Question

A gourmet coffee shop in downtown SF is open 200 days a year and sells an average of 73 pounds of Kona Coffee beans a day. (Demand can be assumed to be distributed normally with a standard deviation of 16 pounds/day.) After ordering (fixed cost = $13 per order), beans are always shipped from Hawaii within exactly 4 days. Per-pound annual holding costs for the beans are $3. a) What is the economic order quantity (EOQ) for Kona coffee beans? b) What are the total annual holding costs of cycle stock for Kona coffee beans? c) What are the total annual fixed ordering costs for Kona coffee beans? d) Assume that management has specified that no more than a 1% risk during stock out is acceptable. What should our reorder point (ROP) be? e) What is the safety stock need to attain a 1% risk of stock-out during lead time? f) What is the annual holding cost of maintaining the level of safety stock needed to support a 1% risk? g) If management specified that a 2% risk of stock-out during lead time would be acceptable, would our safety stock holding costs decrease or increase?

Answer 1

Solution:

1. What is the economic order quantity (EOQ) for Kona coffee beans?

sol:

d= 73 lbs/day 200 days per year

D= 14,600 lb/year

H= $3/lb/year

   S= $13/order

EOQ= √(2*14,600*13)/3 = 366 approx. lb of beans

2. What are the total annual holding costs of cycle stock for Kona coffee beans?

sol:

Total annual holding cost = Q/2 * H = 366/2 * 3 = $549 approx

3. What are the total annual fixed ordering costs for Kona coffee beans?

sol:

Total annual order cost = D/Q * S = 14,600/366 * 13 = $519 approx

4. Assume that management has specified that no more than a 1% risk during stock out is acceptable. What should our reorder point (ROP) be?

sol:

LT= 4 days with = 16Stockout risk = 1%s= 2.33,

Z value for 99% service level = 2.33

ROP = Lead time demand + SS,

Re-order point = Average Lead Time*Average Demand + Service Level*SQRT(Avg. Lead Time*Standard Deviation of Demand^2)

ROP= 4*73 + 2.33 * sqrt(4*16^2 )

ROP= 292 + 74.56

ROP= 366.56

5. What is the safety stock need to attain a 1% risk of stock-out during lead time?

sol:

SS= 74.56 from part (d)

6. What is the annual holding cost of maintaining the level of safety stock needed to support a 1% risk?

sol:

Annual safety stock holding cost = $223.68

7. If management specified that a 2% risk of stock-out during lead time would be acceptable, would our safety stock holding costs decrease or increase?

sol:

   2% stockout level → Z= 2.054

The lower we make our target service level, the less SS we need.