Chapter 4 Optimization

1. Modeling

This problem has many solutions. Here is one possibility.

Control variables (from the statement of the problem):

• x_i: starting point of flight i

• d_i: duration of flight i, d_i=15

• The cost of ticket for the ith flight, t_i

Note that the number of passengers in a flight is not a control parameter, because it is related to the cost of a ticket; once the cost of the ticket is determined, the number of passengers cannot be independently controlled.

Fixed parameters:

• The possible take-off locations, V

• The cost of chase vehicle (gas needed, maintenance, etc.) per kilometer of travel.

• Location of the roads, R

• The cost of the natural gas, g, per minute of flight

• Pilot’s wages, w, per minute of flight

Input parameters: