For the inventory system of Sec. 1.5, suppose that if the inventory level I(t) at the beginning of a month is less than zero, the company places an express order to its supplier. [If 0 ≤ I(t) < s, the company still places a normal order.] An express order for Z items costs the company 48 + 4Z dollars, but the delivery lag is now uniformly distributed on [0.25, 0.50] month. Run the simulation for all nine policies and estimate the expected average total cost per month, the expected proportion of time that there is a backlog, that is, I(t) < 0, and the expected number of express orders placed. Is express ordering worth it?
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