I have a model with the following condition:
z[i] = min{t*x[i][t] | x[i][t] = 1},
x[i][t] - boolean,
z[i] - integer
Which means I am trying to find a minimum positive value over a set of integer expressions. The "min" condition can be easily converted into a set of linear conditions if only we weren't looking for a positive value but a boolean (0 or 1) one.
Here the situation is a bit more complicated. Let's say that
t*x[i][t]
can have the following values:
0,3,4,5
I am looking for a way to get the value 3 (minimum positive one) and assign it to another variable (z[i])
Is there a way to convert the condition into a set of linear ones so that my model is not a non-linear programming model?