Question

Direct Cruise operates a 1000 passenger Cruise ship from Miami to San Jose, Costa Rica, once a week. Cancellation distribution is normal with mean 100 and s.d. 20. A vacant seat in the cruise is considered to cost $1000 for the Direct Cruise. An overbooked passenger, who has to be turned away (booked in the next cruise), costs $1500 to the firm.

What is the cost of excess (in the context of single period inventory management)? What is the cost of shortage (in the context of single period inventory management)? What is the appropriate ratio to determine the correct number of seats to be overbooked?
What should be the number of seats overbooked (round to nearest integer)?
Suppose that all vacant seats can be filled and the cost of a vacant seat is only $500 each, would your answer to number of overbooked seats be more than your answer to part (d)? Yes (Should make more overbookings now)   or No (Should make less overbookings now)   Neither (Should make same overbookings now)Explain.
Suppose that the s.d. of cancellations is 0, all other things remaining the same, how many seats would you overbook? Explain.

Answer 1

Solurion:-

Hope its helpfull to you..

a):-

Cost of excess, Ce = $1500 (If we overbook more than required)

b):-

Cost of shortage, Cs = $1000

c):-

Critical ratio = Cs / (Ce+Cs)
= 1000 / 2500 = 2/5 = 0.40

d):-

Z-score = -0.25

for Critical ratio = 0.40 (Refer standard normal distribution table)

Optimal overbooking = Mean cancellation + Std deviation of cancellation * Z-score
= 100 + 20*-0.25 = 95

e):-

If we can fill the vacant seat for $500, Cs = $500, Critical ratio gets lowered.

A lower critical ratio means a lower Z-score and hence the Number of over bookings should be lesser.

f):-

Optimal overbooking = Mean = 100 (Since s.d = 0)