Hello everyone,

I am trying to apply the benders decomposition using CPLEX (strategy 3), I want to know if I am doing it the right way because I only found one example using it. Here is the link

https://www.gams.com/latest/gamslib_ml/libhtml/gamslib_cbenders.html

Also, I want to know if there is an accelerated version of Benders using Cplex or is there any other possibility to accelerate it by adding heuristics or cutting plans using BCH facility? https://www.gams.com/latest/docs/UG_SolverUsage.html#ADVANCED_USAGE_BCHFacility

Or can we use these CPLEX facilities Benders feasibility cut tolerance, Benders optimality cut tolerance or RLT cuts in GAMS: https://www.ibm.com/support/knowledgecenter/SSSA5P_12.7.0/ilog.odms.studio.help/CPLEX/ReleaseNotes/topics/releasenotes127/newParameters.html

You find below my code:

```
Sets i products / i0*i55 /
j suppliers / j0*j55 /
t time periods / t0*t55 /
sub_j(j) dynamic subset for j
sub_t(t) dynamic subset for t
sub_i(i) dynamic subset for i ;
Alias ( k , t ) ;
Parameter D( i , t ) demand of product ;
Parameter C( i , j ) porduction capacity ;
Parameter P( i , j ) purchase price ( $ per unit );
Parameter H( i ) product-dependent holding cost ( $ per unit ) ;
Parameter O( j ) supplier-dependent ordering cost ( $ per unit ) ;
Variables x ( i , j , t )
y ( j , t )
R( i , t )
cost ;
Positive Variables x ,R;
Binary Variable y ;
Equations obj objective function
con1 ( i , t )
con2 ( i , j , t ) feasibility constraint;
obj .. cost =E= sum ( ( sub_i(i) , sub_j(j) , sub_t(t) ) ,P( i , j )* x ( i , j , t ))+sum ( ( sub_j(j) , sub_t(t) ) ,O( j )* y ( j , t ) )
+ sum ( ( sub_i(i) , sub_t(t) ) ,H( i ) * ( sum ( k$ ( ord ( t ) GE ord ( k ) ) , sum ( sub_j(j) , x ( i , j , k))-D( i , k ) ) ) ) ;
con1 ( sub_i(i) , sub_t(t) ) .. R( i , t ) =E= sum ( k$ ( ord ( t ) GE ord ( k ) ) , sum ( sub_j(j) , x ( i , j , k))-D( i , k ) ) ;
con2 ( sub_i(i) , sub_j(j) , sub_t(t) ) .. C( i , j )* y ( j , t ) - x ( i , j , t ) =G= 0 ;
display "---------------------formulation ----------------------";
$onEcho > cplexd.op3
BendersStrategy 3
$offEcho
option optcr =0;
option limrow =0;
option limcol =0;
option reslim =1800;
option solver = cplexd;
option solveLink = %solveLink.loadLibrary%;
Model my_model /all/;
option savepoint = 3;
Scalar cpxOptFile;
File myput;
Put myput;
put_utility 'gdxin' / 'data.gdx';
execute_load D, P, C, H, O, sub_i, sub_j,sub_t;
Execute_unload;
my_model.optFile = 3;
Solve my_model minimizing cost using mip ;
Put_utility 'exec' / 'gdx2xls my_model.gdx ';
```