Dear staff,

I would like to receive your help with linearizing the following constraint.

Given the indexes i, j, c, a

I have the following variables and parameters:

x (i,j,a) continuous variable

y (i,j,a) continuous variable

R (i,j,c,a) binary variable

A (i,j) parameter

B (c) parameter

The constraint that I need to write is the following:

y(i,j,a) = (x(i,j,a) / A(i,j)) * (1 - sum((c,a1)|ord(a1) <= ord(a), R(i,j,c,a1))) + sum((c,a1)|ord(a1) <= ord(a), (x(i,j,a) / B(c)) * R(i,j,c,a1)) forall i, j, a

I am struggling in particular with the linearization of the second part:

sum((c,a1)|ord(a1) <= ord(a), (x(i,j,a) / B(c)) * R(i,j,c,a1))

Please note that there are already other constraints imposing that sum((c,a), R(i,j,c,a)) <= 1 forall i, j, therefore the summation of sum((c,a1)|ord(a1) <= ord(a), R(i,j,c,a1)) is always either 0 or 1.

Thank you,

Kind regards,