Walled-In Books stocks the novel War and Peace. Demand averages 15 copies per month, but is quite variable (i.e., is well represented by a Poisson distribution). Replenishments from the publisher require a two-week lead time. The wholesale cost is $12, and Walled-In uses a weekly holding cost rate of ½ percent. It also estimates that the fixed cost of placing and receiving a replenishment order is $5.
a) Compute the approximately optimal order quantity, using EOQ formula and rounding to the nearest integer. Using this order quantity, find the reorder point that makes the fill rate at least 90 percent. Computed the resulting average inventory (in dollars).
b) Using the order quantity computed in part (a) find the reorder point that makes the type I approximation of fill rate at least 90 percent. Compute the true fill rate and inventory level resulting from this reorder point and compare to the values in part (a). What does this say about the accuracy of the type I service approximation.
c) Using the order quantity computed in part (a), find the reorder point that makes the type II approximation of fill rate at least 90 percent. Compute the true fill rate and inventory level resulting from this reorder point and compare to the values in part (a). What does this say about accuracy of the type II service approximation? How does the value of Q affect the accuracy of the type II approximation?
d) Cut the order quantity from part (a) in half, and computed the reorder point needed to make fill rate at least 90 percent. How does the resulting inventory compare to that from part (a) Does this imply that the EOQ approximation is poor? Why or why not?