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

• Published in: International journal of production research Vol. 53; no. 2; pp. 607 - 628
• Main Authors: Pan, Xiaojun, Li, Shoude
• Format: Journal Article
• Language: English
• Published: London Taylor & Francis 17.01.2015; Taylor & Francis LLC
• Subjects: deteriorating items; Deterioration; Emission; emission tax; Environmental tax; Financing; Inventory control; Investment; Mathematical models; Optimal control; Pollution abatement; pollution abatement investment; Sensitivity analysis; Stochastic models; stochastic production-inventory; Stochasticity; Studies
• ISSN: 0020-7543; 1366-588X
• DOI: 10.1080/00207543.2014.961201

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.