Multi-period multi-product inventory control with substitution and an exponential criterion

In this article, we study a multi-period multi-product inventory control problem. In the problem, there are N inventory classes which can be substituted for one another to satisfy the demand for a given reservation class (perhaps at a cost). The objective of management is to jointly determine overbooking levels for the reservation classes, taking into account the substitution options. Because of uncertain demand and forecast errors, costs observed at the end of the reservation period often deviate from their pre-calculated expectations. Instead of maximising revenue expectation, this article presents a new model that combines inventory management with risk analysis. Specifically, the exponential utility function is used in the model to reflect the manager's risk preference. Our results show that risk consideration has a significant impact on overbooking levels and revenues.