$ontext

  These are some tough small MIP models.

  They are the final MIP of some cutting stock problems solved with a
  column generation approach



$offtext


sets
    p 'patterns'
    i 'item'
;

parameters
    d(i) 'demand'
    waste(p)
    aip(i,p) 'matrix'
;

$gdxin finalmipdata1.gdx
$load p i
$loaddc d waste aip

integer variables xp(p);
variable z;

xp.up(p) = sum(i, d(i));


equations
   master_waste
   master_demand(i)
;

master_waste..      z =e= sum(p,waste(p)*xp(p));
master_demand(i)..  sum(p, aip(i,p)*xp(p)) =e= d(i);
model master /master_waste,master_demand/;


option optcr=0;
solve master using mip minimizing z;