The Mediterranean Restaurant stocks a red Chilean table wine it purchases from a wine merchant in a nearby city. The daily demand for the wine at the restaurant is normally distributed, with a mean of 18 bottles and a standard deviation of 8 bottles. The wine merchant sends a representative to check the restaurant’s wine cellar every 35 days, and during a recent visit there were 35 bottles in stock. The lead time to receive an order is 4 days. The restaurant manager has requested an order size that will enable him to limit the probability of a stockout to 5%.
We know the following
Daily demand (d) = 18
Standard deviation (σ) = 8
Time interval (T) = 35
Current inventory (I) = 35
Lead time (LT) = 4
Value of z for 95% service level = 1.64
Order up to level (M) = d*(LT + T) + z*σ*sqrt(LT + T)
M = 18*(35 + 4) + 1.64*8*sqrt(35 + 4) = 783.93 or 784 bottles
Order quantity (Q) = M – I
Thus, order quantity = 784 – 35 = 749 bottles
The Mediterranean Restaurant stocks a red Chilean table wine it purchases from a wine merchant in...