There is a decision variable \(x \ge 0\) and a given parameter \(\text{MIN}\). The quantity \(mk\) is calculated as \(mk = \text{MIN} - x\). I want to distinguish cases as far as the sign of \(mk\) is concerned. I have defined a binary decision variable that is \(1\) when \(mk \ge 0\) and \(0\) otherwise. I have the following constraint \(y \le \text{A} + b \cdot mk\). \(\text{A}\) is a parameter/constant. How can I linearize it? Thanks in advance, Standrul |

Assuming you have an upper bound \(U\) on \(x\): \(y \le A+mk-(1-b) \times (MIN-U)\) and \(y \le A+b \times MIN\)
answered
Paul Rubin ♦♦ fbahr ♦ |

From AIMMS' Modeling Guide, chapter on "Integer Programming Tricks": > 7.3 Either-or constraints and 7.4 Conditional constraints.
answered
fbahr ♦ |

Is b a decision variable? How does it fit with the rest?

Sorry! Yes b is the binary decision var I defined that is 1 when mk>=0 and 0 otherwise.