Re: [Help-glpk] More conditional variables fun

[Andrew Makhorin]

> Now I #39;d like to be able to model conditional non-binary
> variables. Does anybody know how to formulate this in mathprog?

> ----------Begin Description -------------------
> *) a,b are binary
> *) c,d,e is continuous.
> *) I #39;d like c to be 
>     - 0 if a=b=0
>     - d if a=0,b=1
>     - e if a=1,b=0
>     - 0 if a=b=1
> ----------End Description

"Conditional" equality constraint:

   t = if z then a else b

where z is binary, t, a, b are continuous, can be modeled as
follows:

   z = 1:    0 <= t - a <= 0
           -M1 <= t - b <= +M2

   z = 0:  -M3 <= t - a <= +M4
             0 <= t - b <= 0

Thus:

   -M3 * (1 - z) <= t - a <= +M4 * (1 - z)
   -M1 * z       <= t - b <= +M2 * z

where M1, M2, M3, M4 are appropriate "big M's".