Question

Prob 1Coffee Beanery in Chicago  is open 365 days a year and sells an average of 120 pounds of Kona Coffee beans a day (Assume demand is to normally distributed with a standard deviation of 40 pounds/day). Beans are ordered from Hawaii, and will arrive in exactly 4 days with a flat rate shipping and handling charge of $150. Per-pound annual holding costs for the beans are $3. Coffee is highly profitable, so the Beanery would like to have at most a 1% chance of running out of beans. Orders should be placed in whole pounds, but otherwise the Kona suppliers can deal with orders of any size. .

1)Calculate the economic order quantity (EOQ) for Kona coffee beans ________lbs

2)Calculate the total annual holding costs of cycle stock for Kona coffee beans $__________

3) Calculate the total annual fixed ordering costs for Kona coffee beans $__________

4)Calculate the Re-Order Point ________lbs

5)If management specified that a 2% stock-out risk is now okay, would safety stock holding costs decrease, increase, remain unchanged or do we not have enough info to tell? (Circle 1)

Problem 1-contd' Now assume that Kona supplier wants to place the Beanery on a fixed order intervals, where they will only deal with orders every 3 weeks (Hawaiians have better things to do than be waiting by the phone for obnoxious Manhattanites). Assume all other parameters remain the same.

1)If the Beanery has only 350lbs of beans left on the day they are allowed to place an order, calculate the probability they will run out before this next order arrives. ________%

2)Compare the cost of safety stock for the Fixed Order interval to that associated with the reorder point. How does it differ and why?

Answer 1

This is a case of variable demand and constant lead time.

Given : Average demand =120 pounds per day

Standard deviation of demand =40 pounds per day

Lead time =4 days

Ordering cost =150

Holding cost per pound per year =3

Number of working days =365

Service level =100-stockout percentage=100-1=99% =0.99

z=NORMSINV(0.99)=2.33

Annual demand =Average demand*Number of working days=120*365=43800

1)

EOQ=sqrt(2*Annual demand*cost per order/holding cost per unit per year)

=sqrt(2*43800*150/3)

=2092.844

=2093 pounds per order

2)Total annual holding cost=Average inventory *holding cost per pound per year

=EOQ/2* 3

=2093/2 *3

=$ 3139.5

3)Number of orders=Annual demand/EOQ=43800/2093=20.92=21 orders per year

Total annual fixed ordering cost =Number of orders *cost per order =21*150=$ 3150

4)Reorder point =ROP=Lead time demand +Safety stock

=Average demand *lead time +z*sqrt(lead time)*standard deviation of demand

=120*4+2.33*sqrt(4)*40

=480+2.33*2*40

=666.4

=666 (rounding to nearest whole number)

5)When stock-out risk increases ,then service level decreases.So,z value decreases and thus safety stock decreases.

Holding cost remains unchanged as increase in stock out risk has no impact.