Question

One of Arthur Alpaca’s best-selling products is an imported sausage that has lots of garlic in it. Annual demand is 2400kg. Holding costs of sausage are quite high at $1.18/kg per year. Every time Arthur places an order it costs him $10.37 regardless of the size of the order.

a. What is the economic order quantity of sausage assuming constant demand?​​[4]

b. If Arthur orders the quantity calculated in (a), how many orders does he place each year? [3]

c. Demand is not constant. The lead time demand can be assumed to be a normal distribution with a standard deviation of 8.37kg. What is safety stock if management specify that the maximum probability of a stockout in a cycle is 10%?​​​​​

Answer 1

Annual demand (A) = 2400 KG

Holding cost (H) = $1.18 per KG per year

Ordering cost (O) = $10.37

A.

Economic order quantity = (2*A*O/H)^.5

Economic order quantity = (2*2400*10.37/1.18)^.5

Economic order quantity = 205.39 or 205 KG

B.

Number of orders placed each year = 2400/205.39 = 11.69

If 205 KG per order is used,

Number of orders placed each year = 2400/205 = 11.71

C.

Value of Z (at 10% stock-out probability) = 1.28

Safety stock = Z*SD = 1.28*8.37 = 10.71 KG