lp02.gms : Simple level and sign test

Description

```In this test series we test if a solver gets the levels
and marginals right.
```

Small Model of Type : LP

Category : GAMS Test library

Main file : lp02.gms

``````\$title Simple level and sign test (LP02,SEQ=67)
\$ontext
In this test series we test if a solver gets the levels
and marginals right.
\$offtext

\$if not set MTYPE   \$set MTYPE lp
\$if not set MSMAX   \$set MSMAX 1
\$if not set TESTTOL \$set TESTTOL 1e-6

sets
i   canning plants   / seattle, san-diego /
j   markets          / new-york, chicago, topeka / ;

parameters

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

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

table d(i,j)  distance in thousands of miles
new-york       chicago      topeka
seattle          2.1           1.7          0.8
san-diego        2.5           1.8          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
supplyg(i)  observe supply limit at plant i
supplyl(i)  observe supply limit at plant i
demandg(j)  satisfy demand at market j
demandl(j)  satisfy demand at market j ;

scalars signz
signx
const;

cost ..   signz*z =e=  signx*sum((i,j), d(i,j)*x(i,j)) + const;

supplyl(i) ..    sum(j, x(i,j))  =l=    a(i) ;
supplyg(i) ..  - sum(j, x(i,j))  =g=  - a(i) ;

demandg(j) ..   sum(i, x(i,j))  =g=    b(j) ;
demandl(j) .. - sum(i, x(i,j))  =l=  - b(j) ;

scalars  COST_l  /    0.0 /
cost_m  /    1.0 /
z_l     / 1542.50 /
z_m     /    0.0  /

parameters
supply_l(i) / seattle  350, san-diego 550 /
supply_m(i) / seattle -0.4, san-diego 0.0 /
demand_l(j) / new-york 325, chicago  300, topeka 275 /
demand_m(j) / new-york 2.5, chicago  1.8, topeka 1.2 /
x_l(i,j)    / SEATTLE  .NEW-YORK   75.000
SEATTLE  .CHICAGO     0.0
SEATTLE  .TOPEKA    275.000
SAN-DIEGO.NEW-YORK  250.000
SAN-DIEGO.CHICAGO   300.000
SAN-DIEGO.TOPEKA      0.0     /
x_m(i,j)    / SEATTLE  .NEW-YORK    0.0
SEATTLE  .CHICAGO     0.3
SEATTLE  .TOPEKA      0.0
SAN-DIEGO.NEW-YORK    0.0
SAN-DIEGO.CHICAGO     0.0
SAN-DIEGO.TOPEKA      0.2     /

models lp02gg / cost,supplyg ,demandg  /
lp02gl / cost,supplyg ,demandl  /
lp02lg / cost,supplyl ,demandg  /
lp02ll / cost,supplyl ,demandl  /

option limcol=0,limrow=0;
* option solprint=off;

scalar tol / %TESTTOL% /;

signz = 1; signx = 1; const = 0; solve lp02gg min z use %MTYPE% ;
abort\$( lp02gg.solvestat <> %solvestat.NormalCompletion% or lp02gg.modelstat > %MSMAX%) 'wrong status codes';
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(-supplyg.l(i)-supply_l(i))) > tol)    'bad supply.l';
abort\$( smax(i, abs(-supplyg.m(i)-supply_m(i))) > tol)    'bad supply.m';
abort\$( smax(j, abs( demandg.l(j)-demand_l(j))) > tol)    'bad demand.l';
abort\$( smax(j, abs( demandg.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)                         'bad cost.m';

signz = 1; signx = 1; const = 0; solve lp02gl min z use %MTYPE% ;
abort\$( lp02gl.solvestat <> %solvestat.NormalCompletion% or lp02gl.modelstat > %MSMAX%) 'wrong status codes';
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(-supplyg.l(i)-supply_l(i))) > tol)    'bad supply.l';
abort\$( smax(i, abs(-supplyg.m(i)-supply_m(i))) > tol)    'bad supply.m';
abort\$( smax(j, abs(-demandl.l(j)-demand_l(j))) > tol)    'bad demand.l';
abort\$( smax(j, abs(-demandl.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)                         'bad cost.m';

signz = 1; signx = 1; const = 0; solve lp02lg min z use %MTYPE% ;
abort\$( lp02lg.solvestat <> %solvestat.NormalCompletion% or lp02lg.modelstat > %MSMAX%) 'wrong status codes';
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( supplyl.l(i)-supply_l(i))) > tol)    'bad supply.l';
abort\$( smax(i, abs( supplyl.m(i)-supply_m(i))) > tol)    'bad supply.m';
abort\$( smax(j, abs( demandg.l(j)-demand_l(j))) > tol)    'bad demand.l';
abort\$( smax(j, abs( demandg.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)                         'bad cost.m';

signz = 1; signx = 1; const = 0; solve lp02ll min z use %MTYPE% ;
abort\$( lp02ll.solvestat <> %solvestat.NormalCompletion% or lp02ll.modelstat > %MSMAX%) 'wrong status codes';
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( supplyl.l(i)-supply_l(i))) > tol)    'bad supply.l';
abort\$( smax(i, abs( supplyl.m(i)-supply_m(i))) > tol)    'bad supply.m';
abort\$( smax(j, abs(-demandl.l(j)-demand_l(j))) > tol)    'bad demand.l';
abort\$( smax(j, abs(-demandl.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)                         'bad cost.m';

signz =-1; signx = 1; const = 0; solve lp02gg max z use %MTYPE% ;
abort\$( lp02gg.solvestat <> %solvestat.NormalCompletion% or lp02gg.modelstat > %MSMAX%) 'wrong status codes';
abort\$( abs(z.l-signz*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)-signz*x_m(i,j))) > tol)  'bad x.m';
abort\$( smax(i, abs(-supplyg.l(i)-supply_l(i))) > tol)    'bad supply.l';
abort\$( smax(i, abs(-supplyg.m(i)-signz*supply_m(i))) > tol) 'bad supply.m';
abort\$( smax(j, abs( demandg.l(j)-demand_l(j))) > tol)    'bad demand.l';
abort\$( smax(j, abs( demandg.m(j)-signz*demand_m(j))) > tol)  'bad demand.m';
abort\$( abs(cost.l-cost_l) > tol)                         'bad cost.l';
abort\$( abs(cost.m-signz*cost_m) > tol)                   'bad cost.m';

signz =-1; signx = 1; const = 0; solve lp02gl max z use %MTYPE% ;
abort\$( lp02gl.solvestat <> %solvestat.NormalCompletion% or lp02gl.modelstat > %MSMAX%) 'wrong status codes';
abort\$( abs(z.l-signz*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)-signz*x_m(i,j))) > tol)  'bad x.m';
abort\$( smax(i, abs(-supplyg.l(i)-supply_l(i))) > tol)    'bad supply.l';
abort\$( smax(i, abs(-supplyg.m(i)-signz*supply_m(i))) > tol) 'bad supply.m';
abort\$( smax(j, abs(-demandl.l(j)-demand_l(j))) > tol)    'bad demand.l';
abort\$( smax(j, abs(-demandl.m(j)-signz*demand_m(j))) > tol)  'bad demand.m';
abort\$( abs(cost.l-cost_l) > tol)                         'bad cost.l';
abort\$( abs(cost.m-signz*cost_m) > tol)                   'bad cost.m';

signz =-1; signx = 1; const = 0; solve lp02lg max z use %MTYPE% ;
abort\$( lp02lg.solvestat <> %solvestat.NormalCompletion% or lp02lg.modelstat > %MSMAX%) 'wrong status codes';
abort\$( abs(z.l-signz*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)-signz*x_m(i,j))) > tol)  'bad x.m';
abort\$( smax(i, abs( supplyl.l(i)-supply_l(i))) > tol)    'bad supply.l';
abort\$( smax(i, abs( supplyl.m(i)-signz*supply_m(i))) > tol) 'bad supply.m';
abort\$( smax(j, abs( demandg.l(j)-demand_l(j))) > tol)    'bad demand.l';
abort\$( smax(j, abs( demandg.m(j)-signz*demand_m(j))) > tol)  'bad demand.m';
abort\$( abs(cost.l-cost_l) > tol)                         'bad cost.l';
abort\$( abs(cost.m-signz*cost_m) > tol)                   'bad cost.m';

signz =-1; signx = 1; const = 0; solve lp02ll max z use %MTYPE% ;
abort\$( lp02ll.solvestat <> %solvestat.NormalCompletion% or lp02ll.modelstat > %MSMAX%) 'wrong status codes';
abort\$( abs(z.l-signz*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)-signz*x_m(i,j))) > tol)  'bad x.m';
abort\$( smax(i, abs( supplyl.l(i)-supply_l(i))) > tol)    'bad supply.l';
abort\$( smax(i, abs( supplyl.m(i)-signz*supply_m(i))) > tol) 'bad supply.m';
abort\$( smax(j, abs(-demandl.l(j)-demand_l(j))) > tol)    'bad demand.l';
abort\$( smax(j, abs(-demandl.m(j)-signz*demand_m(j))) > tol)  'bad demand.m';
abort\$( abs(cost.l-cost_l) > tol)                         'bad cost.l';
abort\$( abs(cost.m-signz*cost_m) > tol)                   'bad cost.m';

signz = 1; signx =-1; const = 0; solve lp02gg max z use %MTYPE% ;
abort\$( lp02gg.solvestat <> %solvestat.NormalCompletion% or lp02gg.modelstat > %MSMAX%) 'wrong status codes';
abort\$( abs(z.l-signx*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)-signx*x_m(i,j))) > tol)  'bad x.m';
abort\$( smax(i, abs(-supplyg.l(i)-supply_l(i))) > tol)    'bad supply.l';
abort\$( smax(i, abs(-supplyg.m(i)-signx*supply_m(i))) > tol) 'bad supply.m';
abort\$( smax(j, abs( demandg.l(j)-demand_l(j))) > tol)    'bad demand.l';
abort\$( smax(j, abs( demandg.m(j)-signx*demand_m(j))) > tol)  'bad demand.m';
abort\$( abs(cost.l-cost_l) > tol)                         'bad cost.l';
abort\$( abs(cost.m-cost_m) > tol)                         'bad cost.m';

signz = 1; signx =-1; const = 0; solve lp02gl max z use %MTYPE% ;
abort\$( lp02gl.solvestat <> %solvestat.NormalCompletion% or lp02gl.modelstat > %MSMAX%) 'wrong status codes';
abort\$( abs(z.l-signx*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)-signx*x_m(i,j))) > tol)  'bad x.m';
abort\$( smax(i, abs(-supplyg.l(i)-supply_l(i))) > tol)    'bad supply.l';
abort\$( smax(i, abs(-supplyg.m(i)-signx*supply_m(i))) > tol) 'bad supply.m';
abort\$( smax(j, abs(-demandl.l(j)-demand_l(j))) > tol)    'bad demand.l';
abort\$( smax(j, abs(-demandl.m(j)-signx*demand_m(j))) > tol)  'bad demand.m';
abort\$( abs(cost.l-cost_l) > tol)                         'bad cost.l';
abort\$( abs(cost.m-cost_m) > tol)                         'bad cost.m';

signz = 1; signx =-1; const = 0; solve lp02lg max z use %MTYPE% ;
abort\$( lp02lg.solvestat <> %solvestat.NormalCompletion% or lp02lg.modelstat > %MSMAX%) 'wrong status codes';
abort\$( abs(z.l-signx*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)-signx*x_m(i,j))) > tol)  'bad x.m';
abort\$( smax(i, abs( supplyl.l(i)-supply_l(i))) > tol)    'bad supply.l';
abort\$( smax(i, abs( supplyl.m(i)-signx*supply_m(i))) > tol) 'bad supply.m';
abort\$( smax(j, abs( demandg.l(j)-demand_l(j))) > tol)    'bad demand.l';
abort\$( smax(j, abs( demandg.m(j)-signx*demand_m(j))) > tol)  'bad demand.m';
abort\$( abs(cost.l-cost_l) > tol)                         'bad cost.l';
abort\$( abs(cost.m-cost_m) > tol)                         'bad cost.m';

signz = 1; signx =-1; const = 0; solve lp02ll max z use %MTYPE% ;
abort\$( lp02ll.solvestat <> %solvestat.NormalCompletion% or lp02ll.modelstat > %MSMAX%) 'wrong status codes';
abort\$( abs(z.l-signx*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)-signx*x_m(i,j))) > tol)  'bad x.m';
abort\$( smax(i, abs( supplyl.l(i)-supply_l(i))) > tol)    'bad supply.l';
abort\$( smax(i, abs( supplyl.m(i)-signx*supply_m(i))) > tol) 'bad supply.m';
abort\$( smax(j, abs(-demandl.l(j)-demand_l(j))) > tol)    'bad demand.l';
abort\$( smax(j, abs(-demandl.m(j)-signx*demand_m(j))) > tol)  'bad demand.m';
abort\$( abs(cost.l-cost_l) > tol)                         'bad cost.l';
abort\$( abs(cost.m-cost_m) > tol)                         'bad cost.m';

signz =-1; signx =-1; const = 0; solve lp02gg min z use %MTYPE% ;
abort\$( lp02gg.solvestat <> %solvestat.NormalCompletion% or lp02gg.modelstat > %MSMAX%) 'wrong status codes';
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(-supplyg.l(i)-supply_l(i))) > tol)    'bad supply.l';
abort\$( smax(i, abs(-supplyg.m(i)-supply_m(i))) > tol)    'bad supply.m';
abort\$( smax(j, abs( demandg.l(j)-demand_l(j))) > tol)    'bad demand.l';
abort\$( smax(j, abs( demandg.m(j)-demand_m(j))) > tol)    'bad demand.m';
abort\$( abs(cost.l-cost_l) > tol)                         'bad cost.l';
abort\$( abs(cost.m-signx*cost_m) > tol)                   'bad cost.m';

signz =-1; signx =-1; const = 0; solve lp02gl min z use %MTYPE% ;
abort\$( lp02gl.solvestat <> %solvestat.NormalCompletion% or lp02gl.modelstat > %MSMAX%) 'wrong status codes';
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(-supplyg.l(i)-supply_l(i))) > tol)    'bad supply.l';
abort\$( smax(i, abs(-supplyg.m(i)-supply_m(i))) > tol)    'bad supply.m';
abort\$( smax(j, abs(-demandl.l(j)-demand_l(j))) > tol)    'bad demand.l';
abort\$( smax(j, abs(-demandl.m(j)-demand_m(j))) > tol)    'bad demand.m';
abort\$( abs(cost.l-cost_l) > tol)                         'bad cost.l';
abort\$( abs(cost.m-signx*cost_m) > tol)                   'bad cost.m';

signz =-1; signx =-1; const = 0; solve lp02lg min z use %MTYPE% ;
abort\$( lp02lg.solvestat <> %solvestat.NormalCompletion% or lp02lg.modelstat > %MSMAX%) 'wrong status codes';
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( supplyl.l(i)-supply_l(i))) > tol)    'bad supply.l';
abort\$( smax(i, abs( supplyl.m(i)-supply_m(i))) > tol)    'bad supply.m';
abort\$( smax(j, abs( demandg.l(j)-demand_l(j))) > tol)    'bad demand.l';
abort\$( smax(j, abs( demandg.m(j)-demand_m(j))) > tol)    'bad demand.m';
abort\$( abs(cost.l-cost_l) > tol)                         'bad cost.l';
abort\$( abs(cost.m-signx*cost_m) > tol)                   'bad cost.m';

signz =-1; signx =-1; const = 0; solve lp02ll min z use %MTYPE% ;
abort\$( lp02ll.solvestat <> %solvestat.NormalCompletion% or lp02ll.modelstat > %MSMAX%) 'wrong status codes';
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( supplyl.l(i)-supply_l(i))) > tol)    'bad supply.l';
abort\$( smax(i, abs( supplyl.m(i)-supply_m(i))) > tol)    'bad supply.m';
abort\$( smax(j, abs(-demandl.l(j)-demand_l(j))) > tol)    'bad demand.l';
abort\$( smax(j, abs(-demandl.m(j)-demand_m(j))) > tol)    'bad demand.m';
abort\$( abs(cost.l-cost_l) > tol)                         'bad cost.l';
abort\$( abs(cost.m-signx*cost_m) > tol)                   'bad cost.m';

scalar otol 'fudge for case where obj const is added';
* scalar xtol 'fudge for case where obj const is added';

otol = tol * 1000;
tol = tol * 100;
signz = 1; signx = 1; const = 1234; solve lp02lg min z use %MTYPE% ;
abort\$( lp02lg.solvestat <> %solvestat.NormalCompletion% or lp02lg.modelstat > %MSMAX%) 'wrong status codes';
abort\$( abs(z.l-(z_l+const)) > otol )                     '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( supplyl.l(i)-supply_l(i))) > tol)    'bad supply.l';
abort\$( smax(i, abs( supplyl.m(i)-supply_m(i))) > tol)    'bad supply.m';
abort\$( smax(j, abs( demandg.l(j)-demand_l(j))) > tol)    'bad demand.l';
abort\$( smax(j, abs( demandg.m(j)-demand_m(j))) > tol)    'bad demand.m';
abort\$( abs(cost.l-(cost_l+const)) > tol)                 'bad cost.l';
abort\$( abs(cost.m-cost_m) > tol)                         'bad cost.m';
``````
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