In MIP, what's the difference of solving time between the following two formulations?
- $x_i = 0$ for $i\in I$, and
- $\sum_{i\in I} x_i = 0$.
Suppose that $x_i, \forall i\in I$ are all binary variables.
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$\begingroup$ Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. $\endgroup$– Community BotCommented Jul 28, 2022 at 22:00
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A basic presolver will immediately remove such fixed variables and the corresponding constraints in either case, so the presolved model that the actual solver sees will be identical. But there is some overhead in both presolving and postsolving, so either option is a bit wasteful in terms of time and memory. An even better third option is to omit these variables from your formulation altogether (omit these indices from the index set for $x$).
