#### Date of Award

9-2004

#### Degree Type

Thesis

#### Degree Name

Master of Philosophy (MPHIL)

#### First Advisor

Professor SUN Daning

#### Abstract

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 ¯xed, 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 pro¯t 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 ¯nd 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 sell- ing price for di®erent risk-averse decision makers in this extended newsvendor problem de¯ned 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 ¯nds 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 dy- namic setting than before, therefore providing an excellent framework for exam- ining how the inventory problem interacting with the marketing issue (selling price) will in°uence decision makers at the ¯rm level. It also provides an inte- grated framework for investigating di®erent variations of newsvendor problems. Thus, this thesis will motivate and encourage more applications of the newsven- dor problem which is a foundation of many supply chain management problems.

#### Copyright

The copyright of this thesis is owned by its author. Any reproduction, adaptation, distribution or dissemination of this thesis without express authorization is strictly prohibited.

#### Recommended Citation

Ye, Z. (2004). A risk-averse newsvendor model with pricing consideration (Master's thesis, Lingnan University, Hong Kong). Retrieved from http://commons.ln.edu.hk/otd/18