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A hotel near the university always fills up on the evening before football games.
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History has shown that when the hotel is fully booked, the number of las-minute
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cancellations has a mean of 5 and a standard deviation of 3.
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The average room rate is $80. When the hotel is overbooked, the policy is to
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find a room in a nerby hotel to pay for the room for the customer.
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This usually costs the hotel approximately $200 because rooms booked on such
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late notice are expensive. How many rooms should the hotel overbook?
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The cost of underestimating the number of cancellations
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is $80 and the cost of overestimating cancellations is $200.
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P <CuCo=
Cost per unit of demand overestimated.
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Co + CuCu=
Cost per unit of demand underestimated.
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NORMSINV
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P <Cu=$80=0,2857142857-0,5659488226
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Co + Cu$200 + $80
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Using NORMSINV (.2857) from Excel gives a Z-Score of 0.56599.
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The negative value indicates that we should overbook by a value less
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than the average of 5. The actual value should be -.56599(3) = -1.69797,
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or 2 reservations less then 5.
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The hotel should overbook three reservations on the evening prior to a
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football game.
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