This document discusses inventory control when facing uncertain demand. It provides an example of weekly sales data for a computer journal over 52 weeks. It shows histograms and normal approximations of the sales data. It also shows the mass function and cumulative distribution function calculated from the sales data. It discusses how starting inventory can be included in the model and how the model can be extended to multiple planning periods with ending inventory carrying over to the next period as starting inventory.

1. Inventory Control Subject to Uncertain Demand The nature of randomness

2. Example 5.1 Number of copies of the Computer Journal 12 14 0 10 18 9 11 6 11 14 12 13 17 14 14 19 17 15 18 11 11 8 16 9 10 9 19 15 15 12 7 6 8 15 14 18 17 4 4 5 9 8 11 8 7 4 22 9 12 9 19 15

3. Frequency Histogram for a 52-week History of Sales of The Computer Journal at Mac’s Fig. 5-1

4. Parameters of the normal distribution

5. Frequency Histogram and Normal Approximation Fig. 5-2

6. Mass function and CDF 1/52 22 2/52 10 5/52 11 0 21 6/52 9 0 20 4/52 8 3/52 19 2/52 7 3/52 18 2/52 6 3/52 17 1/52 5 1/52 16 3/52 4 5/52 15 0 3 5/52 14 0 2 1/52 13 0 1 4/52 12 1/52 0 F(Q) f(Q) Q F(Q) f(Q) Q

7. Mass function and CDF 1 1/52 22 21/52 2/52 10 26/52 5/52 11 51/52 0 21 19/52 6/52 9 51/52 0 20 13/52 4/52 8 51/52 3/52 19 9/52 2/52 7 48/52 3/52 18 7/52 2/52 6 45/52 3/52 17 5/52 1/52 5 42/52 1/52 16 4/52 3/52 4 41/52 5/52 15 1/52 0 3 36/52 5/52 14 1/52 0 2 31/52 1/52 13 1/52 0 1 30/52 4/52 12 1/52 1/52 0 F(Q) f(Q) Q F(Q) f(Q) Q

8. Mass function and CDF 1.0000 1/52 22 0.4038 2/52 10 0.5000 5/52 11 0.9808 0 21 0.3564 6/52 9 0.9808 0 20 0.2500 4/52 8 0.9808 3/52 19 0.1731 2/52 7 0.9231 3/52 18 0.1346 2/52 6 0.8654 3/52 17 0.0962 1/52 5 0.8077 1/52 16 0.0769 3/52 4 0.7885 5/52 15 0.0192 0 3 0.6923 5/52 14 0.0192 0 2 0.5962 1/52 13 0.0192 0 1 0.5769 4/52 12 0.0192 1/52 0 F(Q) f(Q) Q F(Q) f(Q) Q