Tuesday, March 3, 2009

big-M and log-normal

The terms big-M (in MIP modeling) and log-normal (the statistical distribution) are examples of concepts where the name has unintended, misleading connotations.

In MIP models a big-M constant should really be chosen as small as possible (for an example see here). I have seen many models where innocent students write something like M=10000000000 causing all kind of problems. Of course if this constant would have been called small-m, we probably would not have seen this as often.

The log-normal distribution is not formed by taking the logarithm of a normally distributed random variable (e.g. this posting). I suspect a better name like exp-normal distribution would have prevented this misconception.
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2 comments:

  1. AnonymousMarch 4, 2009 at 11:41 AM

    bigM should be selected as the lowerbound of relaxing the constraints...........
    could anyone tell me why larger bigM cause problems especially in GAMS

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  2. Erwin KalvelagenMarch 4, 2009 at 6:40 PM

    This is not related to GAMS at all, but to how MIP solvers work. See e.g. "Cutting Big M down to Size" by Jeffrey D. Camm, Amitabh S. Raturi and Shigeru Tsubakitani, Interfaces, Vol. 20, No. 5 (Sep. - Oct., 1990), pp. 61-66.

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