Suppose you manage the banana inventory for a grocers association. Holding cost is $0.15/lb per week. The cost of bananas is $0.22/lb with an order setup cost of $50. Your demand rate is 450 lbs per week.

a. Using the Economic Order Quantity model, how many pounds of bananas should you order at a time to minimize order setup plus holding costs? Q* = ___________

b. What is the corresponding optimal interval of time between orders? T* = ___________

c. What are the two unrealistic assumptions of the EOQ model that the ROP and OUT models fix? 1. ________________________________________________ 2. ________________________________________________

d. Due to the issues listed in part c, suppose instead that you decide to use the Reorder Point Model to manage the inventory of bananas. If the standard deviation of the banana demand rate is 65 lbs per week and the delivery leadtime takes an average of 0.5 weeks with a standard deviation of 0.15 weeks, at what quantity should you set the ROP to achieve a service level of 99%? ROP = ___________

e. When inventory falls to the ROP found in part d, how many lbs of bananas should you order? Q = ___________

f. Now suppose you decide to use the Order-Up-To Level model to manage the inventory. How often will you order? T = ___________

g. What is the OUT level that best manages the inventory? OUT = ___________

h. What quantity of the OUT level found in part g is safety stock? SS = __________

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