Optimal Production Planning with Emissions Trading

Emissions trading is a market-based mechanism for curbing emissions, and it has been implemented in Europe, North America, and several other parts of the world. To study its impact on production planning, we develop a dynamic production model, where a manufacturer produces a single product to satisfy random market demands. The manufacturer has access to both a green and a regular production technology, of which the former is more costly but yields fewer emissions. To comply with the emissions regulations, the manufacturer can buy or sell the allowances in each period via forward contracts in an outside market with stochastic trading prices while needing to keep a nonnegative allowance account balance at the end of the planning horizon. We first derive several important structural properties of the model, and based upon them, we characterize the optimal emissions trading and production policies that minimize the manufacturer's expected total discounted cost. In particular, the optimal emissions trading policy is a target interval policy with two thresholds that decrease with the starting inventory level. The optimal production policy is established by first determining the optimal technology choice and then showing the optimality of a base-stock type of production policy. We show that the optimal base-stock level is independent of the starting inventory level and the allowance level when the manufacturer trades the allowance or uses both technologies simultaneously. A numerical study using representative data from the cement industry is conducted to illustrate the analytical results and to examine the value of green technology for the manufacturer.