306_Logical_constraints

# 306_Logical_constraints - B and C happen If A happens then...

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Modeling Logical Conditions with Binary Variables A, B, C are binary variables indicating if events A, B, C happen. Part I: Basic (two events A and B) A and B do not happen at the same time ( A and B are mutually exclusive): If A happens, then B happens ( A is conditional on B ): If A happens, then B does not happen: (same as A + B < 1) A happens if and only if B happens ( A is a co-requisite for B ): A = B A happens if and only if B does not happen: (same as A+B=1) At most one of A and B happens: At least one of A and B happens ( A or B happens): Extended: (more-than-two events A, B and C) If A or B happens, then C happens: , If A or B happens, then C does not happen: , (or A + C < 1, B + C < 1) If A happens, then both

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Unformatted text preview: B and C happen: , If A happens, then B or C happens: If A does not happen, then both B and C happen: , If A does not happen, then B or C happens: If A does not happen, then neither B nor C happens: 1 , (same as , ) Part II: The key ingredients of logic modeling Five Golden Rules 1. If A then B or C 2. If A then B and C Rewrite as: (If A then B) and (If A then C) , 3. If A or B then C Rewrite as: (If A then C) and (If B then C) , 4. If A and B then C 5. “A does not happen” or “not A” is modeled using 1 – A . * Read page 84-86 in our textbook and learn how to model logical constraints. 2...
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