Balance equation

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A constraint of the form $LaTeX: I(x) - O(x) = 0$, where $LaTeX: I(x)$ is the input and $LaTeX: O(x)$ is the output, each as a function of the decision variables, $LaTeX: x$. Typically this is linear, conserving flows, measured in units of volume or mass. In an ordinary network in which there are no gains or losses, this appears as:

$LaTeX: I(x) - O(x) = \sum_{i} x_{i,j} - \sum_{k} x_{j,k} = 0.$