Newsboy

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Newsboy

  1. 1. Inventory Control Subject to Uncertain Demand The nature of randomness
  2. 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. 3. Frequency Histogram for a 52-week History of Sales of The Computer Journal at Mac’s Fig. 5-1
  4. 4. Parameters of the normal distribution
  5. 5. Frequency Histogram and Normal Approximation Fig. 5-2
  6. 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. 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. 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
  9. 9. Extension to include starting inventory <ul><li>Starting inventory u > 0 </li></ul><ul><li>Apply to products with a shelf life that exceeds one period </li></ul><ul><li>If u < Q*  replenish Q*-u </li></ul><ul><li>If u > Q*  Do not order </li></ul>
  10. 10. Multiple Planning Periods <ul><li>Ending inventory in one period  starting inventory of next period </li></ul><ul><li>Infinite horizon is considered </li></ul><ul><li>Interpretation of c u and c o will be different </li></ul><ul><li>As long as excess demand is backordered, the number of units sold = demand over an longer period of time </li></ul><ul><ul><li>c u  interpreted as loss of good will </li></ul></ul><ul><ul><li>c o  Holding cost </li></ul></ul>

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