مدیریت میزان کربن در مدیریت موجودی

There is a broad consensus that mankind must reduce carbon emissions to mitigate global warming. It is generally accepted that carbon emission trading is one of the most effective market-based mechanisms to curb the amount of carbon emissions. This paper investigates how firms manage carbon footprints in inventory management under the carbon emission trading mechanism. We derive the optimal order quantity, and analytically and numerically examine the impacts of carbon trade, carbon price, and carbon cap on order decisions, carbon emissions, and total cost. We make interesting observations from the numerical examples and provide managerial insights from the analytical results.

The Intergovernmental Panel on Climate Change (IPCC) reports that global warming poses a grave threat to the world's ecological system and the human race, and it is very likely caused by increasing concentrations of carbon emissions, which mainly results from such human activities as fossil fuel burning and deforestation (IPCC, 2007). In order to alleviate global warming, the United Nations (UN), the European Union (EU), and many countries have enacted legislation or designed mechanisms to curb the total amount of carbon emissions. These include the Kyoto Protocol (UNFCCC, 1997) and the European Union Emission Trading System (EU-ETS), which implements a mandatory “cap and trade” system in the 27 EU (2009) member countries. Among these legislation and mechanisms, carbon emission trading is generally accepted as one of the most effective market-based mechanisms, which has been broadly adopted by UN, EU, and many governments. There are now more than 20 platforms for trading carbon in the world. Australia, Canada, Japan, and the USA are also paving the way for domestic carbon emission markets. The global carbon market is expected to reach US$2 trillion by 2025. The EU carbon market is estimated to be worth US$131 billion a year (Bothra, 2010), while that in the USA will reach US$60 billion in 2012 (Environmentalleader, 2009). To respond to the regulations on carbon emissions, firms tend to adopt more energy efficient equipment, facilities, or vehicles. On the other hand, they can also optimize their operations decisions in production, transportation, and inventory to reduce carbon emissions. This approach may reduce more carbon emissions with less or no cost than adopting low-energy-consumption technologies (Benjaafar et al., 2010). However, industry and academia seem to have largely ignored this approach to environmental protection. According to a survey by Accenture, only 10% of companies actively model their supply chain carbon footprints and have implemented successful sustainability initiatives. More than one-third (37%) of supply chain executives have no awareness of the levels of supply chain emissions in their supply chain networks (Accenture, 2009). The literature on carbon footprint management in supply chain is also very sparse. Some studies focus on the measurement method of carbon emissions in supply chains. Carbontrust (2006) develops a methodology to determine the carbon footprints of different products by analyzing the carbon emissions generated by the energy used across the supply chain. Cholette and Venkat (2009) calculate the energy and carbon emissions associated with each transportation link and storage echelon in a wine supply chain. They find that different supply chain configurations can result in vastly different energy consumption and carbon emissions. Mtalaa et al. (2009) review the current measurement and calculation models that compute CO2 emissions from truck transportation. Sundarakani et al. (2009) present an analytical model that measures carbon emissions from both stationary and non-stationary supply chain processes. Chaabane et al. (2010) introduced a mixed-integer linear programming based framework for sustainable supply chain design, their model demonstrated that efficient carbon management strategies will help decision makers to achieve sustainability objectives in a cost-effective manner. There are few studies on the operations decisions under carbon emission regulations. Penkuhn et al. (1997) present a nonlinear programming model for joint production planning problems by integrating emission taxes. Letmathe and Balakrishnan (2005) present two models for firms to determine their optimal product mix and production quantities in the presence of different types of environmental constraints. Rosič et al. (2009) examine a single-period dual model that incorporates the carbon emission cost. Kim et al. (2009) examine the relationship between the freight transport costs and CO2 emissions in given intermodal and truck-only freight networks by multi-objective optimization. Cachon (2009) discusses how the new objective of reducing carbon footprints is likely to affect supply chain operations and structures. Hoen et al. (2010) examine the effects of two regulation mechanisms (emission cost vs. emission constraint) on the transport mode selection decision and suggest that policy-makers impose a constraint on freight transportation emissions. Benjaafar et al. (2010) introduce a series of simply models to illustrate how carbon footprint considerations could be incorporated into operations decisions. Pan et al. (2010) examined the environmental impact of pooling of supply chains, they found the supply network pooling is an efficient approach in reducing CO2 emissions. Harris et al. (2011) investigated the relationship between total logistics costs and the environmental impact in terms of CO2 emissions from transportation and electricity usage in depots when using a traditional cost-based optimization approach. Bonney and Jaber (2010) examined the importance of inventory planning to the environment and the possibility of using models to perform analyses. This paper mainly examines the operations decisions in inventory management with a view to managing a firm's carbon footprints under the carbon emission trading mechanism, where a carbon footprint measures the total greenhouse gas emissions caused directly and indirectly by a person, organization, event, or product in tonnes (or kg) of CO2 equivalent (Carbontrust, 2009). We found that Benjaafar et al. (2010) also presented a relatively simple inventory model incorporating cap-and-trade mechanism, but their model is so general that they cannot present an algorithm for their model and any theoretical analysis except for some observations. Based on the EOQ model, we introduce an environmental inventory model under the cap-and-trade system, derive the optimal order quantity, compare our model with the classical EOQ model, and analytically and numerically examine the impacts of carbon emission trading, carbon price, and carbon cap on order decisions, carbon emissions, and total cost. We make interesting observations and provide managerial insights from the research findings. The rest of this paper is organized as follows: In Section 2 we formulate the carbon footprint management problem, derive the optimal order quantity, and examine analytically and numerically the impacts of carbon trading, carbon price, and carbon cap on order decisions, carbon emissions, and total cost. In Section 3 we provide some numerical examples to gain practical insights from the analytical results derived in Section 2. Finally we conclude the paper and suggest topics for future research in Section 4. 2. Optimal order quantity with carbon emission trading In this section we consider the single-product replenishment problem with carbon trading based on the EOQ model. Carbon trading is also known as cap and trade. A firm is allocated a limit or cap on carbon emissions. If its amount of carbon emissions exceeds the carbon cap, it can buy the right to emit extra carbon from the carbon trading market. Otherwise, it can sell its surplus carbon credit. Obviously, this market mechanism can unify environmental objective and economic objective. We derive the optimal order quantity and examine the impacts of carbon trading on the optimal order policy, carbon emissions, and total order cost.

With the enactment of regulations and legislation on low-carbon development, firms worldwide have to incorporate carbon footprint management into their business decisions. We studied how firms manage carbon footprints in inventory management under the cap-and-trade mechanism, compared the optimal decision with that for the classical EOQ model, and examined the impacts of carbon cap and carbon price on order size, carbon emissions, and total cost. We provided a series of numerical examples to illustrate the analytical results and make some interesting observations from these examples. We found that the optimal order size is between the optimal EOQ order size and the order size that minimizes carbon emissions since both order cost and carbon emissions are incorporated into our model, which is intuitive. Compared with the classical EOQ model, the cap-and-trade mechanism induces the retailer to reduce carbon emissions, which may result in an increase in the total cost. However, the retailer may reduce carbon footprints and total cost simultaneously under some conditions. Carbon cap and carbon price have a great impact on the retailer's order decisions, carbon footprints, and total cost. Whether the retailer should buy carbon credit depends on the carbon cap as follows: when the cap is less (higher) than a threshold, the retailer should buy (sell) carbon credit, whereas when the cap equals the threshold, he should neither buy nor sell. With increasing carbon price, the retailer may order more or fewer products, which depends on the cost and carbon emissions from logistics and warehouse. With increasing carbon price, the total cost may increase or decrease, depending on the carbon cap. When the cap is lower than one threshold, the total cost will increase; when the cap is higher than another higher threshold, the total cost will decrease; and when the cap is between the two thresholds, the cost will initially increase and then decrease. There are several topics for further research. In this paper we assumed that the demand faced by the retailer is deterministic. A natural extension is to examine the setting in which the demand is stochastic. We did not incorporate price decisions into the model. Future research may consider the joint order and pricing decisions and examine the impact of the cap-and-trade mechanism on the end-customers. Since different transportation modes will result in different amounts of carbon emissions, another interesting issue is to examine the joint order and transportation mode decisions