An EOQ model with stepwise ordering cost and the finite planning horizon under carbon cap-and-trade regulations

Abstract

In this study, under the carbon cap-and-trade mechanism, the ordering cost presents a stepwise function for ordering quantity, and the optimal economic ordering quantity model aims to explore the manufacturer's total cost minimization in the finite planning horizon, in combination with the actual situation that the product will produce carbon emissions during transportation and storage. The economic order quantity (EOQ) model with stepwise ordering cost is applicable to the decision environment in which goods are utilized by sea, by rail or by air (e.g., the order cost is charged in addition to the basic fixed cost, the importer of raw materials will pay an additional freight related to delivery, such as the rent for the use of container numbers.). A heuristic algorithm is also proposed to analyze the relevant properties of the optimal solution of the model and to solve the optimal order times and quantities of the manufacturer under the constraint of carbon policy.We further compared the optimal order times with the case without carbon constraint and the order times corresponding to the manufacturer's realization of the minimum carbon emission, and obtained the conditions for the manufacturer to achieve low cost and low emission under the carbon policy.Finally, the theoretical results of the model are verified by numerical examples,and the influence of relevant parameters on the inventory strategy of manufacturers is discussed. The results show that under the carbon cap-and-trade policy, there is an optimal ordering strategy that minimizes the total cost of the manufacturer in the finite horizon. When the demand of the manufacturer is under finite horizon and the carbon policy is equal to the specific multiplier of orders, the manufacturer can achieve a win-win result of low cost and low emissions.