Consumer demand for short delivery windows has driven companies to compete for faster shipping to clients. Recently, Amazon and Walmart along with other major companies have started offering same-day delivery. That translates into not using full truckload capacities, requiring more frequent dispatch, and in turn, increases transportation cost. However, inefficient routes are not only more expensive for the shipper but they are also more carbon-intensive. In this context, and from an operative level, we analyze the environmental impact of inbound logistics caused by fast shipping. We create a discrete-event simulation model to understand and compare the effect that certain parameters (i.e., delivery windows, inventory management policies, truck type) have on sustainability inbound logistics. We validate this model with the largest retailer in Mexico in order to analyze how sustainable fast shipping actually is and how to reduce its environmental impact. Results from the simulation model show that fast shipping produces significantly higher CO2 emissions since it imposes a challenge for cargo consolidation. We found that fast-shipping increases both total CO2 emissions and costs up to 15% and 68%, respectively.