| The carbon dioxide emission increases rapidly with the growth of energy and resource consumption, leading to the greenhouse effect. Due to the deteriorating global environment, many governments of developed countries have established a series of policies to control carbon emission.In this paper, based on the classical EOQ model with production time and backlogging and considering carbon cap and carbon trading mechanisms, we establish four an environmental inventory models, design an exact algorithm to obtain optimal production quantity. We analysis the impact of carbon emission factors on the production strategy, the total costs and the carbon emissions, and obtain some satisfactory results.Firstly, we introduce carbon-cap into the classical EOQ model with production time, and point out that The optimal total cost is decreasing and convex in the carbon cap while the carbon emission is linearly increasing in the carbon cap. Furthermore, we obtain an observation that the relative change rate in cost also is less than in emission under certain cases. Carbon-cap policies can regulate the balance of economic and business environment in some extent.Secondly, the carbon trade mechanism is introduced into the classical EOQ model with production time, when the cost parameters and the parameters satisfy the conditions, the optimal total cost will be reduced. Furthermore, we analyze production rate, carbon trade price and carbon cap how to affect the optimal solution, respectively. Finally, we discover the effect of carbon cap and carbon trade price on carbon trade behaviors. The carbon emission will be reduced though carbon trade.Thirdly, we establish an EOQ model with backlogging under the case of carbon cap. We analyze the relation between the optimal solution to classical EOQ model and that in the case of emission constraint, and the latter can be obtained by adjusting the former. When the latter is not equal to the former, the carbon emission will be reduced. By adjusting production around the optimal production without the carbon-constraint, carbon emission can drastically decrease while the total cost may increase very little. The optimal cost is decreasing and convex in the carbon cap, while the optimal emission is linearly increasing in the carbon cap.Finally, we establish the EOQ model with production time under the case of carbon trade. The results show that when the carbon price is constant, the carbon cap will not affect the optimal production and carbon emissions, and the total cost is a decreasing in carbon cap. When fixed production is greener than the average store, we can reduce the production to reduce the carbon emission at most cases. When carbon cap is higher then the carbon emissions, we can sell the excess carbon rights; in contrast, we can buy the carbon rights. The optimal total cost is increasing concave in the optimal storage rate.By building on a number of environmental inventory models, solving and analyzing, we obtain that the carbon trade mechanism becomes one of the most important tools for carbon emission reduction. The conclusions make some scientific basis for the production decision and abundant the inventory theory. |
