Optimal Control of a Stochastic Production-Inventory System under a Emission Rate Related Pollution Tax

Abstract

In this paper, we model a stochastic optimal control system of production-inventory under an emission rate related pollution tax. In our model, the inventory evolves according to a standard geometric Brownian motion process, and the evolution of emission in per unit output according to a determining dynamic process. Our objective is to apply optimal control theory to investigate the stochastic production-inventory system under uncertainties of inventory dynamics; and derives the optimal production level that maximizes the objective function value. The results are discussed with some illustrative examples for different demand rate functions.