Answers to: How to linearize this expression?http://www.or-exchange.com/questions/13343/how-to-linearize-this-expression<p>Hi,</p>
<p>I wonder how I can linearize the following expression:</p>
<p>$$z = \sum_{i=1}^{n} \max_{j=1,...,n} (y_{ij})$$</p>
<p>Thanks in advance.</p>enFri, 12 Feb 2016 13:48:39 -0500Answer by monashhttp://www.or-exchange.com/questions/13343/how-to-linearize-this-expression/13360<p>I found the best possible strategy is to impose these constraints sets:</p>
<p>$$x_i \geq \frac 1n \sum_{j=1}^{n} y_{ij}, \quad \forall i = 1,...,n$$</p>
<p>$$x_i \leq \sum_{j=1}^{n} y_{ij}, \quad \forall i = 1,...,n$$</p>
<p>and then:</p>
<p>$$z = \sum_{i=1}^{n} x_i$$</p>monashFri, 12 Feb 2016 13:48:39 -0500http://www.or-exchange.com/questions/13343/how-to-linearize-this-expression/13360Answer by Rob Pratthttp://www.or-exchange.com/questions/13343/how-to-linearize-this-expression/13347<p>Hint: introduce a new variable \(x_j\) to represent the summand, linearize that in the usual way, and take \(z = \sum_{j=1}^n x_j\).</p>Rob PrattThu, 11 Feb 2016 13:33:36 -0500http://www.or-exchange.com/questions/13343/how-to-linearize-this-expression/13347