Hello
I would like to use a GLPK linear programming model in Ruby using the Rglpk
wrapper.
Unfortunately, I do not get the same solution when comparing the glpk and Rglpk
outputs. Despite I am setting the column kind to Binary (cols.kind =
Rglpk::GLP_BV), the solution shows integer values instead of boolean.
I want to model the following linear programming capital budgeting problem:
Maximize NPV of projects (x1…x5) by taking into account Budget and Resource
constraints (c1, c2). Solution can only be 0 or 1
Maximize: 928 x1 + 908 x2 + 801 x3 + 543 x4 + 944 x5
Constraints:
c1: 398 x1 + 151 x2 + 129 x3 + 275 x4 + 291 x5 <= 800
c2: 111 x1 + 139 x2 + 56 x3 + 54 x4 + 123 x5 <= 200
Result is binary (0 or 1): x1 x2 x3 x4 x5
The model is rather simple, but somehow I am missing something in the ruby
code.
Do you have any hint what could be wrong?
Many thanks in advance and best regards,
Lukas
Please find below my code (1) ruby using Rglpk module, 2) GLPK in mathprog)
1) Ruby with Rglpk (returns WRONG solution):
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require 'rglpk'
p = Rglpk::Problem.new
p.name = "Project selection"
p.obj.dir = Rglpk::GLP_MAX
rows = p.add_rows(2)
rows[0].name = "p"
rows[0].set_bounds(Rglpk::GLP_UP, 0, 800)
rows[1].name = "q"
rows[1].set_bounds(Rglpk::GLP_UP, 0, 200)
cols = p.add_cols(5)
cols[0].name = "x1"
cols[0].kind = Rglpk::GLP_BV
cols[0].set_bounds(Rglpk::GLP_BV, 0, 1)
cols[1].name = "x2"
cols[1].kind = Rglpk::GLP_BV
cols[1].set_bounds(Rglpk::GLP_BV, 0, 1)
cols[2].name = "x3"
cols[2].kind = Rglpk::GLP_BV
cols[2].set_bounds(Rglpk::GLP_BV, 0, 1)
cols[3].name = "x4"
cols[3].kind = Rglpk::GLP_BV
cols[3].set_bounds(Rglpk::GLP_BV, 0, 1)
cols[4].name = "x5"
cols[4].kind = Rglpk::GLP_BV
cols[4].set_bounds(Rglpk::GLP_BV, 0, 1)
p.obj.coefs = [928, 908, 801, 543, 944]
p.set_matrix([
398, 151, 129, 275, 291,
111, 139, 56, 54, 123
])
p.simplex
z = p.obj.get
x1 = cols[0].get_prim
x2 = cols[1].get_prim
x3 = cols[2].get_prim
x4 = cols[3].get_prim
x5 = cols[4].get_prim
printf("z = %g; x1 = %g; x2 = %g; x3 = %g; x4 = %g; x5 = %g\n", z, x1, x2, x3,
x4, x5)
————————————————————————————
2) glpk in mathprog format (returns CORRECT solution):
————————————————————————————
set PROJECT;
param Budget {i in PROJECT};
param Resources {i in PROJECT};
param NPV {i in PROJECT};
var x {i in PROJECT} >=0, binary;
maximize z: sum{i in PROJECT} NPV[i]*x[i];
s.t. Bud : sum{i in PROJECT} Budget[i]*x[i] <= 800;
s.t. Res : sum{i in PROJECT} Resources[i]*x[i] <= 200;
data;
set PROJECT := p1 p2 p3 p4 p5;
param Budget:=
p1 398
p2 151
p3 129
p4 275
p5 291;
param Resources:=
p1 111
p2 139
p3 56
p4 54
p5 123;
param NPV:=
p1 928
p2 908
p3 801
p4 543
p5 944;
end;
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