Transportation problem: Difference between revisions

Code taken from [https://github.com/dylanomics/transportation_problem here] using [https://jump.dev/JuMP.jl/stable/ JuMP].

<lang julia>using JuMP, Ipopt

# cost vector

c = [3, 5, 7, 3, 2, 5];

N = size(c,1);

# constraints Ax (<,>,=) b

0 0 1 0 0 1];

b = [ 25, 35, 20, 30, 10];

s = ['<', '<', '=', '=', '='];

# construct model

model = Model(Ipopt.Optimizer)

@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])]

<pre>

solution vector of quantities = [20.000000008747048, 0.0, 4.9999996490783145, 0.0, 30.000000007494098, 5.0000003509216855]

minimum total cost = 179.99999927567436</pre>