Being new to Linear Programming and Gurobi, I am dealing with an Integer Linear program where I have two binary decision variables defined as B[u_v, x_y] and A[u_x], I am trying to implement this constraint in Gurobi via Python but I am stuck on how to translate the sum of the product of the two decision variables defined in this loop :

for each edge(u,v) in Set_of_edges:for each vertex x in Set_of_vertices:Sum_over(y) (B[u_v,x_y]) * A[u_x] == 1

From this book, it has to be linearized but I am not able to do it. Anyone could shed some light and provide me with some insights ?

Thanks

If you got two binary-variables x and y, you can add a new auxiliary binary variable z = x*y by these constraints:

• z <= x
• z <= y
• z >= x + y - 1

As i can't follow your task (incomplete pseudo-code) you will have to do the rest yourself, using the newly introduced variable z.