A newsvendor model with capital constraint and demand forecast update

Abstract

We study a newsvendor problem with capital constraint and demand forecast update. The newsvendor has two instants to order from a supplier prior to a single selling season. While the demand is uncertain, the newsvendor can improve the forecast by utilizing the market signal observed between the first and second instants. We analyze the newsvendor’s optimal ordering policy in two cases: risk-neutrality and risk-aversion. Our analysis suggests that the optimal policy in each case is characterized by a critical value: a target safety capital. Under this policy, part of capital is left to use at instant 2 if and only if the initial capital is above the target safety capital. When this happens, the order quantity at instant 1 decreases as the initial capital increases. We further analyze the effect of information update on the newsvendor’s ordering policy. Our results indicate that more capital should be left to use at instant 2 when the correlation coefficient between market information and demand becomes large or when the newsvendor is more risk-averse.

Keywords:

• inventory
• newsvendor
• demand forecast update
• risk-aversion

Acknowledgments

The authors would like to give their indebted thanks to editor-in-chief Alexandre Dolgui, the associate editor and anonymous referees for their valuable suggestions, who helped them improve the paper greatly.

Notes

This work was partially supported by National Natural Science Foundation of China [grant number 71201027], [grant number 71272085]; Humanity and Social Science Youth Foundation of Ministry of Education of China [grant number 12YJC630260], [grant number 12YJA630135] and Guangdong Natural Science Foundation [grant number S2012040007919].