Inventory control with advance ordering and expedited replenishments

We study a finite horizon multi-stage inventory control problem where demand is stochastic and nonstationary. The demand distribution across periods is a function of a demand signal which is random at the beginning of the planning horizon. The firm has the option of contracting its supplies in advance of realization of the market signal to benefit from price discounts. It is also possible for the firm to replenish its inventories during the selling season by paying higher spot market prices after the market signal is observed. Our research is motivated by applications in cruise line industry where contracts are made before the final number of bookings is realized. Based on the finalized bookings and consumption rates, additional purchases can be made at intermediate stops with higher prices. We investigate optimal combination of advance contracting and expedited replenishment policies under such settings.