Description
Small Model of Type : LP
Main file : lp06.gms
$title Test iteration interrupts and optimal restarts (LP06,SEQ=71)

  Sets
       i   canning plants   / seattle, austin, san-diego /
       j   markets          / new-york, madison, chicago, topeka /

  Parameters

       a(i)  capacity of plant i in cases
         /    seattle     350
              austin      200
              san-diego   600  /

       b(j)  demand at market j in cases
         /    new-york    325
              madison     150
              chicago     300
              topeka      275  / ;

  Table c(i,j)  distance in thousands of miles
                    new-york  madison     chicago      topeka
      seattle          2.5      .05         1.7          1.8
      austin           2.3     1.2          1.0           .5
      san-diego        3.5     3.9          2.8          1.4  ;

  Variables
       x(i,j)  shipment quantities in cases
       z       total transportation costs in thousands of dollars ;

  Positive Variable x ;

  Equations
       cost        define objective function
       supply(i)   observe supply limit at plant i
       demand(j)   satisfy demand at market j;

  cost ..        z  =e=  sum((i,j), c(i,j)*x(i,j));

  supply(i) ..   sum(j, x(i,j))  =l=  a(i) ;

  demand(j) ..   sum(i, x(i,j))  =g=  b(j) ;

  Model lp06 /all/ ;


parameters x_l(i,j)
           x_m(i,j)
           z_l
           z_m
           cost_l
           cost_m
           supply_l(i)
           supply_m(i)
           demand_l(j)
           demand_m(j) ;

scalar tol /1e-6 /;

option limcol=0,limrow=0,solprint=on;

****  1. Solve the model to optimality and save the results

Solve lp06 using lp minimizing z ;
abort$( lp06.solvestat <> %solveStat.normalCompletion% or lp06.modelstat <> %modelStat.optimal%) 'wrong status codes';
abort$( lp06.numnopt  <> 0 ) 'bad numopt';
abort$( lp06.numinfes <> 0 ) 'bad infes';

x_l(i,j)    = x.l(i,j)    ;
x_m(i,j)    = x.m(i,j)    ;
z_l         = z.l         ;
z_m         = z.m         ;
cost_l      = cost.l      ;
cost_m      = cost.m      ;
supply_l(i) = supply.l(i) ;
supply_m(i) = supply.m(i) ;
demand_l(j) = demand.l(j) ;
demand_m(j) = demand.m(j) ;

*****  2. Restart from scratch but interrupt at the iteration used in the first run.

lp06.iterlim = lp06.iterusd+1;
option clear=x,clear=z,clear=cost,clear=supply,clear=demand;
Solve lp06 using lp minimizing z ;
abort$( lp06.solvestat <> %solveStat.normalCompletion% or lp06.modelstat <> %modelStat.optimal%) 'wrong status codes';
abort$( lp06.numnopt  <> 0 ) 'bad numopt';
abort$( lp06.numinfes <> 0 ) 'bad infes';
abort$( lp06.iterusd+1 <> lp06.iterlim ) 'bad iterations';
abort$( abs(z.l-z_l) > tol ) 'bad z.l';
abort$( abs(z.m-z_m) > tol ) 'bad z.m';
abort$( smax((i,j), abs(x.l(i,j)-x_l(i,j)))   > tol ) 'bad x.l';
abort$( smax((i,j), abs(x.m(i,j)-x_m(i,j)))   > tol ) 'bad x.m';
abort$( smax(i, abs(supply.l(i)-supply_l(i))) > tol ) 'bad supply.l';
abort$( smax(i, abs(supply.m(i)-supply_m(i))) > tol ) 'bad supply.m';
abort$( smax(j, abs(demand.l(j)-demand_l(j))) > tol ) 'bad demand.l';
abort$( smax(j, abs(demand.m(j)-demand_m(j))) > tol ) 'bad demand.m';
abort$( abs(cost.l-cost_l) > tol ) 'bad cost.l';
abort$( abs(cost.m-cost_m) > tol ) 'nad cost.m';

****  3. Restart from the optimal solution and use zero iteration limit.

lp06.iterlim = 1;
Solve lp06 using lp minimizing z ;
abort$( lp06.solvestat <> %solveStat.normalCompletion% or lp06.modelstat <> %modelStat.optimal%) 'wrong status codes';
abort$( lp06.numnopt  <> 0 ) 'bad numopt';
abort$( lp06.numinfes <> 0 ) 'bad infes';
abort$( lp06.iterusd <> 0 ) 'bad iterations';
abort$( abs(z.l-z_l) > tol ) 'bad z.l';
abort$( abs(z.m-z_m) > tol ) 'bad z.m';
abort$( smax((i,j), abs(x.l(i,j)-x_l(i,j)))   > tol ) 'bad x.l';
abort$( smax((i,j), abs(x.m(i,j)-x_m(i,j)))   > tol ) 'bad x.m';
abort$( smax(i, abs(supply.l(i)-supply_l(i))) > tol ) 'bad supply.l';
abort$( smax(i, abs(supply.m(i)-supply_m(i))) > tol ) 'bad supply.m';
abort$( smax(j, abs(demand.l(j)-demand_l(j))) > tol ) 'bad demand.l';
abort$( smax(j, abs(demand.m(j)-demand_m(j))) > tol ) 'bad demand.m';
abort$( abs(cost.l-cost_l) > tol ) 'bad cost.l';
abort$( abs(cost.m-cost_m) > tol ) 'nad cost.m';

****  4. Restart and see if we still need only zero iterations

lp06.iterlim = 10000;
Solve lp06 using lp minimizing z ;
abort$( lp06.solvestat <> %solveStat.normalCompletion% or lp06.modelstat <> %modelStat.optimal%) 'wrong status codes';
abort$( lp06.numnopt  <> 0 ) 'bad numopt';
abort$( lp06.numinfes <> 0 ) 'bad infes';
abort$( lp06.iterusd <> 0 ) 'bad iterations';
abort$( abs(z.l-z_l) > tol ) 'bad z.l';
abort$( abs(z.m-z_m) > tol ) 'bad z.m';
abort$( smax((i,j), abs(x.l(i,j)-x_l(i,j)))   > tol ) 'bad x.l';
abort$( smax((i,j), abs(x.m(i,j)-x_m(i,j)))   > tol ) 'bad x.m';
abort$( smax(i, abs(supply.l(i)-supply_l(i))) > tol ) 'bad supply.l';
abort$( smax(i, abs(supply.m(i)-supply_m(i))) > tol ) 'bad supply.m';
abort$( smax(j, abs(demand.l(j)-demand_l(j))) > tol ) 'bad demand.l';
abort$( smax(j, abs(demand.m(j)-demand_m(j))) > tol ) 'bad demand.m';
abort$( abs(cost.l-cost_l) > tol ) 'bad cost.l';
abort$( abs(cost.m-cost_m) > tol ) 'nad cost.m';