In the time interval between t and t 1 seconds beforethe departure of Braneast Airlines Flight 313, there is aprobability pt that the airline will receive a reservation for 19.4 Further Examples of Probabilistic Dynamic Programming Formulations 1035 the flight and a probability 1 pt that the airline will receiveno reservation. The flight can seat up to 100 passengers. Atdeparture time, if r reservations have been accepted by theairline, there is a probability q(y|r) that y passengers willshow up for the flight. Each passenger who boards the flightadds $500 to Braneast’s revenues, but each passenger whoshows up for the flight and cannot be seated receives $200in compensation. Formulate a dynamic programmingrecursion to enable the airline to maximize its expectedrevenue from Flight 313. Assume that no reservations arereceived more than 100,000 seconds before flight time.
In the time interval between t and t 1 seconds before
the departure of Braneast Airlines Flight 313, there is a
probability pt that the airline will receive a reservation for
19.4 Further Examples of Probabilistic Dynamic Programming Formulations 1035
the flight and a probability 1 pt that the airline will receive
no reservation. The flight can seat up to 100 passengers. At
departure time, if r reservations have been accepted by the
airline, there is a probability q(y|r) that y passengers will
show up for the flight. Each passenger who boards the flight
adds $500 to Braneast’s revenues, but each passenger who
shows up for the flight and cannot be seated receives $200
in compensation. Formulate a dynamic programming
recursion to enable the airline to maximize its expected
revenue from Flight 313. Assume that no reservations are
received more than 100,000 seconds before flight time.
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