Any good practice for using bigM?

Answered

永宁 赵

• November 17, 2020 11:36

Hi,

I am using many big-Ms in my model, which makes my coefficient statistics very bad. I think that is the main reason for the very slow solving of my optimisation.

Matrix range [2e-02, 4e+06]
Objective range [1e+00, 2e+02]
Bounds range [1e+00, 1e+04]
RHS range [1e+00, 4e+06]

Is there any method to avoid using bigMs, or if I have to, how can I avoid numerical issues caused by bigM?

Thanks.

0

• 

  Richard Oberdieck

  Gurobi Staff

  • November 17, 2020 12:27

  Hi Yongning,

  in general, I can recommend to you this blog post by Paul Rubin on the subject, it covers a lot of important aspects.

  Beyond that, you could try to "calculate" your tightest big-M for a given model. So suppose you use a big-M formulation

  such as this:

  ```

  t <= y*M

  ```

   

  Then, you could find out what the largest value is that `t` can attain. You can do this by solving the model with the objective function:

   

  ```

  max. t

  ```

   

  This will then return to you the biggest value that the variable t can have, and consequently the smallest value that M can have. This of course only works for this particular model; if your data changes, this value may change. However, it can (a) give you an indication on how "good" your big-M value is and (b) inspire you to find ways to tighten the formulation.

   

  Hope this helps.

  Best

  Richard

   

   

  0
• 

  永宁 赵

  • November 17, 2020 12:50

  

  

  

  Many thanks, Richard. That's quite informative and useful.

  0

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