Introduction to Management Science 12th Edition by Bernard Taylor

Exercise 40

In the event of a disaster situation at Tech from weather, an accident, or terrorism, victims will be transported by emergency vehicles to three area hospitals: Montgomery Regional, Radford Memorial, and Lewis Galt. Montgomery Regional is (on average) 10 minutes away from Tech, Radford Memorial is 20 minutes away, and Lewis Galt is 35 minutes away. Tech wants to analyze a hypothetical disaster situation in which there are 15 victims with different types of injuries. The emergency facilities at Montgomery Regional can accommodate, at most, 8 victims; Radford Memorial can handle 10 victims; and Lewis Galt can admit 7 victims. A priority has been assigned for each victim according to the hospital that would best treat that victim's type of injury, as shown in the following table (where 1 reflects the best treatment).
For example, for victim 1's type of injury, the best hospital is Montgomery Regional, the next best is Radford Memorial, and Lewis Galt is the third best.
a. Formulate and solve a linear programming model that will send the victims to the hospital best suited to administer to their specific injuries while keeping the average transport time to 22 minutes or less.
b. Formulate and solve a linear programming model that will minimize the average transport time for victims while achieving an average hospital priority of at least 1.50 or better.