681015.2016.1210682
   Google Scholar
• Zanoni, S., Mazzoldi, L., Zavanella, L. E., & Jaber, M. Y. (2014). A joint economic lot size model with price and environmentally sensitive demand. Production and Manufacturing Research, 2(1), 341–354. https://doi.org/10.1080/21693277.2014.913125
   Google Scholar