Problem:
2 new fire stations are to be located in a city and the major of the city wants to decide where to locate the 2 fire stations. For planning purposes, the region has been divided into five tracts, with no more than one fire station to be located in any given tract. The decisions to be made consist of the tracts to receive a fire station and the assignment of each of the tracts to one of the fire stations. The objective is to minimize the overall average of the response times to fires.
The following table gives the average response times to a fire in each tract if that tract is served by a station in a given tract. The bottom row gives the forecasted number of fires that will occur in each of the tracts per day.
Required:
Question 1) Formulate an integer programming model for this problem and solve it using Excel Solver.
response times (in times) fire in tract
|
Assigned station located in tract
|
1
|
2
|
3
|
4
|
5
|
|
1
|
5
|
12
|
30
|
20
|
15
|
|
2
|
20
|
4
|
15
|
10
|
25
|
|
3
|
15
|
20
|
6
|
15
|
12
|
|
4
|
25
|
15
|
25
|
4
|
10
|
|
5
|
10
|
25
|
15
|
12
|
5
|
|
Average frequency of fires
|
2 per day
|
1 per day
|
3 per day
|
1 per day
|
3 per day
|
Solve the given numerical problem and illustrate step by step calculation.