gams:formulate_logical_expressions_in_equations

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gams:formulate_logical_expressions_in_equations [2008/09/23 12:18] support |
gams:formulate_logical_expressions_in_equations [2009/03/05 17:18] support |
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====== How do I formulate logical expressions in equations? ====== | ====== How do I formulate logical expressions in equations? ====== | ||

- | GAMS does not reformulate logical expressions. You need to do this by hand. If you need help coming up with the right model you should try to read HP Willams Book on Modeling (http://www.amazon.com/Model-Building-Mathematical-Programming-4th/dp/0471997889). It explains how to use the ''bigM'' method to linearize logical constraints. | + | GAMS does not reformulate logical expressions. You need to do this by hand. If you need help coming up with the right model you should try to read HP Williams Book on Modeling (http://www.amazon.com/Model-Building-Mathematical-Programming-4th/dp/0471997889). It explains how to use the ''bigM'' method to linearize logical constraints. |

For example, if you have a logical expression ''i=1 <=> a > b'' then you can reformulate this as | For example, if you have a logical expression ''i=1 <=> a > b'' then you can reformulate this as | ||

- | ''a %%<=%% b + bigM*i'' | + | ''a %%<=%% b + bigM * i'' |

- | ''a > b - bigM*(1-i)'' | + | ''a > b - bigM * (1-i)'' |

Try to evaluate: If ''i=1'' then the first constraint will not be effective if ''bigM'' is big enough while the second equation will read ''a>b''. If ''i=0'', the first constraint ensures ''a<=b'' while the second will | Try to evaluate: If ''i=1'' then the first constraint will not be effective if ''bigM'' is big enough while the second equation will read ''a>b''. If ''i=0'', the first constraint ensures ''a<=b'' while the second will |

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