Many theoretical models adopt a normative approach and assume that decision makers are perfect optimizers. In contrast, this paper takes a descriptive approach and considers bounded rationality, in the sense that decision makers are prone to errors and biases. Our decision model builds on the quantal choice model: While the best decision need not always be made, better decisions are made more often. We apply this framework to the classic newsvendor model and characterize the ordering decisions made by a boundedly rational decision maker. We identify systematic biases and offer insight into when overordering and underordering may occur. We also investigate the impact of these biases on several other inventory settings that have traditionally been studied using the newsvendor model as a building block, such as supply chain contracting, the bullwhip effect, and inventory pooling. We find that incorporating decision noise and optimization error yields results that are consistent with some anomalies highlighted by recent experimental findings.