conditional constraint in optimization

Question

Does anybody know how to write conditional constraint in mixed integer programming for this case:

if a == 0 then b = 1
else b = 0
-M <= a <= M
b={0,1}

Note that M can be any continuous number. Thanks.

Regards,

Erwin Kalvelagen · Accepted Answer · 2016-06-12 01:44:15Z

2

I would approach this as follows. First use a variable splitting approach by introducing two non-negative variables aplus, amin:

0 <= aplus <= d*M
0 <= amin <= (1-d)*M
a = aplus-amin
d in {0,1}

Now we can do:

0.001*(1-b) <= aplus + amin <= M*(1-b)

In many cases we can simplify this but that requires knowledge of the rest of the model.

answered Jun 12, 2016 at 1:44

Erwin Kalvelagen

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2 Comments

It worked! Just a small correction for the last equation: 0.001*(1-b) <= aplus + amin <= M*(1-b) should be 0.001*(1-b) <= aplus + amin <= M*b

I think my version is correct. If b=1 then 0<=aplus+amin<=0 ==> aplus+amin=0. If b=0 then 0.01 <= aplus+amin <= M.