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150 lines (114 loc) · 4.57 KB
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(!
Math6002: Deterministic OR Methods
Coursework XPress IVE Model
Name: Emma Tarmey
ID: 2940 4045
!)
model LPModel
uses "mmxprs";
declarations
! constants
C = 6
constituencies = 1..49
shires = 1..14
! data
b: array(shires) of real
y: array(constituencies) of real
M: array(shires, constituencies) of real
! variables
x: array(constituencies) of mpvar ! decision variable
end-declarations
! vector of size 14
b :: [1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1]
! vector of size 49
y :: [0, 1, 0,
0, 1, 0, 0, 1,
1, 1, 0, 1, 0,
0, 0, 1, 1, 0,
0, 1, 1, 1, 1,
0, 1, 0, 1,
1, 0, 1, 0, 1,
1, 1, 0, 0, 1,
0, 0, 0, 0, 1,
0, 0, 0, 1, 1,
1,
0]
! M is matrix of size (14 x 49)
! linebreaks inserted for formatting when included in report
M :: [0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1,
1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1,
1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0,
0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1,
0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]
! As a sanity check, we may check that all of the columns in M
! columns should sum to 1, 2, 3 or 4 as appropriate
writeln("\nSanity check of columns sums in M:")
forall (j in constituencies) do
if (j = 4 or j = 28 or j = 49)
then writeln("\n")
end-if
writeln("Con j = ", j, ", sum (of shires i) of M(i, j) = ",
sum (i in shires) (M(i, j)))
end-do
! objective function
total_representatives := sum(i in constituencies) ( x(i) * y(i) )
! constraints
! decision variable x is binary vector
forall (i in constituencies) x(i) is_binary
forall (i in shires) do
! check each shire appears exactly once
allocation(i) := sum (j in constituencies) (M(i, j) * x(j)) = 1
end-do
! map partition must contain C constituencies
sum (i in constituencies) x(i) = C
! run optimisation
maximise(total_representatives)
! output results
writeln("\nBegin running model\n")
writeln("Optimal number of representatives = ", getobjval, "\n")
writeln("Solution of Chosen Constituencies: ")
forall (i in constituencies) do
write ("\tcon = ", i)
write (", x = ", (getsol(x(i))))
write ("\n")
end-do
writeln("\nEnd running model")
end-model