to decide on how many copies of a book to purchase at the start of the upcoming

Question

to decide on how many copies of a book to purchase at the start of the upcoming selling season. The book retails for $28.00. The publisher sells the book to Dan for $20. Dan will dispose of all the unsold copies of the book at 50% off the retial price, at the end of the season. Dan estimates that demand for this book during the season is Normally distributed with a mean of 1000 and a standard deviation of 250. (a) Suppose Dan orders 1415 copies of the book. What would be his expected mismatch costs? (6)

Explanation / Answer

Underage Cost = Cs = 20

Cost of Excess = Underage Cost - Sink Cost = 20- 50% of 28 = 20-14 = 6

Optimal Service Level = Underage Cost/(Underage Cost+Cost of Excess) = 20/(20+6) = 0.7692

Z(0.7692) = 0.736

So Dan should buy = 1000 + 0.736*250 = 1184

If Dan brings 1415 copies, he will exceed the optimal count by = 1415 - 1184 = 231

Loss Due to Mismatch = Excess Quantity * Cost of Excess = 231 * 6 = 1386

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