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I have two variables that are continuous: $$\gamma^n \geq 0\\ z_{ij}^n \geq 0$$ and one binary variable: $$y_{jk} = \{0,1\}$$

How can I linearize an equation that involves two kinds of variable products, specifically this? $$\sum_i z_{ij}^n(a_{jk} \varepsilon_{i}^n + b_{jk}) y_{jk} \leq \sum_i z_{ij}^nc_j + M(\gamma^n - 1)\sum_i z_{ij} ~~~ \forall j,k,n$$

$a_{jk}, \varepsilon_i^n, b_{jk}, c_j$ and $M$ are all constants.

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You're effectively asking if $\gamma z \geq k$ can be linearized. The answer is no. You can only linearize binary multiplied with continuous.

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  • $\begingroup$ Hmm, alright. After some searching I was thinking of using McCormick envelopes, but I also realised that I did not need to have $z_{ij}^n$ in that part of the constraint due to the inpretation of $\gamma^n$. So I managed to avoid the nonlinearity. In any case, thank you for your response! $\endgroup$ Commented Mar 9, 2017 at 22:37

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