Optimal control of a stochastic production-inventory system under deteriorating items and environmental constraints

In this paper, we present an optimal control model of a stochastic production-inventory with deteriorating items, emission tax and pollution abatement investment. In our model, the emission tax is levied on the firm's environmental obsolescence rate of technology rather than the total amount of the environmental externality. Our objective is to apply Hamilton-Jacobi-Bellman (HJB) equation to solve the stochastic production-inventory system with deteriorating items, emission tax and pollution abatement investment; and derive the optimal production rate and pollution abatement investment rate that maximise the objective function value. The results are discussed with some illustrative examples for different demand rate functions, and sensitivity analysis is conducted to study the effect of changing the parameters and coefficients on the objective function value.