Stochastic Inventory Control with Carbon Emissions Regulations

October 27, 2013

Abstract
This study analyzes an inventory control problem of a company in stochastic demand environment under carbon emissions regulations. In particular, a continuous review inventory model is investigated under three regulation policies: carbon cap, carbon tax, and carbon cap-and-trade. We analyze and compare the optimal (Q, R) policies under each carbon emissions regulation policy. Furthermore, the effects of demand variability on carbon emissions are analyzed under each policy.
Keywords: Carbon emissions, Continuous Review Inventory

1

Introduction

There is a growing consensus that carbon emissions are a leading contributor to global climate change, which has created increasing pressure around the world to enact legislation to curb these emissions.
Carbon emission regulations have emerged to address these issues and to incentivize firms to curb greenhouse gas (GHG) emissions, primarily carbon-dioxide (other GHG emissions can be measured in terms of carbon-dioxide, see, e.g., EPA, 2013). The US EPA reports that the industrial and commercial sectors contribute 29% and 17%, respectively, to GHG emissions (largely through electricity generation), with transportation adding another 28% (EPA, 2013). Thus, a very large fraction of carbon emissions are due to supply chain activities including inventory holding, freight transportation, and logistics and warehousing activities.
Inventory management is particularly important for a company as this determines not only the level of inventory carried and warehousing activities, but also the amount and the frequency of freight shipments and logistical operations. Hence, the inventory control policy of a company is inextricably linked with its carbon emissions. The objective of this study is to analyze a company’s inventory and transportation operations in light of economic and environmental pressures in the presence of demand volatility. Specifically, we capture the tradeoff between traditional economic objectives (cost minimization) and environmental performance (carbon emissions) to allow broader optimization on both dimensions. To this end, this study models and solves a supply chain agent’s stochastic inventory control and transportation planning problem under three well-known proposed carbon emission regulation policies: carbon cap, carbon tax, and carbon cap-and-trade. Under the carbon cap policy, the supply chain agent is subject to an upper limit or “cap” on its carbon emissions. Under the carbon tax policy, the supply chain agent is taxed based on its carbon emissions. Under the carbon cap-and-trade policy, similar to carbon cap policy, the supply chain agent is subject a carbon cap; however, it can sell or buy carbon allowances through a trading system such as the European Emissions Trading System.

2

Literature Review

We note that sustainability has been considered in various operations and supply chain management problems. In this study, our focus is on inventory control studies that consider sustainability. There is a growing body of literature on inventory control models with environmental considerations and we can categorize such studies in two classes: models with deterministic demand and models with stochastic demand. 1

2.1

Deterministic Inventory Control Models with Environmental Considerations

Most of the inventory control models with environmental considerations revisit the classic Economic
Order Quantity (EOQ) model. The EOQ model analyzes the trade-off between inventory holding and order setup costs for a product that has deterministic demand. Environmental considerations are integrated to the EOQ model either by considering the environmental regulations or by directly associating costs with environmental pollution generated from inventory control related operations or by regarding environmental objectives along with