I'm trying to solve the CVRP with based on flow-formulaton. In such model, we have a decision variable with two-index, $x_ij$, where I'm using the MTZ forumlas to eleminate sub-tours. We have then a continuous variable that represent the flow of the vehicle after visiting a customer. Let's say $y_i$. In the case of delivery, the constraints that I formulate is:
$y_j <= y_i + d_i - Q*(1-x_{ij})$ where $ 0<=y_i <= Q - d_i$
For this example with 5 customers : $\{1:19;2:30;3:16;4:23;5:11\}$ and $Q=35$
The solution I got is: $x : {(0,3);(3,1);(1,0);(0,2);(2,0);(0,4);(4,5);(5,0)}$ for the other variables $x$ is null and for $y$ $\{1:0;2:0;3:16;4:12;5:0\}$. I exepected 11 for $y_4 = 35 - 23 = 12$ and $y_5 = 12 - 11 = 1$
Something wrong that I can not identify it.
Thank you for your help