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:

Please give me a thumbs-up if this helps you out. Thank you!