Abstract
In this paper, we deal with the problem of cost allocation among multiple retailers in an inventory system with transportation quantity discount under the widely-used carbon tax regulation. We first develop an inventory model with transportation discount under the carbon tax policy, and determine the optimal order quantity per order such that the total cost is minimized in the case of individual and joint ordering. We show that the total cost for the group of retailers can be reduced by placing joint orders while the total carbon emissions may increase. Then, we provide a sufficient condition which indicates that when the costs and carbon emissions associated with each order initiated are relatively high, enterprises can achieve dual objectives (both carbon emission reduction and cost reduction) through joint ordering. To allocate the total cost among the retailers, we introduce an inventory game and show that this game is concave. Based on this, we propose a cost allocation rule, which belongs to the core of the game.
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References
Aljazzar S M, Gurtu A, Jaber M Y (2018). Delay-in-payments-Astrategy to reduce carbon emissions from supply chains. Journal of Cleaner Production 170: 636–644.
Annicchiarico B, Di Dio F (2015). Environmental policy and macroeconomic dynamics in a new Keynesian model. Journal of Environmental Economics and Management 69: 1–21.
Bai P, Ma Z, Wei X, Jia R (2023). Allocation scheme selection for transportation carbon allowance-evidence from China’s top ten economic regions. Journal of Cleaner Production 428: 139310.
Benjaafar S, Li Y, Daskin M (2012). Carbon footprint and the management of supply chains: Insights from simple models. IEEE Transactions on Automation Science and Engineering 10(1): 99–116.
Buffa F P (1988). An empirical study of inbound consolidation opportunities. Decision Sciences 19(3): 635–653.
Chan Y T (2020). Collaborative optimal carbon tax rate under economic and energy price shocks: A dynamic stochastic general equilibrium model approach. Journal of Cleaner Production 256: 120452.
Chen X, Zhang J (2020). A stochastic programming duality approach to inventory centralization games. Operations Research 57(4): 840–851.
Chen X, Benjaafar S, Elomri A (2013). The carbon-constrained EOQ. Operations Research Letters 41: 172–179.
Dror M, Hartman B C (2007). Shipment consolidation: Who pays for it and how much? Management Science 53: 78–87.
Dye C Y, Yang C T (2015). Sustainable trade credit and replenishment decisions with credit-linked demand under carbon emission constraints. European Journal of Operational Research 244(1): 187–200.
Feng H, Zeng Y, Cai X, Qian Q, Zhou Y (2021). Altruistic profit allocation rules for joint replenishment with carbon cap-and-trade policy. European Journal of Operational Research 290(3): 956–967.
Fiestras-Janeiro M G, Garcia-Jurado I, Meca A, Mosquera M A (2011a). Cooperative game theory and inventory management. European Journal of Operational Research 210(3): 459–466.
Fiestras-Janeiro M G, Garcia-Jurado I, Meca A, Mosquera M A (2011b). Cost allocation in inventory transportation systems. Top 20(2): 397–410.
Fiestras-Janeiro M G, García-Jurado I, Meca A, Mosquera M A (2013). A new cost allocation rule for inventory transportation systems. Operations Research Letters 41(5): 449–453.
Fiestras-Janeiro M G, Garcia-Jurado I, Meca A, Mosquera M A (2024). Evaluating the impact of items and cooperation in inventory models with exemptable ordering costs. International Journal of Production Economics 269: 109151.
Guardiola L A, Meca A, Puerto J (2009). Production-inventory games: A new class of totally balanced combinatorial optimization games. Games and Economic Behavior 65(1): 205–219.
Halat K, Hafezalkotob A, Sayadi M K (2021). Cooperative inventory games in multi-echelon supply chains under carbon tax policy: Vertical or horizontal? Applied Mathematical Modelling 99: 166–203.
Heutel G (2012). How should environmental policy respond to business cycles? Optimal policy under persistent productivity shocks. Review of Economic Dynamics 15(2): 244–264.
Jia R, Shao S, Yang L (2021). High-speed rail and CO2 emissions in urban China: A spatial difference-in-differences approach. Energy Economics 99: 105271.
K P A, Panicker V V (2020). Multimodal transportation planning with freight consolidation and volume discount on rail freight rate. Transportation Letters 14(3): 227–244.
Khan M A-A, Cárdenas-Barrón L E, Treviño-Garza G, Cáspedes-Mota A, Loera-Hernández IJ (2023). Integrating prepayment installment, pricing and replenishment decisions for growing items with power demand pattern and non-linear holding cost under carbon regulations. Computers & Operations Research 156: 106225.
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.
Li J, Feng H, Zeng Y (2014). Inventory games with permissible delay in payments. European Journal of Operational Research 234: 694–700.
Li W, Xu G, Su J (2021). Inventory games with quantity discount. Journal of Systems Science and Complexity 34: 1538–1554.
Li Y, Du Q, Lu X, Wu J, Han X (2019). Relationship between the development and CO2 emissions of transport sector in China. Transportation Research Part D: Transport and Environment 74: 1–14.
Meca A, Timmer J, Garcia-Jurado I, Borm P (2004). Inventory games. European Journal of Operational Research 156: 127–139.
Nollet J, Beaulieu M (2005). Should an organisation join a purchasing group? Supply Chain Management 10(1): 11–17.
Saavedra-Nieves A (2020). A multi-agent inventory problem with general transportation cost. Operations Research Letters 48(1): 86–92.
San-José L A, Sicilia J, Cárdenas-Barrón L E, González-de-la-Rosa M (2024). A sustainable inventory model for deteriorating items with power demand and full back-logging under a carbon emission tax. International Journal of Production Economics 268: 109098.
Shi Y, Zhang Z, Chen S C, Cárdenas-Barrón L E, Skouri K (2020). Optimal replenishment decisions for perishable products under cash, advance, and credit payments considering carbon tax regulations. International Journal of Production Economics 223: 107514.
Shi Y, Zhang Z, Tiwari S, Yang L (2023). Pricing and replenishment strategy for a perishable product under various payment schemes and cap-and-trade regulation. Transportation Research Part E: Logistics and Transportation Review 174: 103129.
Shinn S W, Hwang H, Park S S (1996). Joint price and lot size determination under conditions of permissible delay in payments and quantity discounts for freight cost. European Journal of Operational Research 91: 528–542.
Stavins R N (2019). Carbon Taxes vs. Cap and Trade: Theory and Practice. Cambridge, Mass.: Harvard Project on Climate Agreements.
Taleizadeh A A, Stojkovska I, Pentico D W (2015). An economic order quantity model with partial backordering and incremental discount. Computers & Industrial Engineering 82: 21–32.
Tamjidzad S, Mirmohammadi S H (2017). Optimal (r, Q) policy in a stochastic inventory system with limited resource under incremental quantity discount. Computers & Industrial Engineering 103: 59–69.
Tsao Y C, Lu J C (2012). A supply chain network design considering transportation cost discounts. Transportation Research Part E: Logistics and Transportation Review 48(2), 401–414.
Zeng Y, Cai X, Feng H (2022). Cost and emission allocation for joint replenishment systems subject to carbon constraints. Computers & Industrial Engineering 168: 108074.
Zeng Y, Wang S, Cai X, Zhang L (2024). Incentive-compatible cost allocations for inventory games with private information. Operations Research Letters 53: 107073.
Acknowledgments
This work was supported by the National Natural Science Foundation of China under Grant No. 72271199 and Guangdong Basic and Applied Basic Research Foundation under Grant No. 2023A1515011158. The authors thank the editor and two anonymous reviewers for their constructive comments that helped us to improve this manuscript.
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Guojing Chen is a Ph.D. candidate in the School of Mathematics and Statistics at Northwestern Polytechnical University. Her research interests include inventory management, sustainable supply chain management, decision theory, and game theory.
Dongshuang Hou is a professor at School of Mathematics and Statistics in Northwestern Polytechnic University, deputy secretary-general of the Game Theory Branch of Operations Research Society of China, director of the Operations Research Society of Shaanxi, and a commentator on Mathematical Reviews. He received his Bachelor’s and Master’s degrees from Northwestern Polytechnical University in 2006 and 2009, respectively, and received his Ph.D. degree from the University of Twente in 2013. His research interests include cooperative game theory and its application to economic problems. He has published more than 40 papers in three major journals in the field of game theory, including Games and Economic Behavior, International Journal of Game Theory, International Game Theory Review, and he is a reviewer for highly ranked journals such as Games and Economic Behavior, European Journal of Operational Research, Journal of the Operational Research Society, etc.
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Chen, G., Hou, D. Cost Allocation for Inventory Problem with Transportation Discount under Carbon Tax Policy. J. Syst. Sci. Syst. Eng. (2024). https://doi.org/10.1007/s11518-024-5611-2
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DOI: https://doi.org/10.1007/s11518-024-5611-2