In: Statistics and Probability
Question #2. Airline Scheduling
Alpha Airline wishes to schedule no more than one flight out of a given airport to each of the following cities: C, D, L,and N. The available departure slots are 8 A.M., 10 A.M., and 12 NOON. Alpha leases the airplanes at the cost of $5000before and including 10 A.M. and $3000after 10 A.M., and is able to lease at most two per departure slot. Also, if a flight leaves for location Nin a time slot, there must be a flight leaving for location Lin the same time slot. The expected profit (in $1000) contribution before rental costs per flight is shown in the table below. Formulate a model for a profit-maximizing (after deducting rental cost) schedule. Define your decision variables carefully; write the objective function and all relevant constraints.
Time Slot |
8 A.M. |
10 A.M. |
12 Noon |
C |
10 |
6 |
6 |
D |
9 |
10 |
9 |
L |
14 |
11 |
10 |
N |
18 |
15 |
10 |
The parameters are:
The formulas are:
The solution is:
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