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Transportation problem: Difference between revisions
→{{header|Julia}}
Line 2,495:
=={{header|Julia}}==
<lang julia>using
# cost vector
c = [3, 5, 7, 3, 2, 5];
N = size(c,1);
# constraints Ax (<,>,=) b
A = [1 1 1 0 0 0
0 0 0 1 1 1
1 0 0 1 0 0
0 1 0 0 1 0
0 0 1 0 0 1];
b = [ 25, 35, 20, 30, 10];▼
s = ['<', '<', '=', '=', '='];▼
# construct model
▲b = [ 25, 35, 20, 30, 10]
model = Model(Ipopt.Optimizer)
▲s = ['<', '<', '=', '=', '=']
@variable(model, x[i=1:N] >= 0, base_name="traded quantities")
cost_fn = @expression(model, c'*x) # cost function
@constraint(model, C1, A[1:2,:]*x .<= b[1:2]) # inequality constraints
@constraint(model, C2, A[3:5,:]*x .== b[3:5]) # equality constraints
@objective(model, Min, cost_fn) # objective function
# solve model
status = JuMP.optimize!(model);
xstar = value.(x);
println("solution vector of quantities = ", xstar)
println("minimum total cost = ", JuMP.objective_value(model))
# recover Lagrange multipliers for post-optimality
λ = [JuMP.dual(C1[1]),JuMP.dual(C1[2])]
μ = [JuMP.dual(C2[1]),JuMP.dual(C2[2]),JuMP.dual(C2[3])]
{{out}}
<pre>
=={{header|Kotlin}}==
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