Consider the singlewarehouse inventory model analyzed in Section 11.5 with leadtime l > 0. Prove that the inventory on hand at the end of period t for some t > l can be written as St−l −

t it−l Di , where St−l is the order-up-to-level in period t −l and Di is the demand in period i.

Conclude that any nonzero leadtime model can be replaced by a model with zero leadtime for which the loss function G(y) is calculated according to (11.2) with y being the inventory position and D the total demand during the leadtime.