Originally posted by: user1234567

I have 2 parts in my code: The first one is used for assignment , and the second is used for scheduling. 

I get this result: 0E0 !! When i should get a result which is better than the monolevel part (without division into 2 parts).

when i run it in one part (before deviding it into two parts), it works well.

 

First part: (.MOD)

 

Second part: (.MOD)

 

.DAT:

 Params = <10, 6, 3, 115>;

Ops = {
  <1,1,0>,
  <2,1,1>,
  <3,1,2>,
  <4,1,3>,
  <5,1,4>,
  <6,1,5>,
   
  <7,2,0>,
  <8,2,1>,
  <9,2,2>,
  <10,2,3>,
  <11,2,4>,
  
  <12,3,0>,
  <13,3,1>,
  <14,3,2>,
  <15,3,3>,
  <16,3,4>,
  
  <17,4,0>,
  <18,4,1>,
  <19,4,2>,
  <20,4,3>,
  <21,4,4>,
 
  <22,5,0>,
  <23,5,1>,
  <24,5,2>,
  <25,5,3>,
  <26,5,4>,
  <27,5,5>,
  
  <28,6,0>,
  <29,6,1>,
  <30,6,2>,
  <31,6,3>,
  <32,6,4>,
  <33,6,5>,
  
  <34,7,0>,
  <35,7,1>,
  <36,7,2>,
  <37,7,3>,
  <38,7,4>,
  
  <39,8,0>,
  <40,8,1>,
  <41,8,2>,
  <42,8,3>,
  <43,8,4>,
  
  <44,9,0>,
  <45,9,1>,
  <46,9,2>,
  <47,9,3>,
  <48,9,4>,
  <49,9,5>,

  <50,10,0>,
  <51,10,1>,
  <52,10,2>,
  <53,10,3>,
  <54,10,4>,
  <55,10,5>,

 
 
};

Modes = {

//job 1
  <1,1,1,5>,
  <1,1,3,4>,
  
  <2,1,5,3>,
  <2,1,3,5>,
  <2,1,2,1>,
   
  <3,1,3,4>,
  <3,1,6,2>,
    
  <4,1,6,5>,
  <4,1,2,6>,
  <4,1,1,1>,
 
  <5,1,3,1>,
  
  <6,1,6,6>,
  <6,1,3,6>,
  <6,1,4,3>,
    
 //job 2
  <7,2,2,6>,
  
  <8,2,3,1>,
 
  <9,2,1,2>, 
  
  <10,2,2,6>, 
  <10,2,4,6>, 

  <11,2,6,5>, 
  <11,2,2,6>, 
  <11,2,1,1>, 
 
//job 3

  <12,3,2,6>,
  
  <13,3,3,4>,
  <13,3,6,2>,
  
  <14,3,6,5>,
  <14,3,2,6>,
  <14,3,1,1>,

  <15,3,3,4>,
  <15,3,2,6>,
  <15,3,6,6>,

  <16,3,1,1>,
  <16,3,5,5>,

//job 4

  <17,3,6,5>,
  <17,3,2,6>,
  <17,3,1,1>,
  
  <18,3,2,6>,

  <19,3,3,1>,
  
  <20,3,5,3>,
  <20,3,3,5>,
  <20,3,2,1>,

  <21,3,3,4>,
  <21,3,6,2>,

//job 5

  <22,5,5,3>,
  <22,5,3,5>,
  <22,5,2,1>,

  <23,5,6,5>,
  <23,5,2,6>,
  <23,5,1,1>,
  
  <24,5,2,6>,
  
  <25,5,1,5>,
  <25,5,3,4>,

  <26,5,2,6>,
  <26,5,4,6>,
  
  <27,5,3,4>,
  <27,5,2,6>,
  <27,5,6,6>,

//job 6

  <28,6,3,4>,
  <28,6,6,2>,

  <29,6,1,2>,
  
  <30,6,3,4>,
  <30,6,2,6>,
  <30,6,6,6>,
  
  <31,6,2,6>,

  <32,6,6,5>,
  <32,6,2,6>,
  <32,6,1,1>,
  
  <33,6,1,3>,
  <33,6,4,2>,

//job 7

  <34,7,6,1>,
  
  <35,7,1,3>,
  <35,7,4,2>,

  <36,7,3,4>,
  <36,7,2,6>,
  <36,7,6,6>,

  <37,7,2,6>,
  <37,7,5,1>,
  <37,7,1,6>,

  <38,7,3,1>,
  
  //job 8

  <39,8,3,4>,
  <39,8,6,2>,
  
  <40,8,3,4>,
  <40,8,2,6>,
  <40,8,6,6>, 
  
  <41,8,6,5>,
  <41,8,2,6>,
  <41,8,1,1>,
  
  <42,8,2,6>, 
  
  <43,8,2,6>,    
  <43,8,4,6>, 
    
  //job 9
 
  <44,9,6,1>,
  
  <45,9,1,1>,
  <45,9,5,5>,
  
  <46,9,6,6>,
  <46,9,3,6>,
  <46,9,4,3>,
  
  <47,9,1,2>, 
  
  <48,9,3,4>,    
  <48,9,2,6>, 
  <48,9,6,6>,   
 
  <49,9,2,6>, 
  <49,9,4,6>,   
  
    //job 10
 
  <50,10,3,4>,
  <50,10,6,2>,
  
  <51,10,3,4>,
  <51,10,2,6>,
  <51,10,6,6>,
  
  <52,10,5,3>,
  <52,10,3,5>,
  <52,10,2,1>,
  
  <53,10,6,1>, 
  
  <54,10,2,6>,    
  <54,10,4,6>, 
 
  <55,10,1,3>, 
  <55,10,4,2>,   
};

 

Please help me to get a feasible result. Thank you.

#CPLEXOptimizers
#DecisionOptimization

Originally posted by: user1234567

The program should make the assignment first (in part 2). Then, according to this assignment, it should generate the corresonding scheduling (in part 1). 

#CPLEXOptimizers
#DecisionOptimization

Hi,

could

https://www.ibm.com/developerworks/community/forums/html/topic?id=8a3c06c4-1571-4148-9fa8-25843c84add8&ps=25

help you ?

regards

#CPLEXOptimizers
#DecisionOptimization

Originally posted by: user1234567

No, it's not helpful unfortunately! i relied on your link to do this work. But, it doesn't work.

Please try to focus on my example and tell me why it doesn't work.

I tried to reduce the number of constraints:

.MOD (first model)

 using CP;
 
int L = 1000;
 
tuple paramsT{
int nbJobs;
int nbMchs;
int nbOper;
int nbOpertotal;
};
 
paramsT Params = ...;
int nbJobs = Params.nbJobs;
int nbMchs = Params.nbMchs;
int nbOper = Params.nbOper;
int nbOpertotal = Params.nbOpertotal;
 
 
range Jobs = 1..nbJobs;
range Mchs = 1..nbMchs; 
range Oper = 1..nbOper; 
range Opertotal = 1..nbOpertotal; 
 
 
tuple Operation {
  int id;    // Operation id
  int jobId; // Job id
  int pos;   // Position in job
};
 
tuple Mode {
  int opId; // Operation id
  int jobId;
  int mch;  // Machine
  int pt;   // Processing time
};
 
{Operation} Ops   = ...;
{Mode}      Modes = ...;
 
 
 
// Position of last operation of job j
int jlast[j in Jobs] = max(o in Ops: o.jobId==j) o.pos;
 
dvar interval ops  [Ops]; 
dvar interval modes[md in Modes] optional size md.pt;
dvar sequence mchs[m in Mchs] in all(md in Modes: md.mch == m) modes[md];
 
dvar int c[i in Jobs][j in Oper][k in Mchs] in 0..1000 ;
dvar int s[i in Jobs][j in Oper][k in Mchs] in 0..1000;
int p[i in Jobs][j in Oper][k in Mchs];
 
 
int c1[i in Jobs];
 
dvar int r[u in Opertotal][k 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];
 
 
execute {
  cp.param.FailLimit = 10000;
}
 
minimize staticLex(max(i in Jobs, o in Ops: o.pos==jlast[i]) endOf(ops[o]),-sum(i in Jobs,j in Oper, k in Mchs) s[i][j][k]);
subject to {

//Operations on a given machine m cannot overlap      
     forall (m in Mchs)
    noOverlap(mchs[m]);
 
 //Alternative machines for a given operation o    
  forall (o in Ops)
    alternative(ops[o], all(md in Modes: md.opId==o.id) modes[md]);    
}
 
execute {
  for (var m in Modes) {
    if (modes[m].present)
      writeln("Operation " + m.opId + "of job" +m.jobId+ " on machine " + m.mch + " starting at " + modes[m].start+ "and ends at" +modes[m].end);
      
       
  }
}
 
tuple solutionT{
int operation;
int job;
int machine;
int start;
int end;
};
{solutionT} solution = {<m.opId, m.jobId, m.mch, startOf(modes[m]), endOf(modes[m])> | m in Modes};

 

.MOD (second model)

 

.DAT (Data for the 2 models)

 Params = <10, 6, 3, 115>;

Ops = {
  <1,1,0>,
  <2,1,1>,
  <3,1,2>,
  <4,1,3>,
  <5,1,4>,
  <6,1,5>,
   
  <7,2,0>,
  <8,2,1>,
  <9,2,2>,
  <10,2,3>,
  <11,2,4>,
  
  <12,3,0>,
  <13,3,1>,
  <14,3,2>,
  <15,3,3>,
  <16,3,4>,
  
  <17,4,0>,
  <18,4,1>,
  <19,4,2>,
  <20,4,3>,
  <21,4,4>,
 
  <22,5,0>,
  <23,5,1>,
  <24,5,2>,
  <25,5,3>,
  <26,5,4>,
  <27,5,5>,
  
  <28,6,0>,
  <29,6,1>,
  <30,6,2>,
  <31,6,3>,
  <32,6,4>,
  <33,6,5>,
  
  <34,7,0>,
  <35,7,1>,
  <36,7,2>,
  <37,7,3>,
  <38,7,4>,
  
  <39,8,0>,
  <40,8,1>,
  <41,8,2>,
  <42,8,3>,
  <43,8,4>,
  
  <44,9,0>,
  <45,9,1>,
  <46,9,2>,
  <47,9,3>,
  <48,9,4>,
  <49,9,5>,

  <50,10,0>,
  <51,10,1>,
  <52,10,2>,
  <53,10,3>,
  <54,10,4>,
  <55,10,5>,

 
 
};

Modes = {

//job 1
  <1,1,1,5>,
  <1,1,3,4>,
  
  <2,1,5,3>,
  <2,1,3,5>,
  <2,1,2,1>,
   
  <3,1,3,4>,
  <3,1,6,2>,
    
  <4,1,6,5>,
  <4,1,2,6>,
  <4,1,1,1>,
 
  <5,1,3,1>,
  
  <6,1,6,6>,
  <6,1,3,6>,
  <6,1,4,3>,
    
 //job 2
  <7,2,2,6>,
  
  <8,2,3,1>,
 
  <9,2,1,2>, 
  
  <10,2,2,6>, 
  <10,2,4,6>, 

  <11,2,6,5>, 
  <11,2,2,6>, 
  <11,2,1,1>, 
 
//job 3

  <12,3,2,6>,
  
  <13,3,3,4>,
  <13,3,6,2>,
  
  <14,3,6,5>,
  <14,3,2,6>,
  <14,3,1,1>,

  <15,3,3,4>,
  <15,3,2,6>,
  <15,3,6,6>,

  <16,3,1,1>,
  <16,3,5,5>,

//job 4

  <17,3,6,5>,
  <17,3,2,6>,
  <17,3,1,1>,
  
  <18,3,2,6>,

  <19,3,3,1>,
  
  <20,3,5,3>,
  <20,3,3,5>,
  <20,3,2,1>,

  <21,3,3,4>,
  <21,3,6,2>,

//job 5

  <22,5,5,3>,
  <22,5,3,5>,
  <22,5,2,1>,

  <23,5,6,5>,
  <23,5,2,6>,
  <23,5,1,1>,
  
  <24,5,2,6>,
  
  <25,5,1,5>,
  <25,5,3,4>,

  <26,5,2,6>,
  <26,5,4,6>,
  
  <27,5,3,4>,
  <27,5,2,6>,
  <27,5,6,6>,

//job 6

  <28,6,3,4>,
  <28,6,6,2>,

  <29,6,1,2>,
  
  <30,6,3,4>,
  <30,6,2,6>,
  <30,6,6,6>,
  
  <31,6,2,6>,

  <32,6,6,5>,
  <32,6,2,6>,
  <32,6,1,1>,
  
  <33,6,1,3>,
  <33,6,4,2>,

//job 7

  <34,7,6,1>,
  
  <35,7,1,3>,
  <35,7,4,2>,

  <36,7,3,4>,
  <36,7,2,6>,
  <36,7,6,6>,

  <37,7,2,6>,
  <37,7,5,1>,
  <37,7,1,6>,

  <38,7,3,1>,
  
  //job 8

  <39,8,3,4>,
  <39,8,6,2>,
  
  <40,8,3,4>,
  <40,8,2,6>,
  <40,8,6,6>, 
  
  <41,8,6,5>,
  <41,8,2,6>,
  <41,8,1,1>,
  
  <42,8,2,6>, 
  
  <43,8,2,6>,    
  <43,8,4,6>, 
    
  //job 9
 
  <44,9,6,1>,
  
  <45,9,1,1>,
  <45,9,5,5>,
  
  <46,9,6,6>,
  <46,9,3,6>,
  <46,9,4,3>,
  
  <47,9,1,2>, 
  
  <48,9,3,4>,    
  <48,9,2,6>, 
  <48,9,6,6>,   
 
  <49,9,2,6>, 
  <49,9,4,6>,   
  
    //job 10
 
  <50,10,3,4>,
  <50,10,6,2>,
  
  <51,10,3,4>,
  <51,10,2,6>,
  <51,10,6,6>,
  
  <52,10,5,3>,
  <52,10,3,5>,
  <52,10,2,1>,
  
  <53,10,6,1>, 
  
  <54,10,2,6>,    
  <54,10,4,6>, 
 
  <55,10,1,3>, 
  <55,10,4,2>,   
};

 

First, cplex should make the assignment of operations : 

     forall (m in Mchs)
    noOverlap(mchs[m]);
 
  forall (o in Ops)
    alternative(ops[o], all(md in Modes: md.opId==o.id) modes[md]);  

 

Then, it should make the corresponding scheduling of these assignments by the command: 

  forall (j in Jobs, o1 in Ops, o2 in Ops: o1.jobId==j && o2.jobId==j && o2.pos==1+o1.pos)
  endBeforeStart(ops[o1],ops[o2]); 

 

That's why i devided these commands into 2 models.

 

Here, cplex displays the result 12 which is not correct, because when i write all the constraints in one model, i get the result 42.

So, does cplex considers the 2 models, and excecutes them correctly ? Or is there any mistake in my code ?

 

Thank you.

#CPLEXOptimizers
#DecisionOptimization

Hi,

in the second part of your main you wrote

var Modelt2Source = new IloOplModelSource("main-Bilevel-instance-brandimarte-10,6-MK01.mod");

var Modelt2Def = new IloOplModelDefinition(Modelt2Source);

  var oplmodel2 = new IloOplModel(Modelt2Def, cp2);

  var Modelt2data = new IloOplDataSource("Bilevel-instance-brandimarte-10,6-MK01 (Data).dat");

  oplmodel2.addDataSource(Modelt2data);

  oplmodel2.generate();

  writeln("cp solve gives",cp.solve()); 

which looks a bit strange:

writeln("cp solve gives",cp2.solve()); 

would be better right ?

Plus here you try to solve model1 and then solve model2 but not keep anything from the first model when you solve the second model. Is that what you try to do ?

regards

#CPLEXOptimizers
#DecisionOptimization

Originally posted by: user1234567

Yes, you are right cp2 instead of cp. I corrected it. But, still the same result.

The program should firstly assign each operation to one of its eligible machines. Then, should schedule these assigned operations.But, there is a link between these 2 models because the second model should rely on the first model in order to make the corresponding scheduling. In other words, the second model have to call the first model in oder to get the suitable result.

In the normal examples of IBM Ilog cplex, the assignment and the scheduling are made in one model (so this is monolevel). But, here i'm trying to solve a bilevel problem. That's why i divided the model into 2 models (one for assignment, one for scheduling).

So, what's wrong here ?

#CPLEXOptimizers
#DecisionOptimization

Hi,

you need to relate the second model with the first.

And up to now you do not. You need to write that in the flow control: take this from solution in the first model and use that as input for the second model

regards

#CPLEXOptimizers
#DecisionOptimization

Originally posted by: user1234567

This bilevel model Is correct ? I get the result of cmax = 902. Whereas, the (LB,UB) of the current instance (.DAT) is 756. So, it's a bit strange that i get a result of 902 with an exact method.

what is wrong in my model ? Is there any(some) mistakes in the first or the second model ? Thank you

//First model:

using CP;
 
int L = 1000;
 
tuple paramsT{
int nbJobs;
int nbMchs;
int nbOper;
int nbOpertotal;
};
 
paramsT Params = ...;
int nbJobs = Params.nbJobs;
int nbMchs = Params.nbMchs;
int nbOper = Params.nbOper;
int nbOpertotal = Params.nbOpertotal;
 
 
range Jobs = 1..nbJobs;
range Mchs = 1..nbMchs; 
range Oper = 1..nbOper; 
range Opertotal = 1..nbOpertotal; 
 
 
tuple Operation {
  int id;    // Operation id
  int jobId; // Job id
  int pos;   // Position in job
};
 
tuple Mode {
  int opId; // Operation id
  int jobId;
  int mch;  // Machine
  int pt;   // Processing time
};
 
{Operation} Ops   = ...;
{Mode}      Modes = ...;
 
 
 
// Position of last operation of job j
int jlast[j in Jobs] = max(o in Ops: o.jobId==j) o.pos;
 
dvar interval ops  [Ops]; 
dvar interval modes[md in Modes] optional size md.pt;
dvar sequence mchs[m in Mchs] in all(md in Modes: md.mch == m) modes[md];
 
dvar int c[i in Jobs][j in Oper][k in Mchs] in 0..1000 ;
dvar int s[i in Jobs][j in Oper][k in Mchs] in 0..1000;
int p[i in Jobs][j in Oper][k in Mchs];
 
 
int c1[i in Jobs];
 
dvar int r[u in Opertotal][k 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];
 
 
execute {
  cp.param.FailLimit = 10000;
}
 
minimize staticLex(max(i in Jobs, o in Ops: o.pos==jlast[i]) endOf(ops[o]),-sum(i in Jobs,j in Oper, k in Mchs) s[i][j][k]);
subject to {
 
 
 
forall (i in Jobs, j in Oper,o in Ops, md in Modes: md.jobId==i && md.opId==j && md.opId == o.id)
sum (k in Mchs) X[i][j][k] == 1;
 
forall (i in Jobs, j in Oper, k in Mchs)
  sum (i in Jobs, j in Oper) X[i][j][k] <= e[i][j][k];
 
forall (i in Jobs,j in Oper, o in Ops, k in Mchs, 
md in Modes: md.jobId==i && md.opId == j && md.mch == k && o.id==md.opId)
ctc1:s[i][j][k] == startOf (modes[md]);
 
 
 
forall (i in Jobs, j in Oper, o in Ops, k in Mchs, md in Modes: md.jobId == i && md.opId == j && md.mch == k && o.id==md.opId)
ctc2:c[i][j][k] == endOf (modes[md]);

 
 
 
//C10
 forall (i in Jobs,j in Oper, o in Ops: o.pos==jlast[i])
 endOf(ops[o]) >= sum (k in Mchs) c[i][j][k];
 
  //C11
  forall (i in Jobs, o in Ops: o.pos==jlast[i])
  max(i in Jobs, o in Ops: o.pos==jlast[i]) endOf(ops[o]) >=  endOf(ops[o]);
 
//C12
forall (i in Jobs,j in Oper, k in Mchs)
  c[i][j][k] >= 0;
 
forall (i in Jobs, j in Oper, k in Mchs)
  s[i][j][k] >= 0;  
 
forall (i in Jobs, j in Oper, k in Mchs)
  p[i][j][k] >= 0;  
 
 
 
 
 
  forall (j in Jobs, o1 in Ops, o2 in Ops: o1.jobId==j && o2.jobId==j && o2.pos==1+o1.pos)
 
  endOf (ops[o1]) <= startOf (ops[o2]);
  
  
 
    
  forall (o in Ops)
    alternative(ops[o], all(md in Modes: md.opId==o.id) modes[md]);
     
     forall (m in Mchs)
    noOverlap(mchs[m]);
  
 
 
}
 
execute {
  for (var m in Modes) {
    if (modes[m].present)
      writeln("Operation " + m.opId + "of job" +m.jobId+ " on machine " + m.mch + " starting at " + modes[m].start+ "and ends at" +modes[m].end);
      
       
  }
}
 
tuple solutionT{
int operation;
int job;
int machine;
int start;
int end;
};
{solutionT} solution = {<m.opId, m.jobId, m.mch, startOf(modes[m]), endOf(modes[m])> | m in Modes};

 

//Second model (main):

 

 

//.DAT

 Params = <10, 10, 3, 115>;

Ops = {
  <1,1,0>,
  <2,1,1>,
  <3,1,2>,
  <4,1,3>,
  <5,1,4>, 
  <6,1,5>,
  <7,1,6>,
  <8,1,7>,
  <9,1,8>,
  <10,1,9>,
  
  <11,2,0>,
  <12,2,1>,
  <13,2,2>,
  <14,2,3>,
  <15,2,4>, 
  <16,2,5>,
  <17,2,6>,
  <18,2,7>,
  <19,2,8>,
  <20,2,9>,
 
  <21,3,0>,
  <22,3,1>,
  <23,3,2>,
  <24,3,3>,
  <25,3,4>,
  <26,3,5>,
  <27,3,6>,
  <28,3,7>,
  <29,3,8>,
  <30,3,9>,
  
  <31,4,0>,
  <32,4,1>,
  <33,4,2>,
  <34,4,3>,
  <35,4,4>,
  <36,4,5>,
  <37,4,6>,
  <38,4,7>,
  <39,4,8>,
  <40,4,9>,
  
  <41,5,0>,
  <42,5,1>,
  <43,5,2>,
  <44,5,3>,
  <45,5,4>,
  <46,5,5>,
  <47,5,6>,
  <48,5,7>,
  <49,5,8>,
  <50,5,9>,
  
  <51,6,0>,
  <52,6,1>,
  <53,6,2>,
  <54,6,3>,
  <55,6,4>,
  <56,6,5>,
  <57,6,6>,
  <58,6,7>,
  <59,6,8>,
  <60,6,9>,
  
  <61,7,0>,
  <62,7,1>,
  <63,7,2>,
  <64,7,3>,
  <65,7,4>,
  <66,7,5>,
  <67,7,6>,
  <68,7,7>,
  <69,7,8>,
  <70,7,9>,
  
  <71,8,0>,
  <72,8,1>,
  <73,8,2>,
  <74,8,3>,
  <75,8,4>,
  <76,8,5>,
  <77,8,6>,
  <78,8,7>,
  <79,8,8>,
  <80,8,9>,
  
  <81,9,0>,
  <82,9,1>,
  <83,9,2>,
  <84,9,3>,
  <85,9,4>,
  <86,9,5>,
  <87,9,6>,
  <88,9,7>,
  <89,9,8>,
  <90,9,9>,
  
  <91,10,0>,
  <92,10,1>,
  <93,10,2>,
  <94,10,3>,
  <95,10,4>,
  <96,10,5>,
  <97,10,6>,
  <98,10,7>,
  <99,10,8>,
  <100,10,9>
};

Modes = {  

//job 1
  <1,1,7,9>,
  
  <2,1,2,81>,
   
  <3,1,5,55>,
    
  <4,1,3,40>,
 
  <5,1,9,32>,
  <5,1,8,32>,
  
  <6,1,4,37>,
  
  <7,1,1,6>,
  
  <8,1,6,19>,
  
  <9,1,10,81>,
  
  <10,1,8,40>,
    
 //job 2
 
  <11,2,8,21>,
  
  <12,2,3,70>,
 
  <13,2,10,65>,
  <13,2,6,65>, 
  
  <14,2,5,64>, 

  <15,2,2,46>,   
  
  <16,2,6,65>,
  
  <17,2,9,25>,
  <17,2,6,25>,
  
  <18,2,1,77>, 
  
  <19,2,4,55>, 
  
  <20,2,7,15>, 
   
//job 3

  <21,3,3,85>,
  
  <22,3,6,37>,
  <22,3,10,37>,
  
  <23,3,1,40>,

  <24,3,4,24>,

  <25,3,2,44>,

  <26,3,7,83>,  
  
  <27,3,5,89>, 
  
  <28,3,9,31>,
  
  <29,3,8,84>, 
  <29,3,4,84>, 
  
  <30,3,10,29>, 
   
//job 4

  <31,4,5,80>,
  
  <32,4,7,77>,
  <32,4,3,77>,

  <33,4,8,56>,
  
  <34,4,1,8>,

  <35,4,3,30>,
  
  <36,4,6,59>,
  
  <37,4,4,38>,
  
  <38,4,2,80>,
  
  <39,4,10,41>,
  
  <40,4,9,97>,

//job 5

  <41,5,1,91>,

  <42,5,7,40>,
  
  <43,5,5,88>,
  <43,5,1,88>,
  
  <44,5,2,17>,

  <45,5,3,71>,
  
  <46,5,4,50>,
  <46,5,3,50>,
  
  <47,5,10,59>,
  
  <48,5,9,80>,
  
  <49,5,6,56>,
  <49,5,9,56>,
  
  <50,5,8,7>,

//job 6

  <51,6,3,8>,
  <51,6,8,8>,

  <52,6,7,9>,
  
  <53,6,4,58>,
  
  <54,6,6,77>,

  <55,6,2,29>,
  
  <56,6,9,96>,
  
  <57,6,1,45>,
  
  <58,6,10,10>,
  
  <59,6,5,54>,
  
  <60,6,8,36>, 

//job 7

  <61,7,5,70>,
  
  <62,7,4,92>,

  <63,7,2,98>,
  
  <64,7,6,87>,

  <65,7,7,99>,
  
  <66,7,8,27>,
  
  <67,7,9,86>,

  <68,7,10,96>,
  
  <69,7,1,28>,

  <70,7,3,73>,

  //job 8

  <71,8,2,95>,
  
  <72,8,8,92>,
  <72,8,3,92>,
  
  <73,8,4,85>,
  
  <74,8,5,52>,
    
  <75,8,7,81>,  

  <76,8,10,32>,  
  
  <77,8,9,39>,  
    
  <78,8,1,59>,  
     
  <79,8,3,41>,  
      
  <80,8,6,56>,  

  //job 9
 
  <81,9,4,60>,
  
  <82,9,9,45>,
  <82,9,5,45>,
  
  <83,9,1,88>,
  
  <84,9,3,12>,
  
  <85,9,2,7>,
  
  <86,9,6,22>,
  
  <87,9,5,93>,
  
  <88,9,10,49>,
  
  <89,9,8,69>,
  
  <90,9,7,27>,  

    //job 10
 
  <91,10,1,21>,
  
  <92,10,3,61>,
  
  <93,10,4,68>,
  <93,10,5,68>,
  
  <94,10,6,26>,
  
  <95,10,7,82>,
  
  <96,10,10,71>,
  
  <97,10,9,44>,
  
  <98,10,5,99>,
  
  <99,10,8,33>,
  
  <100,10,2,84>
  
};

#CPLEXOptimizers
#DecisionOptimization

Originally posted by: user1234567

Sorry, the (LB,UB)=(857, 864). So, is it normal to get the result 902 with an exact method ?

#CPLEXOptimizers
#DecisionOptimization