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## Re: [Help-glpk] Modelling constaints

 From: Michael Hennebry Subject: Re: [Help-glpk] Modelling constaints Date: Mon, 30 Mar 2015 15:36:58 -0500 (CDT) User-agent: Alpine 1.00 (DEB 882 2007-12-20)

```On Thu, 26 Mar 2015, john tass wrote:

```
```Let U, K in {-6, .. , 6} integers
Let A in {0, 1} binary
Let D in {0, 1} binary
What I want to do  is to model the condition:
D = 1, iff (U > 0 OR K > 0) AND A = 1
Otherwise, D should equal 0.
I can not figure out how to model this situation.
Can any one give me an answear or even a hint? It would be very welcome.
```
```
I'd suggest two binaries to flag U>=1 and K>=1 .
Call them Qu and Qk respectively.

u want Qu = 1 -> U>=1
U >= 1 - (1-Qu)*M
making M big enough will ensure that U can be in -6..0 when Qu=0
-6 >= 1 - (1-0)*M
M=7 will work
U - 7*Qu >= -6

You want Qu = 0 -> -U>=0 .
The same kind of math gives
-U + 6*Qu >= 0

Likewise for Qk:
U - 7*Qk >= -6
-U +6*Qk >=  0

Another way to get those constraints is to graph the valid values.
The extreme points for (Qu, U) are:
(0, -6) (0, 0) (1, 1) (1, 6)

Now you just need constraints on the binaries A, D, Qu and Qk.
Doing it crudely, you could use 8 constraints
to cut off each of 8 invalid combinations.
Actually, you only need 4 constraints.
http://en.wikipedia.org/wiki/Karnaugh_map
You will be more interested in zeros than in ones.

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