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4

If, given inventory level ($q_{i,t}$) and bucket decisions ($z_{i,t,k}$), profit is maximized by maximizing the supplied quantities, you probably can drop the big M constraints and trust the objective to prevent selection of a supplied quantity less than the min of the two upper limits. As an experiment, you could try running without those constraints and ...


1

I think your constraint is equivalent to $$ \neg \left[\begin{pmatrix} A\\ C \end{pmatrix} x \leq \begin{pmatrix} b\\ d\end{pmatrix}\right] $$ because $$ \begin{align} &Cx \leq d \;\Longrightarrow\;\bigvee(a_i^Tx \geq b_i)\\ \Longleftrightarrow\;&\neg(Cx \leq d) \;\vee\;\neg(Ax\leq b)\\ \Longleftrightarrow\;&\neg(Ax\leq b \;\wedge Cx\leq d) \end{...


11

You can model the logical implication $$Cx < d \implies \bigvee_{i=1}^m \left(a_i^T x \ge b_i\right)$$ by introducing $m+1$ binary variables $y_i$, where $i\in\{0,\dots,m\}$, and linear constraints \begin{align} d - Cx &\le M_0 y_0 \tag1\\ \sum_{i=1}^m y_i &\ge y_0 \tag2 \\ b_i - a_i^T x &\le M_i (1-y_i) &&\text{for $i\in\{1,\dots,m\}$}...


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