Reference
Alireza Soroudi, Power System Optimization Modelling in GAMS, Model TransportationOn-Off (Gcode2.12) in chapter Simple Examples in GAMS, 2017
$title Transportation model with On/off state modeling of production side

$onText
For more details please refer to Chapter 2 (Gcode2.12), of the following book:
Soroudi, Alireza. Power System Optimization Modeling in GAMS. Springer, 2017.
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Model type: MINLP
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Contributed by
Dr. Alireza Soroudi
IEEE Senior Member
email: alireza.soroudi@gmail.com
We do request that publications derived from the use of the developed GAMS code
explicitly acknowledge that fact by citing
Soroudi, Alireza. Power System Optimization Modeling in GAMS. Springer, 2017.
DOI: doi.org/10.1007/978-3-319-62350-4
$offText

Set
   i / s1*s3 /
   j / d1*d4 /;

Table c(i,j)
       d1      d2      d3      d4
   s1  0.0755  0.0655  0.0498  0.0585
   s2  0.0276  0.0163  0.096   0.0224
   s3  0.068   0.0119  0.034   0.0751;

Table data(i,*)
      'Pmin'  'Pmax'
   s1  100     450
   s2  50      350
   s3  30      500;

Parameter demand(j) / d1 217, d2 150, d3 145, d4 244 /;

Variable of, x(i,j), P(i);
Binary Variable U(i);
Equation eq1, eq2(i), eq3(i), eq4(j), eq5(i);

eq1..    of   =e= sum((i,j), c(i,j)*sqr(x(i,j)));
eq2(i).. P(i) =l= data(i,'Pmax')*U(i);
eq3(i).. P(i) =g= data(i,'Pmin')*U(i);
eq4(j).. sum(i, x(i,j)) =g= demand(j);
eq5(i).. sum(j, x(i,j)) =e= P(i);

P.lo(i)   = 0;
P.up(i)   = data(i,'Pmax');
x.lo(i,j) = 0;
x.up(i,j) = 100;

Model minlp1 / all /;
solve minlp1 using minlp minimizing of;