Linearization of IFF between a binary and an integer

Question

I'm trying to find the mathematical linearization of this constraint:

p = 0 if and only if s = 0

Where p is binary and s is an integer >= 0 (thus it cannot be treated as a binary!!!)

Thanks in advance to anyone willing to help.

Erwin Kalvelagen · Accepted Answer · 2021-08-27 04:08:05Z

1

The constraint:

  p = 0 if and only if s = 0
  p binary, s non-negative integer

is sometimes written as:

 p = 0 <=> s = 0

This can be restated as the set of implications:

  p = 0 => s = 0
  p = 1 => s >= 1

If your solver has support for indicator constraints this can be implemented as is. If not, we can write:

 p <= s <= U⋅p
 s ∈ {0,1,2,..,U}
 p ∈ {0,1}

Here U is an upper bound on s. Note that most likely, you will need to write this as two separate inequalities.

answered Aug 26, 2021 at 15:56

Erwin Kalvelagen

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1 Comment

Thanks Erwin!!! Where would I be without your help!