linear-programmingmixed-integer-programming

How to express Modulo operator constraint in linear programming

I want to state the modulo operation constraint in any open source optimisation modelling language.

How can we state the following constraint : y = x mod 3. Where x, y are integer variables.

Struggling to formulate the above.

Solution

  • y = x mod 3 can be modelled as follows:

    x = 3b + y
0 <= y <= 2
x, y, b are integers

    Since y can only take values : 0, 1 or 2, x can be determined by some unique values of b and y such that x = 3b + y

    b and y are respectively the quotient and remainder of x mod 3

    edited : per @reinderien comments