QQ-Mart is a local grocery store. It sells a certain type of cheese. Excess demand can be backordered. The weekly 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 Qwhen 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 month. 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.)
a)What is the mean and variance of the demand in lead time?
b)What is Qand Rsuch that the desired service level can be achieved?
c)What is the safety stock?
Given that:
Monthly mean demand = 250
1) Mean demand during lead time = Average demand during lead time = 250 / 4 = 62.5 (one month = 4 weeks)
Variance during lead time = Variance * Lead time = 225 * 1 = 225
2) Annual demand, D = 250 * 12 = 3000
Order cost, S = $10
Holding cost , h = 10% * 5 = 0.5
Economic order quantity : EOQ :
Q = square root( 2DS / h) = square root (2 * 3000 * 10/0.5) = 346.41 or 346
Reorder point = Mean demand during lead time + Z-score * Standard deviation * square root (lead time)
Z-score = 1.96 for 95% service level
Standard deviation = square root (variance) = square root (225) = 15
Reorder point = 62.5 + 1.96 * 15 * 1 = 966.9
Safety Stock = Z-score * Standard deviation * Square root (lead time) = 1.96 * 15 * 1= 29.4 ≈ 30
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