gurobi04.gms : GUROBI test suite - multi objective

Description

```Contributor: Michael Bussieck
```

Small Model of Type : GAMS

Category : GAMS Test library

Main file : gurobi04.gms

``````\$TITLE 'GUROBI test suite - multi objective' (GUROBI04,SEQ=712)
\$ontext
Contributor: Michael Bussieck
\$offtext

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          2.5           1.7          1.8
san-diego        2.5           1.8          1.4  ;

Scalar f  freight in dollars per case per thousand miles  /90/ ;

Parameter c(i,j)  transport cost in thousands of dollars per case ;

c(i,j) = f * d(i,j) / 1000 ;

Variables
x(i,j)   shipment quantities in cases
tcost    total transportation costs in thousands of dollars
pSeattle total production in Seattle
z        combined objective function;

Positive Variable x ; x.up(i,j) = 1e5;

Equations
defobj      define objective function
defcost     define objective function
defpSeattle define total production in Seattle
supply(i)   observe supply limit at plant i
demand(j)   satisfy demand at market j ;

Scalar psDirection optimization direction for production in Seattle;

defobj ..      z  =e=  tcost + psDirection*0.1*pSeattle;

defcost ..     tcost  =e=  sum((i,j), c(i,j)*x(i,j)) ;

defpSeattle .. pSeattle =e=  sum(j, x('Seattle',j)) ;

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

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

Model transport /all/ ;

\$ echo multobj 1 > gurobi.opt
option solver=gurobi;
transport.optfile = 1;

* Maximize production in Seattle
psDirection = -1;
Solve transport using mip minimizing z ;
abort\$(transport.modelstat <> 1) 'expect optimal solution';
abort\$(abs(pSeattle.l-350)>1e-6) 'expect max production of 350 in Seattle', pSeattle.l;

* Minimize production in Seattle
psDirection = 1;
Solve transport using mip minimizing z ;
abort\$(transport.modelstat <> 1) 'expect optimal solution';
abort\$(abs(pSeattle.l-300)>1e-6) 'expect min production of 300 in Seattle', pSeattle.l;
``````