Good morning,

I’m working on a MILP model where a non-linear function is linearized using PiecewiseLinearOpt and Gurobi.

The model is solved and the objective value reached is correct, but the constraints are not met.

For example:

constraint Demand[1]: g_gen[1] + g_gen_h[1] = 351

but the solution is g_gen_h[1] = 0 ; g_gen[1] = 101

JuMP.value(g_gen_h[1]) is not getting the correct value.

The code is available on https://github.com/salvaguerrero/NonConvexPLF_code/blob/master/hydro.jl

```
model = Model()
set_optimizer(model, Gurobi.Optimizer)
@variable(model, g_gen[t in Time] >= 0)
@variable(model, g_gen_h[t in Time] >= 0)
@variable(model, w_tur[t in Time] >= 0)
@variable(model, w_lev[t in 0:T_num]>= 0)
@variable(model, w_spi[t in Time] >= 0)
@objective(model, Min, sum(g_gen[t]*Opex for t in Time) )
@constraint(model,Demand[t in Time], g_gen_h[t] + g_gen[t] == dem[t] )
@constraint(model, [t in Time], L_lim <= g_gen[t] <= U_lim)
@constraint(model, [t in Time], L_lim <= g_gen_h[t] <= U_lim)
@constraint(model, Reservoir[t in Time], w_lev[t] == w_lev[t-1] + w_apo -(w_tur[t] + w_spi[t]) )
@constraint(model, w_lev[0] == w_lev_0 )
@constraint(model, w_lev[T_num] == w_lev_f )
p(q,v) = 9.81*q*v#/a/b*eff
q_range = w_tur_m:1:w_tur_M #0:128
v_range = w_lev_m:1:w_lev_M #0:128
for t in Time
g_gen_h[t] = piecewiselinear(model, w_tur[t] , w_lev[t], v_range, q_range, p)
end
optimize!(model)
```

Thank you in advance, Salvador