# A business executive must make the four round trips

June 4, 2016

Question
A business executive must make the four round trips between the head office in Dallas and a branch office in Atlanta.

Departure date from Dallas

Return date to Dallas

Monday, July 6

Friday, July 10

Monday, July 13

Wednesday, July 15

Monday, July 20

Friday, July 24

Tuesday, July 28

Friday, July 31

The price for a round ticket from Dallas is \$400. A discount of 25% is granted if the dates of arrival and departure of a ticket span a weekend (Saturday and Sunday). If the stay in Atlanta lasts more than 21 days, the discount is increased to 30%. A one-way ticket between Dallas and Atlanta (either direction) costs \$250. How should the executive purchase the tickets?

Set up this problem as an assignment problem and formulate this problem as LP model.

Describe the plan for the trips.

Hint:

Use the code (city, date) to define the rows and columns of the assignment problem. For example: the assignment (D, 6) – (A, 10) means leaving Dallas on July 6 and returning from Atlanta July 10 at a cost of \$400. Please complete the following table then solve this problem as an assignment problem.

(A,10)

(A,31)

(D, 6)

\$400

300

300

400

300

300

300

(D, 28)