Multi-item production planning with carbon cap and trade mechanism

Carbon emission control becomes a challenge in recent years, and carbon emission trading is an effective way to curb carbon emission. This paper investigates the multi‐item production planning problem with carbon cap and trade mechanism, in which a firm uses a common capacity and carbon emission quota to produce multiple products for fulfilling independent stochastic demands, and the firm can buy or sell the right to emit carbon on a trading market of carbon emission. A profit‐maximization model is proposed to characterize the optimization problem. The optimal policy of production and carbon trading decisions is analyzed, and an efficient solution method with linear computational complexity is presented for solving the optimal solution. The impacts of carbon price, carbon cap on the shadow price of the common capacity, production decisions, carbon emission and the total profit are investigated. The comparisons of the carbon cap and trade policy and the taxation policy are given to show the effectiveness of the policies. Numerical analyses are presented for illustrating our findings and obtaining some managerial insights and policy implication.