Question 2. QQ-Mart is a local grocery store. It sells a certain type of cheese.

Question

Question 2. QQ-Mart is a local grocery store. It sells a certain type of cheese. Excess demand can be backordered. The monthly demand of the cheese follows a normal distribution with mean of 250 and variance of 225. QQ-Mart reviews its inventory continuously and will place order with size Q when the inventory level hits R. The fixed cost per ordering is $10. The unit purchase price is $5. The annual interest rate of 10% is used to estimate the holding cost. The lead time for purchasing the cheese from the manufacturer is one week. QQ-mart wants to achieve a service level target that no stock-out in 95% the cycles. (Assume there are four weeks in one month.) 1) What is the mean and variance of the demand in lead time? 2) What is Q and R such that the desired service level can be achieved? 3) What is the safety stock?

Explanation / Answer

1) Mean of demand during lead time, = Monthly demand * lead time in months = 250*(1/4) = 62.5

Variance of demand in lead time, v = Variance of monthly demand * lead time in months = 225*(1/4) = 56.25

2) Annual demand, D = 250*12 = 3000

Ordering cost, S = 10

Holding cost, H = 5*0.1 = 0.5

z value for 95% service level = NORMSINV(0.95) = 1.645

Q = (2DS/H) = (2*3000*10/0.5) = 346.4

R = + zv = 62.5 + 1.645*56.25 = 155

3) Safety stock = zv = 1.64556.25 = 92.5

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