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## Re: [Help-glpk] Size of big-M changes solution of MIP problem

**From**: |
Michael Hennebry |

**Subject**: |
Re: [Help-glpk] Size of big-M changes solution of MIP problem |

**Date**: |
Fri, 8 Apr 2011 09:36:58 -0500 (CDT) |

**User-agent**: |
Alpine 1.00 (DEB 882 2007-12-20) |

On Thu, 7 Apr 2011, Yaron Kretchmer wrote:

The problem is a stock hedging problem, with one of the component of a
correct hedge being that the strike price of the option is >= the value of
the stock.
The enclosde model should have no solution, since I'm fixing the variable
such that the price of the option is does not follow the constaint above.
When my big-M = 9099999, I get the correct "No primal feasible" answer. But
when I increase M to 9100000, a succesful solution is found, which is not
correct.

The issue is probably round off.
As a rule one should use the smallest big-M that is mathematically correct.
Small big-Ms give tighter linear constraints.

Are there any upper limits to the size of big-M that can be used?

--
Michael address@hidden
"Pessimist: The glass is half empty.
Optimist: The glass is half full.
Engineer: The glass is twice as big as it needs to be."