# Homework 4

instructions: Due: Mar 30, 2016At the beginning of the class
Page 1 of 1
Homework 4
MGT 472 – Advanced Operations Management
(1) The booking limits for four fare classes are given as b = (b1, b2, b3, b4) = (20, 15, 5, 2).
Suppose that until now 5 bookings are made for class 2 and 4 bookings are made for class 3.
The following parts are independent.
a) Process a request for 2 bookings for class 4. Decide on accept/reject and then report the
cumulative booking vector B.
b) Process a request for 6 bookings for class 1. Decide on accept/reject and then report the
cumulative booking vector B.
c) Process a request for 2 bookings for class 3. Decide on accept/reject and then report the
cumulative booking vector B.
d) Process a cancellation of 2 bookings for class 3. Report the cumulative booking vector B.
(2) A hotel numbers its fare classes from higher to lower as 1, 2, 3 and 4. The room prices for
these classes are p1=\$300, p2=\$250, p3=\$200, p4=\$150. The demands for these fare classes are
denoted by D1, D2, D3 and D4. The hotel considers the cumulative demands
D1=D1, D1,2 =D1+D2, D1,2,3 = D1+D2+D3, D1,2,3,4 = D1+D2+D3+D4.
These demands turn out to have uniform distributions with the following ranges:
D1 ∈ [0, 10], D1,2 ∈ [0, 20], D1,2,3 ∈ [0, 30], D1,2,3,4 ∈ [0, 40].
a) Before applying EMSR-b heuristic, the hotel needs aggregate prices p1, p1,2, p1,2,3 and p1,2,3,4.
Compute these prices.
b) What is the protection level y3 for classes {1, 2, 3}?
c) What is the protection level y2 for classes {1, 2}?
d) What is the protection level y1 for class {1}?
(3) A hotel numbers its fare classes from higher to lower as 1, 2, 3 and 4. The room prices for
these classes are p1=\$300, p2=\$250, p3=\$200, p4=\$150. The demands for these fare classes are
denoted by D1, D2, D3 and D4.
These demands turn out to have uniform distributions with the following ranges:
D1 ∈ [0, 10], D2 ∈ [0, 10], D3 ∈ [0, 10], D4 ∈ [0, 10].
a) Use EMSR-a heuristic to find the protection level y3 for classes {1, 2, 3}?
b) Use EMSR-a heuristic to find the protection level y2 for classes {1, 2}?
(4) An airline has two fare classes and protects 40 seats for the higher fare class while reserving
for the lower fare class. The demand for the higher fare class ranges from 30 to 70 and it is
uniformly distributed. If the discount ticket costs \$300, how much should the full fare ticket
cost to make the protection level of 40 optimal?
Hint: Use the formula pd/pf = P(df > y) = 1-[(y-a)/(b-a)] for the uniformly distributed demand
over [a,b]. 