3.10. Consider a discrete-time, periodic review inventory model and let 6, be the total demand in period n, and let X,, be the inventory quantity on hand at the end-of-period n. An (s, S) inventory policy is used: If the endof-

period stock is not greater than s, then a quantity is instantly procured to bring the level up to S. If the end-of-period stock exceeds s, then no replenishment takes place.

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= (a) Suppose that s = 1, S = 4, and X = S = 4. If the period demands turn out to be 2, 23, 34, 4 = 0, s = 2, 6 = 1, =2, 82, what are the end-of-period stock levels X,, for periods n = 1, 2,..., 8? (b) Suppose 1, 2, Pr{0} = 0.1, Pr{ are independent random variables where = = 1} = 0.3, Pr{2} = 0.3, Pr{ = 3} =