Finding an Irreducible Infeasible Set (lpsole04)

/***************************************************************/
/*                                                             */
/*            S A S   S A M P L E   L I B R A R Y              */
/*                                                             */
/*    NAME: lpsole04                                           */
/*   TITLE: Finding an Irreducible Infeasible Set (lpsole04)   */
/* PRODUCT: OR                                                 */
/*  SYSTEM: ALL                                                */
/*    KEYS: OR                                                 */
/*   PROCS: OPTMODEL                                           */
/*    DATA:                                                    */
/*                                                             */
/* SUPPORT:                             UPDATE:                */
/*     REF:                                                    */
/*    MISC: Example 4 from the Linear Programming Solver       */
/*          chapter of Mathematical Programming.               */
/*                                                             */
/***************************************************************/


proc optmodel presolver=none;
   /* declare variables */
   var x{1..3} >=0;

   /* upper bound on variable x[3] */
   x[3].ub = 3;

   /* objective function */
   min obj = x[1] + x[2] + x[3];

   /* constraints */
   con c1: x[1] + x[2] >= 10;
   con c2: x[1] + x[3] <= 4;
   con c3: 4 <= x[2] + x[3] <= 5;

   solve with lp / iis=true;

   print x.status;
   print c1.status c2.status c3.status;

   expand / IIS;

   /* relax upper bound on constraint c3 */
   c3.ub = constant('BIG');

   solve with lp / iis=true;

quit;