Supply Chain Design and the Cost of Greenhouse Gas Emissions

The design of a supply chain not only in‡uences a retailer’s cost, it in‡uences its customers’costs with stores few and far between, consumers must travel a long distance to shop, whereas their shopping trips are short with a dense network of stores. This supply chain design problem is the combination of two well studied problems: the Traveling Salesmen problem and the k-median problem. A solution is provided and the following question is asked: what is the consequence of failing to charge the full externality cost of greenhouse gas emissions? A bound is derived on the “carbon penalty”, the gap between realized costs and minimal costs. A key measure in this bound is the carbon e¢ ciency of the vehicles used in the supply chain, where carbon e¢ ciency is the ratio of the carbon emitted per kilometer to the variable operating cost per kilometer. Given current estimates of carbon e¢ ciency, it is found that the carbon penalty is small (0:1%). Thus, the supply chain design problem is robust to misspeci…cations in its inputted parameters even if the potentially costly cost of carbon emissions is ignored, the chosen supply chain design may nevertheless yield a total cost (including emission costs) that is nearly as small as possible.