Solve using brute force and heuristic method 4 Three compute

4. Three computers were purchased for use by six departments in a small appliance manufacturing factory. The transportation time from the center of each department to each of the possible locations for the computers is shown in the accompanying table, along with each department\'s daily demands Location Department 1 5 6 Demand 7.0 4.0 2.0 6.0 3.5 1.0 4.0 2.5 3.0 0.0 5.0 2.0 16 2.0 3.0 10 4.04.0 3.0 1.0 6.0 7.0 5.02.0 0.0 10 3.0 8.0 2.07.5 6.0 8.0 5.0 0.0 9.4. 4.0 5.0 15 24 4 a. Use the brute force method to determine the best locations for the computers.

Solution

Brute force method considers all the possible alternatives for determining the optimal solution. Using brute force method, we calculate the total transportation for every possible alternative of locaitons for the three computers and select the best locations which minimize the total transportation time.

The Minimum transportation time from department A is 1 to location 6.

Minimum transportation time from department B is 0 for location 4

Minimum transportation time from department C is 1 for location 3

Minimum transportation time from department D is 0 for location 6

Minimum transportation time from department E is 2 for location 3

Minimum transportation time from department F is 0 for location 2.

First alternative solution: locations 3,4 and 6, to service all the six departments. Total transportation time

= 1*8 + 0*16 + 1*24 + 0*10 + 2*4 + 4*15

= 100

Second alternative solution:

locations 2,3 and 6, to service all the six departments. Total transportation time

= 1*8 + 2*16 + 1*24 + 0*10 + 2*4 + 0*15

= 72

Second alternative provies the minimum transportation time.

Therefore, the best locations for the computers are 2, 3 and 6