More and more companies are paying attention to their carbon footprint beyond production emissions. In this work we consider a 'carbon-aware' company (either by choice or enforced by regulation) that is reconsidering the transport mode selection decision. Traditionally the trade-off has been between lead time (and corresponding inventory costs) and transportation costs but now emission costs come into the equation. We use a carbon emission measurement methodology based on real-life data and incorporate it into an inventory model. We consider the results for different types of emission regulation (including voluntary targets). We find that even though large emission reductions can be obtained by switching to a different mode, the actual decision depends on the regulation and non-monetary considerations, such as lead time variability.

C arbon footprinting is a tool for firms to determine the total greenhouse gas (GHG) emissions associated with their supply chain or with a unit of final product or service. Carbon footprinting typically aims to identify where best to invest in emission reduction efforts, and/or to determine the proportion of total emissions that an individual firm is accountable for, whether financially and/or operationally. A major and underrecognized challenge in determining the appropriate allocation stems from the high degree to which GHG emissions are the result of joint efforts by multiple firms. We introduce a simple but general model of joint production of GHG emissions in general supply chains, decomposing the total footprint into processes, each of which can be influenced by any combination of firms. We analyze two main scenarios. In the first scenario, the social planner allocates emissions to individual firms and imposes a cost on them (such as a carbon tax) in proportion to the emissions allocated. In the second scenario, a carbon leader voluntarily agrees to offset all emissions in the entire supply chain and then contracts with individual firms to recoup (part of) the costs of those offsets. In both cases, we find that, to induce the optimal effort levels, the emissions need to be overallocated, even if the carbon tax is the true social cost of carbon. This is in contrast to the usual focus in the life-cycle assessment (LCA) and carbon footprinting literatures on avoiding double counting. Our work aims to lay the foundation for a framework to integrate the economics-and LCA-based perspectives on supply chain carbon footprinting.

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The transport sector is the second largest carbon emissions contributor in Europe and its emissions continue to increase. Many shippers are committing themselves to reducing transport emissions voluntarily, possibly in anticipation of increasing transport prices. In this paper we study a shipper that has outsourced transport and has decided to cap its carbon emissions from outbound logistics for a group of products. Setting an emission constraint for a group of products allows taking advantage of reducing emissions substantially where it is less costly and less where it is more costly. We focus on reducing emissions by switching transport modes within an existing network, since this has a large impact on emissions. In addition, the company sets the sales prices for the products, which influences demand. We develop a solution procedure that uses Lagrange relaxation. Conditions on total logistics cost and unit emissions are derived that determine which transport mode is selected for a product. It is observed that a diminishing rate of return applies in reducing emissions by switching transport modes. In a case study we apply our method to a producer of bulk liquids and find that emissions can be reduced by 10% at only a 0.7% increase in total logistics cost.

In many production systems a certain level of flexibility in the production capacity is either inherent or can be acquired. In that case, system costs may be decreased by managing the capacity and inventory in a joint fashion. In this paper we consider such a maketo-stock production environment with flexible capacity subject to periodic review under non-stationary stochastic demand, where we allow for positive fixed costs both for initiating production and for acquiring external capacity. Our focus is on tactical-level capacity management which refers to the determination of in-house production capacity while the operational-level integrated capacity and inventory management is executed in an optimal manner. We first develop a simple model to represent this relatively complicated problem. Then we elaborate on the characteristics of the general problem and provide the solution to some special cases. Finally, we develop several useful managerial insights as to the optimal capacity level, the effect of operating at a suboptimal capacity level and the value of utilizing flexible capacity.

We consider an inventory control problem where it is possible to collect some imperfect information on future demand. We refer to such information as imperfect Advance Demand Information (ADI), which may occur in different forms of applications. A simple example is a company that uses sales representatives to market its products, in which case the collection of sales representatives' information as to the number of customers interested in a product can generate an indication about the future sales of that product, hence it constitutes imperfect ADI. Other applications include internet retailing, Vendor Managed Inventory (VMI) applications and Collaborative Planning, Forecasting, and Replenishment (CPFR) environments. We develop a model that incorporates imperfect ADI with ordering decisions. Under our system settings, we show that the optimal policy is of order-up-to type, where the order level is a function of imperfect ADI. We also provide some characterizations of the optimal solution. We develop an expression for the expected cost benefits of imperfect ADI for the myopic problem. Our analytical and empirical findings reveal the conditions under which imperfect ADI is more valuable.

KEYWORDSValue of information; imperfect advance demand information; returning excess inventory to upstream; lost-sales; inventory ABSTRACT Motivated by real-life applications, we consider an inventory system where it is possible to collect information about the quantity and timing of future demand in advance. However, this Advance Demand Information (ADI) is imperfect as (i) it may turn out to be false; (ii) a time interval is provided for the demand occurrences rather than its exact time; and (iii) there are still customer demand occurrences for which ADI cannot be provided. To make best use of imperfect information and integrate it with inventory supply decisions, we allow for returning excess stock built up due to imperfections to the upstream supplier and we propose a lost-sales inventory model with a general representation of imperfect ADI. A partial characterization of the optimal ordering and return policy is provided. Through an extensive numerical study, we investigate the value of ADI and factors that affect that value. We show that using imperfect ADI can yield substantial savings, the amount of savings being sensitive to the quality of information; the benefit of the ADI increases considerably if the excess stock can be returned. We apply our model to a spare parts case. The value of imperfect ADI turns out to be significant. . His research is focused on spare parts management, production-inventory systems, maintenance and availability management of capital goods, and the effect of design decisions on the total cost of ownership of capital goods. Much of his research is based on a close collaboration with, for example, ASML, Dutch Railways, Philips, and the Royal Airforce. He is associate editor of Manufacturing and Service Operations Management, OR Spectrum, and Flexible Services and Manufacturing. Rommert Dekker is a professor of operations research, quantitative logistics, and IT at the Erasmus School of Economics. He currently leads an industrysponsored research program on service logistics. Professor Dekker began his career working at Shell Research. During his 7 years at the company he published over 100 papers on topics including reverse logistics, service logistics, inventory control, maintenance optimization, container logistics, and transport optimization. He was also co-founder of the well-known network for reverse logistics REVLOG.

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