In Section 6.2 we developed a dynamic programming approach for finding the optimal order-up-to values over a finite planning horizon of N periods when there are no fixed ordering costs. Suppose that N = 6, and h = 1 and b = 10. Let α = 1 and assume the unit cost is constant over time. Suppose demand is Poisson distributed and independent from period to period.

(a) Suppose the demand rates in the 6 periods are 10, 20, 40, 40, 3, 1, respectively. Find s¯i and s∗
i for each period, i = 1,...,6.

(b) Suppose the demand rates for these 6 periods are 50, 50, 50, 20, 5, 1, respectively.
Find ¯si and s∗
i , i = 1,...,6.