a)
Underbooking cost, Cu = $ 145
Overbooking cost, Co = $ 205
Critical ratio = Cu/(Cu+Co)
= 145/(145+205)
= 0.4143
Cumulative probability distribution
# of no shows | Probability | Cumulative probability |
0 | 0.07 | 0.07 |
1 | 0.07 | 0.14 |
2 | 0.1 | 0.24 |
3 | 0.02 | 0.26 |
4 | 0.12 | 0.38 |
5 | 0.01 | 0.39 |
6 | 0.04 | 0.43 |
7 | 0.19 | 0.62 |
8 | 0.16 | 0.78 |
9 | 0.22 | 1 |
In the above table, look for cumulative probability just greater than 0.4143
That value of cumulative probability is 0.43 and corresponding # of no shows is 6
Therefore, Recommendation overbooking is: 6
----------------------------------------------------
b)
Loss occurs when # of no shows is greater than overbooking, i.e. for 7, 8, 9 no shows
Expected # of no shows greater than overbooking = (7-6)*0.19+(8-6)*0.16+(9-6)*0.22
= 1.17
Expected loss = 1.17*Cu
= 1.17*145
= $ 169.65
1 # of No-Probability of No- Shows Shows occurring (d) P(d) 0 0.07 0.07 2 0.10...
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