[GAMSlinks] solving parametric Integer programming using GAMS

[Stefan Vigerske]

Hi,

this list is about interfaces from GAMS to solvers.
Questions regarding the GAMS modeling language should be directed to the 
GAMS support (support at gams.com).
Probably you'll need to implement your "single branch and bound" in GAMS 
  with an IP solver as subsolver.

Best,
Stefan

atanu chaudhuri wrote:
> Hi,
>     I am trying to solve the following parametric Integer programming problem. 
> 
> max 2x 1 + 5x 2
> s.t. 2x 1-x 2< 9 + 3(1-a),
> 2x 1 + 8x 2_< 31 + 4(1-a),
> Xl, X 2 >= 0,
> X 1, X 2 ~ [0,1]
> 0<a_<l.
> 
> I want the values of x1 and x2 for different ranges of 'a'. that is why it is a parametric IP
> 
> The solution of that problem, as mentioned in a paper by Herrera and Verdegay in a paper in EJOR is as follows:
> 
> x(a) = (5,3), z(a) = 25 Va ~ (0, 0.25],
> x(a) = (4,3), z(a) = 23 Va ~ (0.25, 0.75],
> x(a) = (3,3), z(a) = 21 Va ~ (0.75, 1],
> 
> As it is a parametric IP, i cannot get the solution starting from 0 and moving upwards to 1 as in LP. A single branch and bound should be able to generate this result.
> Let me know how I can generate this result using GAMS .
> 
> Regards
> 
> Atanu Chaudhuri
> 
> 
> 
> 
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-- 
Stefan Vigerske
Humboldt University Berlin, Numerical Mathematics
http://www.math.hu-berlin.de/~stefan