Q$3.[$QAP$]$ Ikea is trying to open $4$ new warehouses $(WH)$ in the UAE to serve more people. Each warehouse

is providing a set of products. Therefore, there is flow among the warehouses. Based on the initial study

by the company, there are $4$ possible locations.

$W=|[0,5,12,30],[5,0,15,20],[12,15,0,25],[30,20,25,0]|,D=|[0,30,20,25],[30,0,65,20],[20,65,0,100],[25,20,100,0]|$

a$.$ Illustrate the heuristic procedures to find the best assigning of the locations. The WH are A$,$ B$,$ C and D are to

be placed in four locations $(1,2,3,4)$ in the UAE. The number of trips per day between the warehouses and the

distances between locations are expressed by the symmetric matrices $W$ and $D,$ respectively $(D$ is in $km,W$ is

$1000$ batches$).$

b$.$ Is the heuristic solution optimal, Why $($Find LB$)?$ If not, make one change in the locations and calculate the

difference. Is it better or not? Why?

c$.$ Using Cplex, find the optimal solution. Write down the total cost and the assignment. Compare the results with

part a$.$

Write your answer in the paper and Upload the Cplex file.

d$.$ Create the activity relationship chart for the clinics.