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2

I think this can be approached using a constraint generation technique (variant of Benders decomposition), although I have no idea if it would efficient. By reordering the rows of $A$, we can assume that $$b(z)=\left[\begin{array}{c} \hat{b}\\ c+e-z \end{array}\right]$$where $\hat{b}\in\mathbb{R}^{d-m}$, $c\in \mathbb{R}^m$, $e=(1,\dots,1)^\prime \in \mathbb{...


4

By Farkas lemma, infeasibility of $Ax\leq b$ is equivalent to feasibility of $A^Ty = 0, y^Tb < 0, y\geq 0$, or more practically useful $A^Ty=0, y^Tb \leq -1, y\geq 0$. Unfortunately, this will lead to a bilinear model when you parameterize $b(z)$. It is fairly similar to an application I worked on a decade ago Oops! I cannot do it again: Testing for ...


6

You need to introduce a binary variable for buying, $b$, and one for selling, $s$. Make sure $b$ and $s$ are active when $varBuyWater$ and $varSellWater$ are positive, respectively: $$ varBuyWater \le M_1 b \\ varSellWater \le M_2 s \\ $$ $M_1$ and $M_2$ are upper bounds on variables $varBuyWater$ and $varSellWater$. And impose that both binaries cannot ...


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