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gams:how_large_should_big_m_be [2007/08/10 11:06] (current)
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 +====== How large should BIG M be? ======
 +
 +//How big should the constant M be in the equation, where Y(J) are binary variables: //
 +   
 +   ​YBIN(J).. SUM(I,​X(I,​J)) =L= M*Y(J);
 +
 +// I said in my model: //
 +
 +   ​SCALAR M /​10000000000/ ​
 +
 +// but that causes problems. //
 +
 +In general the answer should be as small as possible. Your model
 +with the M of 1.0E10 could not be solved by any of the MIP solvers
 +we tried out. It causes enormous scaling problems. However further
 +on in your model you have 
 +
 +     ​CAP(J).. SUM(I,​X(I,​J)) =L= MAXCAP;
 +
 +We can combine these two equations in one: 
 +
 +     ​YBIN(J).. SUM(I,​X(I,​J)) =L= MAXCAP*Y(J);​
 +
 +Which both sets M to the smallest possible value and reduces the
 +number of constraints. ​
 +
 +We have seen MIP models fail miserably when using a real big M.
  
IMPRESSUM / LEGAL NOTICEPRIVACY POLICY gams/how_large_should_big_m_be.txt ยท Last modified: 2007/08/10 11:06 (external edit)