Problem Definition: We study the strategic interactions between a supplier and a retailer under demand uncertainty when the supplier has two options for how to ship a product: (i) road transport, which is expensive, high-emission and flexible, and (ii) rail transport, which is cheap, green, and is constrained by a minimum transport quantity (MTQ). Academic / Practical Relevance: Rail transport has been regarded as one of the most practical ways to increase supply chain sustainability. However, the volume shifted from road to rail has remained modest during the last decades. One of the reasons is that rail transport lacks flexibility in its delivery quantity and often requires an MTQ. Methodology: The supplier and the policymaker prefer rail transport because of the advantages of low cost and low emission. However, the shipment quantity, which is determined by the retailer, may not reach the MTQ. The supplier and the policymaker can design incentives (contracts and emission tax) to encourage the use of rail transport. In this work, we build a game-theoretic model for this setting and investigate the impact of the MTQ on the economic and environmental performance of the supply chain and the effect of a tax on emissions. Results: We find that, although MTQ is operationally constraining and can lead to overproduction, it can be turned into a beneficial factor through proper decisions, which would lead to several merits as follows. (1) The MTQ can significantly improve the efficiency of simple supply chain contracts (e.g., price-only contracts). (2) The MTQ does not hurt the efficiency of coordinating contracts (e.g., buy-back contracts) and can increase the supplier's Pareto-optimal profit. (3) The MTQ can enable coordinating contracts to achieve a higher supply chain profit and fewer total emissions simultaneously, which is not possible without the MTQ. Moreover, we show that, although it can lead to fewer total emissions, an emission tax is more likely to be ineffective in encouraging the use of the green transport mode when firms use coordinating contracts compared to price-only contracts. Managerial Implications: We provide suggestions to firms on how to make optimal decisions and make the best use of different transport modes when dealing with demand risk. Also, we provide suggestions to policymakers on how to design the proper emission tax to promote green logistics
