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.


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

  2. 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.