Question

1. A retailer sells Rocky Flier football dolls. The 2 weeks lead time demand is normally distributed with a mean of 384.61 dolls and standard deviation of 196.11 dolls. The ordering cost is $20 per order, and the holding cost is $2 per doll per year.
   1. What is the economic order quantity?
   2. How many cycles are there on the average per year?
   3. For a service level of 0.955, find the re-order point and the safety stock.
   4. Management estimates the shortage cost per cycle where shortage occurs is $25. Calculate the annual estimated shortage cost for the service level of 0.995.

Answer 1

(a)

Annual demand, D = 384.61 * (52/2) = 10,000 units [Assuming 1 year = 52 weeks]
Ordering cost, K = 20
Unit carrying cost, h = 2

EOQ = (2.D.K / h)^1/2 = SQRT(2*10000*20/2) = 447 units

(b)

Number of cycles on an average per annum = D / Q = 10000 / 447 = 22.37

(c)

F(z) = 0.955; z = NORMSINV(0.955) = 1.695

d_LT = 384.61
σ_LT = 196.11

Safety stock, SS = z.σ_LT = 1.695*196.11 = 333 units (rounded up)

ROP = d_LT + Safety stock = 384.61 + 333 = 718 units

(d)

Service level = 99.5%

So, probability of shortages = 0.5%

We have seen that the number of cycles = 22.37 in a year.

So, the expected number of cycles when a shortage occurs = 22.37 * 0.5% = 0.11185

So, the expected cost of shortage = 0.11185*$25 = $2.80