I'm trying to implement a Benders decomposition on MILP. But I cannot understand a notation in the sub-problem constraints. What does ":" mean in the following sub-problem? The implementation works except for the dual variable which I don't know where should I put it. $$ minimize \quad \mathcal z_{s_1}=-\frac{3}{2}y_1-2y_2+40w\\ -y_1-3y_2+2x-w\le2\\ y_1+3y_2-x-w\le3\\ x= 100 :\lambda_1\\ y_1,y_2\ge 0\\ y_1,y_2 \in R $$ I used pulp to implement it but the ":" in constraint $x= 100 :\lambda_1$ confused me.
It is the computational example 6.2 in Decomposition technique book by Antonio J. Conejo on page 246.
Thank you.