22 Braneast Airlines must staff the daily flights between New York and Chicago shown in Table 81. Each of Braneast’s crews lives in either New York or Chicago. Each day a crew must fly one New York–Chicago and one Chicago–New

York flight with at least 1 hour of downtime between flights.
Braneast wants to schedule the crews to minimize the total downtime. Set up an assignment problem that can be used to accomplish this goal. (Hint: Let xij 1 if the crew that flies flight i also flies flight j, and xij 0 otherwise. If xij
1, then a cost cij is incurred, corresponding to the downtime associated with a crew flying flight i and flight j.) Of course, some assignments are not possible. Find the flight assignments that minimize the total downtime. How many crews should be based in each city? Assume that at the end of the day, each crew must be in its home city.

Transcribed Image Text:

TABLE 81 Leave Arrive Leave Flight Chicago New York Flight New York Arrive Chicago 1 6 A.M. 10 A.M. 1 7 A.M. 9 A.M. 2 9 A.M. 1 P.M. 2 8 A.M. 10 A.M. 3 12 noon 4 P.M. 3 10 A.M. 12 noon 4 3 P.M. 7 P.M. 4 12 noon 2 P.M. 5 5 P.M. 9 P.M. 5 2 P.M. 4 P.M. 6 7 P.M. 11 P.M. 6 4 P.M. 6 P.M. 7 8 P.M. 12 midnight 7 6 P.M. 8 P.M.