A risk-averse newsvendor model with pricing consideration

A decision maker who is facing a random demand for a perishable product, such as newspapers, decides how many units to order for a single selling period. This single-period inventory problem is often referred to as the "classic newsvendor problem", in which the selling price is fixed, the order must be made before the selling period, and the decision maker is risk-neutral. If the decision maker orders too many (overage), the inventory cost will be too high. If the decision maker orders too few (underage), the potential profit will be lost. The optimal order quantity is a balance between the expected costs of overage and underage. This thesis investigates an extension of the classic newsvendor problem. In this extension the demand depends on the selling price, the decision maker may obtain an additional order at a higher price during the selling period, and the decision maker is risk-averse (not risk-neutral). The problem is to find optimal order quantity and selling price so that the expected utility of the risk-averse decision maker is maximized. This thesis examines the relationship between the order quantity and the selling price for different risk-averse decision makers in this extended newsvendor problem defined above. The result shows that the relationships are consistent for some decision makers but not for others. For example, if the decision maker exhibits a constant absolute risk aversion (CARA), the optimal order quantity will decline when the selling price increases. If the decision maker has constant relative risk aversion (CRRA), the relationship is complex. This thesis finds that if it is just known that the decision maker is risk-averse, the optimal order quantity placed is less than that made by a risk-neutral decision maker. Further more, the risk-averse decision maker's optimal order quantity falls when her/his risk aversion increases. However, the relationship between order quantity and selling price is still indeterminate in this case. This extension of the classic newsvendor problem provides a more realistic dynamic setting than before, therefore providing an excellent framework for examining how the inventory problem interacting with the marketing issue (selling price) will influence decision makers at the firm level. It also provides an integrated framework for investigating different variations of newsvendor problems. Thus, this thesis will motivate and encourage more applications of the newsvendor problem which is a foundation of many supply chain management problems.