Originally posted by: user1234567

Hello, i have a variable size of a matrix. Each Job have 5 or 6 operations which is declared as follows in the .DAT:

nbJobs = 10;
nbMchs = 36;
nbOper=36;

Ops = [
 [ <1,1,1,5>,<1,1,2,0>,<1,1,3,4>,<1,1,4,0>,<1,1,5,0>, <1,1,6,0> ,<2,1,1,0>,<2,1,2,1>, <2,1,3,5>, <2,1,4,0>, <2,1,5,3>, <2,1,6,0> ,<3,1,1,0>,<3,1,2,0>, <3,1,3,4>, <3,1,4,0>, <3,1,5,0>, <3,1,6,2> ,<4,1,1,1>,<4,1,2,6>, <4,1,3,0>, <4,1,4,0>, <4,1,5,0>, <4,1,6,5> ,<5,1,1,0>,<5,1,2,0>, <5,1,3,1>, <5,1,4,0>, <5,1,5,0>, <5,1,6,0> ,<6,1,1,3>,<6,1,2,0>, <6,1,3,6>, <6,1,4,3>, <6,1,5,0>, <6,1,6,6> ],
 
  
 [ <1,2,1,0>,<1,2,2,6>, <1,2,3,0>, <1,2,4,0>, <1,2,5,0>,<1,2,6,0> ,<2,2,1,0>,<2,2,2,0>, <2,2,3,1>, <2,2,4,0>, <2,2,5,0>,<2,2,6,0> ,<3,2,1,2>,<3,2,2,0>, <3,2,3,0>, <3,2,4,0>, <3,2,5,0>,<3,2,6,0> ,<4,2,1,0>,<4,2,2,6>, <4,2,3,0>, <4,2,4,6>, <4,2,5,0>,<4,2,6,0> ,<5,2,1,1>,<5,2,2,6>, <5,2,3,0>, <5,2,4,0>, <5,2,5,0>,<5,2,6,5> ],
 
 [ <1,3,1,0>,<1,3,2,6>, <1,3,3,0>, <1,3,4,0>, <1,3,5,0>,<1,3,6,0> ,<2,3,1,0>,<2,3,2,0>, <2,3,3,4>, <2,3,4,0>, <2,3,5,0>,<2,3,6,2> ,<3,3,1,1>,<3,3,2,6>, <3,3,3,0>, <3,3,4,0>, <3,3,5,0>,<3,3,6,5> ,<4,3,1,0>,<4,3,2,6>, <4,3,3,4>, <4,3,4,0>, <4,3,5,0>,<4,3,6,6> ,<5,3,1,1>,<5,3,2,0>, <5,3,3,0>, <5,3,4,0>, <5,3,5,5>,<5,3,6,0> ], 

 [ <1,4,1,1>,<1,4,2,6>, <1,4,3,0>, <1,4,4,0>, <1,4,5,0>,<1,4,6,5> ,<2,4,1,0>,<2,4,2,6>, <2,4,3,0>, <2,4,4,0>, <2,4,5,0>,<2,4,6,0> ,<3,4,1,0>,<3,4,2,0>, <3,4,3,1>, <3,4,4,0>, <3,4,5,0>,<3,4,6,0> ,<4,4,1,0>,<4,4,2,1>, <4,4,3,5>, <4,4,4,0>, <4,4,5,3>,<4,4,6,0> ,<5,4,1,0>,<5,4,2,0>, <5,4,3,4>, <5,4,4,0>, <5,4,5,0>,<5,4,6,2> ],  
 
 [ <1,5,1,0>,<1,5,2,1>, <1,5,3,5>, <1,5,4,0>, <1,5,5,3>,<1,5,6,0> ,<2,5,1,1>,<2,5,2,6>, <2,5,3,0>, <2,5,4,0>, <2,5,5,0>,<2,5,6,5> ,<3,5,1,0>,<3,5,2,6>, <3,5,3,0>, <3,5,4,0>, <3,5,5,0>,<3,5,6,0> ,<4,5,1,5>,<4,5,2,0>, <4,5,3,4>, <4,5,4,0>, <4,5,5,0>,<4,5,6,0> ,<5,5,1,0>,<5,5,2,6>, <5,5,3,0>, <5,5,4,6>, <5,5,5,0>,<5,5,6,0> , <6,5,1,0>,<6,5,2,6>, <6,5,3,4>, <6,5,4,0>, <6,5,5,0>,<6,5,6,6> ], 
 
 
 [ <1,6,1,0>,<1,6,2,0>, <1,6,3,4>, <1,6,4,0>, <1,6,5,0>,<1,6,6,2> ,<2,6,1,2>,<2,6,2,0>, <2,6,3,0>, <2,6,4,0>, <2,6,5,0>,<2,6,6,0> ,<3,6,1,0>,<3,6,2,6>, <3,6,3,4>, <3,6,4,0>, <3,6,5,0>,<3,6,6,6> ,<4,6,1,0>,<4,6,2,6>, <4,6,3,0>, <4,6,4,0>, <4,6,5,0>,<4,6,6,0> ,<5,6,1,1>,<5,6,2,6>, <5,6,3,0>, <5,6,4,0>, <5,6,5,0>,<5,6,6,5> , <6,6,1,3>,<6,6,2,0>, <6,6,3,0>, <6,6,4,2>, <6,6,5,0>,<6,6,6,0> ], 
 
 [ <1,7,1,0>,<1,7,2,0>, <1,7,3,0>, <1,7,4,0>, <1,7,5,0>,<1,7,6,1> ,<2,7,1,3>,<2,7,2,0>, <2,7,3,0>, <2,7,4,2>, <2,7,5,0>,<2,7,6,0> ,<3,7,1,0>,<3,7,2,6>, <3,7,3,4>, <3,7,4,0>, <3,7,5,0>,<3,7,6,6> ,<4,7,1,6>,<4,7,2,6>, <4,7,3,0>, <4,7,4,0>, <4,7,5,1>,<4,7,6,0> ,<5,7,1,0>,<5,7,2,0>, <5,7,3,1>, <5,7,4,0>, <5,7,5,0>,<5,7,6,0> ], 
 
 
 [ <1,8,1,0>,<1,8,2,0>, <1,8,3,4>, <1,8,4,0>, <1,8,5,0>,<1,8,6,2>,<2,8,1,0>,<2,8,2,6>, <2,8,3,4>, <2,8,4,0>, <2,8,5,0>,<2,8,6,6>,<3,8,1,1>,<3,8,2,6>, <3,8,3,0>, <3,8,4,0>, <3,8,5,0>,<3,8,6,5>,<4,8,1,0>,<4,8,2,6>, <4,8,3,0>, <4,8,4,0>, <4,8,5,0>,<4,8,6,0>,<5,8,1,0>,<5,8,2,6>, <5,8,3,0>, <5,8,4,6>, <5,8,5,0>,<5,8,6,0> ], 
 
 [ <1,9,1,0>,<1,9,2,0>, <1,9,3,0>, <1,9,4,0>, <1,9,5,0>,<1,9,6,1> ,<2,9,1,1>,<2,9,2,0>, <2,9,3,0>, <2,9,4,0>, <2,9,5,5>,<2,9,6,0> ,<3,9,1,0>,<3,9,2,0>, <3,9,3,6>, <3,9,4,3>, <3,9,5,0>,<3,9,6,6> ,<4,9,1,2>,<4,9,2,0>, <4,9,3,0>, <4,9,4,0>, <4,9,5,0>,<4,9,6,0> ,<5,9,1,0>,<5,9,2,6>, <5,9,3,4>, <5,9,4,0>, <5,9,5,0>,<5,9,6,6> , <6,9,1,0>,<6,9,2,6>, <6,9,3,0>, <6,9,4,6>, <6,9,5,0>,<6,9,6,0> ], 

 [ <1,10,1,0>,<1,10,2,0>, <1,10,3,4>, <1,10,4,0>, <1,10,5,0>,<1,10,6,2> ,<2,10,1,0>,<2,10,2,6>, <2,10,3,4>, <2,10,4,0>, <2,10,5,0>,<2,10,6,6> ,<3,10,1,0>,<3,10,2,1>, <3,10,3,5>, <3,10,4,0>, <3,10,5,3>,<3,10,6,0> ,<4,10,1,0>,<4,10,2,0>, <4,10,3,0>, <4,10,4,0>, <4,10,5,0>,<4,10,6,1> ,<5,10,1,0>,<5,10,2,6>, <5,10,3,0>, <5,10,4,6>, <5,10,5,0>,<5,10,6,0> , <6,10,1,3>,<6,10,2,0>, <6,10,3,0>, <6,10,4,2>, <6,10,5,0>,<6,10,6,0> ]
 
];

In the .MOD, it is declared as follows:

tuple Operation {
 int id;
 int jobId;
 int mch; // Machine
 int pt;  // Processing time

};

Operation Ops[i in Jobs][j in Oper] = ...;

But the problem is that the program takes more than hour and does not dispaly anything ! So, i think that the problem comes from the declaration of the data and because that the column size is different from one job to another (sometimes 6 operations, sometimes 5 operations).

How can i write this data correctly ? Thank you.

Hi

.mod

int nbJobs = ...;
int nbMchs = ...;
int nbOper=...;

range Oper=1..nbOper;
range Jobs=1..nbJobs;
 
 tuple Operation {
 int id;
 int jobId;
 int mch; // Machine
 int pt;  // Processing time

};

Operation Ops[i in Jobs][j in Oper] = ...;

execute
{
writeln(Ops);
}

.dat

nbJobs = 10;
nbMchs = 36;
nbOper=36;

Ops = [
 [ <1,1,1,5>,<1,1,2,0>,<1,1,3,4>,<1,1,4,0>,<1,1,5,0>, <1,1,6,0> ,<2,1,1,0>,<2,1,2,1>, <2,1,3,5>, <2,1,4,0>, <2,1,5,3>, <2,1,6,0> ,<3,1,1,0>,<3,1,2,0>, <3,1,3,4>, <3,1,4,0>, <3,1,5,0>, <3,1,6,2> ,<4,1,1,1>,<4,1,2,6>, <4,1,3,0>, <4,1,4,0>, <4,1,5,0>, <4,1,6,5> ,<5,1,1,0>,<5,1,2,0>, <5,1,3,1>, <5,1,4,0>, <5,1,5,0>, <5,1,6,0> ,<6,1,1,3>,<6,1,2,0>, <6,1,3,6>, <6,1,4,3>, <6,1,5,0>, <6,1,6,6> ],
 
 
 [ <1,2,1,0>,<1,2,2,6>, <1,2,3,0>, <1,2,4,0>, <1,2,5,0>,<1,2,6,0> ,<2,2,1,0>,<2,2,2,0>, <2,2,3,1>, <2,2,4,0>, <2,2,5,0>,<2,2,6,0> ,<3,2,1,2>,<3,2,2,0>, <3,2,3,0>, <3,2,4,0>, <3,2,5,0>,<3,2,6,0> ,<4,2,1,0>,<4,2,2,6>, <4,2,3,0>, <4,2,4,6>, <4,2,5,0>,<4,2,6,0> ,<5,2,1,1>,<5,2,2,6>, <5,2,3,0>, <5,2,4,0>, <5,2,5,0>,<5,2,6,5> ],
 
 [ <1,3,1,0>,<1,3,2,6>, <1,3,3,0>, <1,3,4,0>, <1,3,5,0>,<1,3,6,0> ,<2,3,1,0>,<2,3,2,0>, <2,3,3,4>, <2,3,4,0>, <2,3,5,0>,<2,3,6,2> ,<3,3,1,1>,<3,3,2,6>, <3,3,3,0>, <3,3,4,0>, <3,3,5,0>,<3,3,6,5> ,<4,3,1,0>,<4,3,2,6>, <4,3,3,4>, <4,3,4,0>, <4,3,5,0>,<4,3,6,6> ,<5,3,1,1>,<5,3,2,0>, <5,3,3,0>, <5,3,4,0>, <5,3,5,5>,<5,3,6,0> ],

 [ <1,4,1,1>,<1,4,2,6>, <1,4,3,0>, <1,4,4,0>, <1,4,5,0>,<1,4,6,5> ,<2,4,1,0>,<2,4,2,6>, <2,4,3,0>, <2,4,4,0>, <2,4,5,0>,<2,4,6,0> ,<3,4,1,0>,<3,4,2,0>, <3,4,3,1>, <3,4,4,0>, <3,4,5,0>,<3,4,6,0> ,<4,4,1,0>,<4,4,2,1>, <4,4,3,5>, <4,4,4,0>, <4,4,5,3>,<4,4,6,0> ,<5,4,1,0>,<5,4,2,0>, <5,4,3,4>, <5,4,4,0>, <5,4,5,0>,<5,4,6,2> ],  
 
 [ <1,5,1,0>,<1,5,2,1>, <1,5,3,5>, <1,5,4,0>, <1,5,5,3>,<1,5,6,0> ,<2,5,1,1>,<2,5,2,6>, <2,5,3,0>, <2,5,4,0>, <2,5,5,0>,<2,5,6,5> ,<3,5,1,0>,<3,5,2,6>, <3,5,3,0>, <3,5,4,0>, <3,5,5,0>,<3,5,6,0> ,<4,5,1,5>,<4,5,2,0>, <4,5,3,4>, <4,5,4,0>, <4,5,5,0>,<4,5,6,0> ,<5,5,1,0>,<5,5,2,6>, <5,5,3,0>, <5,5,4,6>, <5,5,5,0>,<5,5,6,0> , <6,5,1,0>,<6,5,2,6>, <6,5,3,4>, <6,5,4,0>, <6,5,5,0>,<6,5,6,6> ],
 
 
 [ <1,6,1,0>,<1,6,2,0>, <1,6,3,4>, <1,6,4,0>, <1,6,5,0>,<1,6,6,2> ,<2,6,1,2>,<2,6,2,0>, <2,6,3,0>, <2,6,4,0>, <2,6,5,0>,<2,6,6,0> ,<3,6,1,0>,<3,6,2,6>, <3,6,3,4>, <3,6,4,0>, <3,6,5,0>,<3,6,6,6> ,<4,6,1,0>,<4,6,2,6>, <4,6,3,0>, <4,6,4,0>, <4,6,5,0>,<4,6,6,0> ,<5,6,1,1>,<5,6,2,6>, <5,6,3,0>, <5,6,4,0>, <5,6,5,0>,<5,6,6,5> , <6,6,1,3>,<6,6,2,0>, <6,6,3,0>, <6,6,4,2>, <6,6,5,0>,<6,6,6,0> ],
 
 [ <1,7,1,0>,<1,7,2,0>, <1,7,3,0>, <1,7,4,0>, <1,7,5,0>,<1,7,6,1> ,<2,7,1,3>,<2,7,2,0>, <2,7,3,0>, <2,7,4,2>, <2,7,5,0>,<2,7,6,0> ,<3,7,1,0>,<3,7,2,6>, <3,7,3,4>, <3,7,4,0>, <3,7,5,0>,<3,7,6,6> ,<4,7,1,6>,<4,7,2,6>, <4,7,3,0>, <4,7,4,0>, <4,7,5,1>,<4,7,6,0> ,<5,7,1,0>,<5,7,2,0>, <5,7,3,1>, <5,7,4,0>, <5,7,5,0>,<5,7,6,0> ],
 
 
 [ <1,8,1,0>,<1,8,2,0>, <1,8,3,4>, <1,8,4,0>, <1,8,5,0>,<1,8,6,2>,<2,8,1,0>,<2,8,2,6>, <2,8,3,4>, <2,8,4,0>, <2,8,5,0>,<2,8,6,6>,<3,8,1,1>,<3,8,2,6>, <3,8,3,0>, <3,8,4,0>, <3,8,5,0>,<3,8,6,5>,<4,8,1,0>,<4,8,2,6>, <4,8,3,0>, <4,8,4,0>, <4,8,5,0>,<4,8,6,0>,<5,8,1,0>,<5,8,2,6>, <5,8,3,0>, <5,8,4,6>, <5,8,5,0>,<5,8,6,0> ],
 
 [ <1,9,1,0>,<1,9,2,0>, <1,9,3,0>, <1,9,4,0>, <1,9,5,0>,<1,9,6,1> ,<2,9,1,1>,<2,9,2,0>, <2,9,3,0>, <2,9,4,0>, <2,9,5,5>,<2,9,6,0> ,<3,9,1,0>,<3,9,2,0>, <3,9,3,6>, <3,9,4,3>, <3,9,5,0>,<3,9,6,6> ,<4,9,1,2>,<4,9,2,0>, <4,9,3,0>, <4,9,4,0>, <4,9,5,0>,<4,9,6,0> ,<5,9,1,0>,<5,9,2,6>, <5,9,3,4>, <5,9,4,0>, <5,9,5,0>,<5,9,6,6> , <6,9,1,0>,<6,9,2,6>, <6,9,3,0>, <6,9,4,6>, <6,9,5,0>,<6,9,6,0> ],

 [ <1,10,1,0>,<1,10,2,0>, <1,10,3,4>, <1,10,4,0>, <1,10,5,0>,<1,10,6,2> ,<2,10,1,0>,<2,10,2,6>, <2,10,3,4>, <2,10,4,0>, <2,10,5,0>,<2,10,6,6> ,<3,10,1,0>,<3,10,2,1>, <3,10,3,5>, <3,10,4,0>, <3,10,5,3>,<3,10,6,0> ,<4,10,1,0>,<4,10,2,0>, <4,10,3,0>, <4,10,4,0>, <4,10,5,0>,<4,10,6,1> ,<5,10,1,0>,<5,10,2,6>, <5,10,3,0>, <5,10,4,6>, <5,10,5,0>,<5,10,6,0> , <6,10,1,3>,<6,10,2,0>, <6,10,3,0>, <6,10,4,2>, <6,10,5,0>,<6,10,6,0> ]
 
];

works fine

regards

Originally posted by: user1234567

Alex, can you try this please, with the same .DAT:

int L=1000;

int nbJobs = ...;
int nbMchs = ...;
int nbOper = ...;

range Jobs = 1..nbJobs;
range Mchs = 1..nbMchs;
range Oper = 1..nbOper;

// Mchs is used both to index machines and operation position in job (cijk)
tuple Operation {
 int id;
 int jobId;
 int mch; // Machine
 int pt;  // Processing time

};

Operation Ops[i in Jobs][j in Oper] = ...;
 
dvar int+ s[j in Jobs][o in Mchs];
dvar int+ c[j in Jobs][o in Mchs];

  dvar boolean X[i in Jobs][j in Oper][k in Mchs];
  dvar int+ e[i in Jobs][j in Oper][k in Mchs];
  dvar boolean y[i1 in Jobs][j1 in Oper][i2 in Jobs][j2 in Oper][k in Mchs];
 
 
minimize max(j in Jobs, k in Mchs) c[j][k];
subject to {

forall (j in Jobs, o in 1..nbMchs) c[j][o]-s[j][o]==Ops[j][o].pt;

   forall (o1,o2 in Mchs) 
   forall(i,j in Jobs:(Ops[i][o1].mch==Ops[j][o2].mch) && ((i!=j) || (o1!=o2)))
   (s[i][o1]>=c[j][o2]) || (s[j][o2]>=c[i][o1]);
   
    
    
 forall (j in Jobs, g in Jobs: j==g, o in 1..nbMchs-1, w in 1..nbMchs)
        if (Ops[j][o].id==Ops[g][w].id   &&   Ops[j][o+1].mch==Ops[j][w].mch + 1 )
     
    
    s[j][o+1]==c[j][o];
    
    
    //Operations of the same job with successive id on successive machines 
    //(example O11 on machine 0 And O21 on machine 1)
    //The start time of the second operation is the completion time of the first operation.
     forall (j in Jobs, g in Jobs: j==g, o in 1..nbMchs-1, w in 1..nbMchs)
        if (Ops[j][o].id==Ops[g][w].id + 1   &&   Ops[j][o+1].mch==Ops[j][w].mch + 1 )
     
    
    s[j][o+1]==c[j][o];
    
    
    forall (i in Jobs, j in Oper, k in Mchs: Ops[i][j].mch==k)
    
    X[i][j][k]==1;
    
    forall(i in Jobs,j in Oper, k in Mchs: (Ops[i][j].mch==k))
  
e[i][j][k]==1;  
    
    //C1
        forall (i in Jobs, j in Oper)
    
    sum (k in Mchs) X[i][j][k]==1;
    
   
//C2
forall(i in Jobs,j in Oper, k in Mchs)
  
sum (i in Jobs, j in Oper) X[i][j][k]==1 <= e[i][j][k];            

  //Precedence
  forall( k in Mchs,o1 in Mchs, o2 in Mchs, i1,i2 in Jobs: i1!=i2, j1 in Oper, j2 in Oper : j1!=j2 &&
Ops[i1][o1].mch==Ops[i2][o2].mch==k && Ops[i1][o1].id==j1 && Ops[i2][o2].id==j2 &&
 Ops[i1][o1].jobId==i1 && Ops[i2][o2].jobId==i2 )
 
 
 
  y[i1][j1][i2][j2][k] == (c[j1][k]>=s[j2][k])|| (c[j2][k]>=s[j1][k]) ;
  
  
  //C3
  forall (i1,i2 in Jobs,j2 in Oper, k in Mchs)
sum (j1 in Oper) y[i1][j1][i2][j2][k] <= 1;

//C10
forall (i in Jobs, k in Mchs, j in Oper)
sum (k in Mchs) c[i][k] >=  c[i][k];

//C11
forall (i in Jobs, k in Mchs)
max(i in Jobs, k in Mchs) c[i][k] >= c[i][k];

//C12
forall (i in Jobs, k in Mchs )
c[i][k]>=0;
       
                          
}

execute {
  for (var j = 1; j <= nbJobs; j++) {
    for (var o = 1; o <= nbMchs; o++) {
 
        
    
      write("Start time of operation" +o+ "job" +j+ "on machine" +o+ "equal to" +s[j][o]+ "and end at" +c[j][o]+ " ");
    } 
    writeln("");
  }
}  

Thank you

Hi,

your model consumes all available memory on my machine.

if you write

nbMchs2 = 36;

in your .dat and

int nbMchs=2;

in your .mod then you ll get a solution quickly.

So my advice would be either to improve your model or to rely on CPO

regards

I ran your model here and CPLEX claims it is infeasible.