IP tutorial

# IP tutorial - Tutorial Supplement IP Modeling Tricks Note...

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- 1 - Tutorial Supplement: IP Modeling Tricks Note: If you introduce any decision variables (integer/continuous), please define them properly; do not leave up to the reader to interpret the correct definition of decision variables. There can be multiple ways of modeling a restriction/logic in IP. But there exists only one truth table that corresponds to a particular restriction/logic condition. Words such as “must”, “can”, “could”, “should” etc. defines the logical conditions, so be careful in interpreting them. Logical Conditions and Zero-One Variable: In Boolean algebra: “v” means “or” (this is inclusive, i.e. A or B or both) “.”means “and” “~”means “not” ± means “implies” (if …. . then) ² means “if and only if” Let X 1 = 1 if statement 1 is true; 0 otherwise. Let X 2 = 1 if statement 2 is true; 0 otherwise. Logic Equivalent to Comments 1 X A v X B X A +X B 1 X A | X B 1|0 0|1 1|1 2 X A .X B X A =1 and X B =1 X A | X B 1|1 3 ~X A X A =0 or 1-X A =1 X A =0 4 X A ± X B X B X A or X B - X A 0 X A | X B 1|1 0|0 or 1 5 X A ± ~X B X B 1-X A X A | X B 1|0 0|0 or 1 6 X A ² X B X A – X B = 0 X A | X B 1|1 0|0 7 Either X A or X B (but not both) is true. (They are mutually exclusive) X A + X B = 1 X A | X B 1|0 0|1

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- 2 - Q.No. 1: Formulate the following restriction to fit an IP model: “ If product A is produced, and B is produced, then product C must be produced” (or “ If statement A is true, and statement B is true, then statement C must be true.”
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IP tutorial - Tutorial Supplement IP Modeling Tricks Note...

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