Let us consider that local authorities want to locate fire brigades at
some places from the set 1, 2, 3 and 4 so that a distance from the
worst located dwelling place from set {1, 2, …, 10} to fire brigade
location be at most 25 km. The number of fire brigades should be
minimised. All dwelling places must be covered.
Transportation network with distances is on the picture below. Use the shortest
distances matrix and calculate incidental matrix from shortest distances matrix in
Mosel.
16
6
10
10
10
12
1
10
8
26
2
3
7
12
14
4
i
10
12
26
10
12
20
22
5
10
9
aij=1
D
j
i’
ai’j=0
customers
1
Mathematic model of the Maximum distance problem
4
Minimize  yi
i 1
4
subject to  aij yi  1
for j  1,...,10
i 1
yi  {0,1} for i  1,...,10
2
Solve the previous problem but now a distance from the worst located
dwelling place from set {1, 2, …, 10} to fire brigade location be at
most 20 km.
Can we obtain feasible solution now? Use getprobstat function.
procedure print_status
! To find out the status of the solution
declarations
status:array({XPRS_OPT, XPRS_UNF, XPRS_INF, XPRS_UNB}) of string
end-declarations
status:=['Optimum found', 'Unfinished', 'Infeasible', 'Unbounded']
writeln(status(getprobstat))
end-procedure
OR
if (getprobstat != XPRS_OPT) then writeln(“Optimal solution not found”)
3
Let us consider that local authorities want to locate 1 ambulance
vehicle at one place from the set 1, 2, 3 and 4 so that the size of the
part of population from set {1, 2, …, 10} , which is out of the time
limit Tmax =30, should be minimized. Solve using the allocation
approach. Population bj in nodes {1, 2, …, 10}:
100, 150, 100, 200, 150, 100, 100, 200, 150, 100
Transportation network with travel times is on the picture below. Use the shortest
distances matrix.
16
6
10
10
10
12
1
10
8
26
2
3
7
10
12
26
10
12
20
22
5
10
12
14
4
We define
cij = bj, if dij >Tmax and
cij = 0 otherwise.
9
4
Distance
Matrix
(travel
time)
dij
1
2
3
4
1
0
12
24
38
2
12
0
12
26
3
24
12
0
14
4
38
26
14
0
5
22
34
48
62
6
10
10
22
36
7
10
20
22
36
8
26
26
20
22
9
22
22
10
24
10
34
22
10
12
5
Minimize
c
iI jJ
Subject to
z
iI
ij
ij
z ij
1
z ij  y i
y
iI
i
for j  J
for i  I , j  J
p
y i  { 0 ,1 }
for i  I
z ij  { 0 ,1 }
for i  I , j  J
6
Let us consider that local authorities want to locate 1 ambulance
vehicle at one place from the set 1, 2, 3 and 4 so that the size of the
part of population from set {1, 2, …, 10} , which is out of the time
limit Tmax =30, should be minimized. Solve using the covering
approach. Population bj in nodes {1, 2, …, 10}:
100, 150, 100, 200, 150, 100, 100, 200, 150, 100
Transportation network with travel times is on the picture below. Use the shortest
distances matrix.
16
6
10
12
10
8
26
2
3
aij=1
12
14
9
i’
ai’j=0
4
10
12
26
10
12
7
5
10
20
22
i
10
10
1
xj=0
Tmax
j
customers
The xj is allowed to be zero only if no ambulance is
located in the radius Tmax from j.
7
Minimize
b x
j
jJ
j
Subject to x j   a ij yi  1
y
iI
for j  J
iI
i
p
yi {0,1}
for i  I
x j {0,1}
for j  J
8