A newsvendor model with capital constraint and demand forecast update

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.