Policy model for pollution control in the copper industry, including a model for the sulfuric acid market

In this paper we develop a policy model for pollution control investment and operational decisions in the copper industry. The system consists of (i) a nonlinear integer model to optimize smelter operations, including the investment decisions relating to smelting capacity and pollution control plants that complies with environmental regulations, and (ii) a network flow model to describe the economic behavior of the sulfuric acid market, which considers the sulfuric acid produced at the pollution abatement stages in the smelting process. This second model solves for an equilibrium among spatially separated markets, that determines the price and distribution of acid in each demand and supply region. The two models interact through the input each receives from the other. Thus, the smelter model uses the sulfuric acid price at each smelter to find optimal operational and investment decisions, whereas the sulfuric acid market model considers sulfuric acid output at the smelters as part of the supply input to find the price of this product at each smelter location. The solution given by the policy model is the global equlibrium obtained when this iterative process between the two models converges. Thus, the price of the sulfuric acid, which is the central component when deciding when and where to locate a sulfuric acid plant, is determined endogenously, rather than assumed exogenous as in most models of this type. Computational experiments show that expected profits associated with the copper industry can increase significantly when the problem is solved in aggregate, as compared with the smelters making their decisions independently. Several applications of the policy model are described.