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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 201708, 13 pages
Research Article

Dynamic Optimal Production Strategies Based on the Inventory-Dependent Demand under the Cap-and-Trade Mechanism

Department of Logistics Engineering and Management, Lingnan College, Sun Yat-sen University, Guangzhou 510275, China

Received 31 December 2013; Accepted 16 February 2014; Published 7 May 2014

Academic Editor: Piermarco Cannarsa

Copyright © 2014 Qiuzhuo Ma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Cap-and-trade system is the most popularly applied mechanism that is currently recognized to be effective in stimulating the enterprises to environmentally friendly operate through emission reduction. In this paper, we consider a single company whose carbon emission is generated from not only its production process but also its inventory management activity. A continuous optimal control model is used to find the optimal dynamic production policy on the objective of profit maximization with respect to the cap-and-trade mechanism. Some properties of the strategies are derived concerning the timing of production rate adjustment and the length of the decision duration period. The capacitated strategy is also discussed, in which different combinations of different decision intervals of different production rates are explicitly explored. The impact of various factors on the length of these intervals is qualitatively described. Through the sensitivity analysis, we further discuss the impact of product prices on the positions of the switch time points between the decision intervals. Company’s performance including profit and emission is numerically compared in the situation of joining or not joining the cap-and-trade system.