Emission permit banking, pollution abatement and production-inventory control of the firm

In this paper, we present a dynamic model modified with emission permit banking and pollution abatement, and investigate the effect of emission permit banking and pollution abatement on the production-inventory strategy of the firm. After introducing emission permit banking and pollution abatement, the cost function consists of the inventory holding and production costs, the cost of investment in abatement capital goods and the emission procurement/selling cost. Furthermore, the inventory holding costs are linear, production costs are non-decreasing and convex functions of the production level, and the costs of investment in abatement capital goods are increasing and convex functions of the investment level. We compare the optimal production-inventory strategy before emission permit banking and pollution abatement and thereafter. The mathematical investigation is based on the Arrow-Karlin model.