gams:how_large_should_big_m_be

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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. | ||

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gams/how_large_should_big_m_be.txt ยท Last modified: 2007/08/10 11:06 (external edit)