Originally posted by: Ahlem

I would like to implement the following MILP in Java CPLEX.

• So, this is the notation:  

• My decision variable : 

• Can some one help with the implementation part of this MILP problem?

And what is your question or problem?

Originally posted by: Ahlem

Yes my question is when we have sums in the constraints influences on the writing of the code and the final result?

To better understand me, take the constraint 4 does this code below give the same result?

// the first possibility
for (int i2 = 0; i2 < job; i2++) {
                                        
                                        IloLinearNumExpr[][][] expr = new IloLinearNumExpr[job][MG.get(m).get(i2).getX()][ressource];
                                        IloLinearNumExpr[][][] expr1 = new IloLinearNumExpr[job][MG.get(m).get(i2).getX()][ressource];
                                        for (int j2 = 0; j2 < MG.get(m).get(i2).getX(); j2++) {
                                                                                                
                                                for (int k = 0; k < ressource; k++) {

                                                        expr[i2][j2][k] = cplex.linearNumExpr();
                                                        expr1[i2][j2][k] = cplex.linearNumExpr();
                                                        
                                                        for (int i1 = 0; i1 < job; i1++) {

                                                                for (int j1 = 0; j1 < MG.get(m).get(i1).getX(); j1++) {
                                                                
                                                                        expr[i2][j2][k].addTerm(1.0, y[i1][j1][i2][j2][k]);     
                                                                        expr1[i2][j2][k].addTerm(1.0, y[i2][j2][i1][j1][k]);
                                                                
                                                                }
                                                                
                                                        }
                                                        
                                                        cplex.addLe(expr[i2][j2][k], 1); //Constraint3
                                                        cplex.addLe(expr[i2][j2][k], expr1[i2][j2][k]); //Constaint4 
                                                        
                                                }
                                        }
                                }
                                
                                

// the second possibility

for (int i1 = 0; i1 < job; i1++) {

                                        for (int j1 = 0; j1 < MG.get(m).get(i1).getX(); j1++) {

                                                for (int i2 = 0; i2 < job; i2++) {

                                                        for (int j2 = 0; j2 < MG.get(m).get(i2).getX(); j2++) {
                                                                
                                                                for (int k = 0; k < ressource; k++) {
                                                                        
                                                                        IloLinearNumExpr expr = cplex.linearNumExpr(); // constraint3                                                                                                                                                                    
                                                                        expr.addTerm(1.0, y[i1][j1][i2][j2][k]);
                                                                        cplex.addLe(expr, 1);

                                                                        IloLinearNumExpr expr1 = cplex.linearNumExpr(); // constraint4
                                                                        expr1.addTerm(1.0, y[i2][j2][i1][j1][k]);
                                                                        cplex.addLe(expr, expr1);

                                                                }
                                                        }
                                                }
                                        }
                                }

I did not check all the indices in detail but in principle your first variant looks correct while the second one is almost certainly wrong.