Optimal strategies for production plan and carbon emission reduction in a hydrogen supply chain under cap-and-trade policy

Hydrogen is now being seen as one of the most promising carbon-free and abundant energy sources on the path to net-zero emissions. However, high transportation, storage, and carbon emission costs in hydrogen supply chains are critical economic barriers that hinder the development of the hydrogen economy. Consequently, hydrogen refuelling stations have to face a trade-off between self-produced and purchased hydrogen quantities while considering transportation and storage costs. Furthermore, hydrogen manufacturers and refuelling stations have to make a trade-off between their hydrogen outputs and carbon emission reduction quantities under a cap-and-trade policy. We develop a differential game model that draws on and extends the literature on hydrogen supply chain design and operation to address this dual dilemma. Therein, state variables include the hydrogen retail price and carbon emission trading price, and control variables involve the hydrogen outputs and carbon emission reduction amounts of the hydrogen manufacturer and refuelling station. We use the feedback control technique to find optimal solutions and implement numerical simulations to validate solutions and the sensitivity of parameters. The results suggest that carbon emission reduction efficiency, hydrogen wholesale price, and carbon trading reference price significantly impact the optimal decisions of production plans and carbon emission reduction. This study may provide theoretical guidance for promoting hydrogen utilisation, cost reduction and low-carbon development.