Benders tests

[guimarqu]

We consider the three following formulations:

A (optimal solution has only x non-zero)

using JuMP, GLPK
m = Model(GLPK.Optimizer)
@variable(m, x[1:2]>= 0)
@variable(m, y[1:2] >= 0)
@constraint(m, -x[1] + 4x[2] + 2y[1] + 3y[2] >= 2)
@constraint(m, x[1] + 3x[2] + y[1] + y[2] >= 3)
@objective(m, Min, x[1] + 4x[2] + 2y[1] + 3y[2])
optimize!(m)
objective_value(m)
value.(x)
value.(y)

B (optimal solution has both x, y non-zero)

 using JuMP, GLPK
 m = Model(GLPK.Optimizer)
 @variable(m, x[1:2] >= 0)
 @variable(m, y[1:2] >= 0)
 @constraint(m, -x[1] + x[2] + y[1] - 0.5y[2] >= 4)
 @constraint(m, 2x[1] + 1.5x[2] + y[1] + y[2] >= 5)
 @objective(m, Min, x[1] + 2x[2] + 1.5y[1] + y[2])
 optimize!(m)
 objective_value(m)
 value.(x)
 value.(y)

C (case with two subproblems)

# TODO

We have to test make sure that the Benders loop finds the optimal solutions for the following cases:

• [x] A with continuous first stage finds optimal solution
• [x] B with continuous first stage finds optimal solution
• [x] C with continuous first stage finds optimal solution
• [x] A with integer first stage finds optimal solution
• [x] B with integer first stage finds optimal solution
• [x] C with integer first stage finds optimal solution
• [x] add quite high lower bounds on y of formulation A -> check Benders finds optimal solution
• [x] change sense optimization (max), of objective function, and constraints of B -> check Benders finds optimal solution
• [x] add quite high upper bounds in y of the previous formulation -> check Benders finds optimal solution
• [ ] add a constraint in the master to make A infeasible -> check Benders returns infeasible
• [ ] add a constraint in the subproblem to make A infeasible -> check Benders returns infeasible
• [ ] create a formulation with unbounded master -> check Benders throws an error
• [ ] create a formulation with unbounded subproblem -> check Benders throws an error