Conditional contraints in linear programming for non boolean variables

Question

Question 1 : x , y are integer non negative variables

i have a condition - if x > 0 then y=0

Question 2 : a , b , c , d , e are integer non negative variables if any one of above > 0 then other 4 will be zero.

How to formulate above constraint as linear equations.I know how to handle above for Boolean variables but could not do for integer variable. I tried searching in other forums and WEB but could not get the solution.

TimChippingtonDerrick · Accepted Answer · 2016-08-21 10:20:28Z

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As a starting point try creating some additional boolean variables, one for each of your non boolean variables. Then you can use a typical 'big m' modelling for each. Once you have something that works you can try reworking it to get a better model.

answered Aug 21, 2016 at 10:20

TimChippingtonDerrick

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Thanks for reply , could you please give an example with equations.
– Mohammad Shariq
Commented Aug 21, 2016 at 11:47
@MohammadShariq Just google indicator-variables in MIP or read AIMMS Modeling Guide - Integer Programming Tricks (e.g. chapter 7.4)
– sascha
Commented Aug 21, 2016 at 12:24

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Michał Urbaniak · Accepted Answer · 2016-09-15 08:29:14Z

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You can use logical implication in CPLEX (if-then). Please check out the following page: Logical constraints for CPLEX

answered Sep 15, 2016 at 8:29

Michał Urbaniak

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