A specialty coffeehouse sells Columbian coffee at a fairly steady rate of 400 pounds annually. The beans are purchased from a local supplier for $2.40 per pound. The quantity ordered is delivered in one shipment and immediately after the order has been placed. The coffeehouse estimates that it incurs a fixed cost of $120 in paperwork and labor to place an order for the coffee. Storing coffee costs 20 cents per pound per month. The inventory is also insured for 30 cents per pound per month. Finally, the company gets a 10% annual interest rate on its cash balance (i.e., capital cost).

Suppose the coffeehouse used to order 200 pounds every time and place each order right when the existing inventory reaches zero.

a) What is the length of an order cycle, which is the time between when two successive orders are placed?

b) What is the total cost per year?

Suppose now they want to improve the inventory management.

c) How much would you recommend the coffeehouse orders every time they call their supplier, instead of 200 pounds?

d) Assume the coffeehouse uses the order quantity you recommended. How many orders do they place in one year and what is the total cost per year?

Now, suppose the coffeehouse can produce beans itself at a cost of $2.2 per pound.

e) The unit production cost is $2.2 per pound. The fixed cost per production run is $500. The production rate is 500 pounds annually. The total holding cost will remain the same. Suppose the coffeehouse can figure out EPQ optimally. Shall the coffee house produce the beans itself or orders from the supplier?