Optimal control of production-maintenance system with deteriorating items, emission tax and pollution R&D investment

It is widely acknowledged today that the control and maintenance of production inventories of deteriorating items have attracted much attention in inventory analysis because most physical goods deteriorate over time. In 2012, Bukhari and El-Gohary modelled an optimal control model of production-maintenance system with deteriorating items, and derived the optimal scheduled production rate and preventive maintenance rate. In this paper, we propose an alternative emission tax policy design, and extend the model of Bukhari and El-Goharys to an even more general model in which the emission tax and pollution R&D investment are taken into account. Our aim is to apply optimal control theory to solve the production-maintenance problem with deteriorating items, emission tax and pollution R&D investment; and derive the optimal schedule production rate, preventive maintenance rate and pollution R&D investment rate that minimise the total cost. The results are discussed with some illustrative examples for different demand rate and obsolescence rate of process performance in the absence of maintenance, and sensitivity analysis is conducted to study the effect of changing the parameters and coefficients on the objective function value.