lp06.gms : Test iteration interrupts and optimal restarts

Description

Small Model of Type : LP

Category : GAMS Test library

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
chicago     300
topeka      275  / ;

Table c(i,j)  distance in thousands of miles
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';
``````
GAMS Development Corp.
GAMS Software GmbH

General Information and Sales
U.S. (+1) 202 342-0180
Europe: (+49) 221 949-9170
GAMS is a registered trademark of GAMS Software GmbH in the European Union