Hi

in CPLEX_Studio129\opl\examples\opl\sched_jobshopflex we have a jobshop example with CPO

And CPO is the right method for jobshopflex.

I often get question on how to write that as a MIP even though CPO is the way to go.

One way is to enumerate time with boolean decision variables.

If you want to adapt the CPO model to MIP you may write the following:

.mod

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

range Jobs = 0..nbJobs-1;
range Mchs = 0..nbMchs-1;
// Mchs is used both to index machines and operation position in job

tuple Operation {
  int mch; // Machine
  int pt;  // Processing time
};

Operation Ops[j in Jobs][m in Mchs] = ...;

dvar int+ s[j in Jobs][o in Mchs];
dexpr int e[j in Jobs][o in Mchs]=s[j][o]+Ops[j][o].pt;

 

minimize max(j in Jobs) e[j][nbMchs-1];
subject to {
  forall (m in Mchs,ordered i,j in Jobs, o1 in Mchs,o2 in Mchs:Ops[i][o1].mch == m && Ops[j][o2].mch == m)
    (e[i][o1]<=s[j][o2]) || (e[j][o2]<=s[i][o1]);
  forall (j in Jobs, o in 0..nbMchs-2)
    //endBeforeStart(itvs[j][o], itvs[j][o+1]);
    e[j][o]<=s[j][o+1];
}

execute {
  for (var j = 0; j <= nbJobs-1; j++) {
    for (var o = 0; o <= nbMchs-1; o++) {
      write(s[j][o] + " ");
    }
    writeln("");
  }
}

.dat

Params = <20, 10>;

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>,
  <11,1,10>,
  <12,1,11>,
  <13,1,12>,
  <14,1,13>,
  <15,2,0>,
  <16,2,1>,
  <17,2,2>,
  <18,2,3>,
  <19,2,4>,
  <20,2,5>,
  <21,2,6>,
  <22,2,7>,
  <23,2,8>,
  <24,2,9>,
  <25,3,0>,
  <26,3,1>,
  <27,3,2>,
  <28,3,3>,
  <29,3,4>,
  <30,3,5>,
  <31,3,6>,
  <32,3,7>,
  <33,3,8>,
  <34,3,9>,
  <35,3,10>,
  <36,4,0>,
  <37,4,1>,
  <38,4,2>,
  <39,4,3>,
  <40,4,4>,
  <41,4,5>,
  <42,4,6>,
  <43,4,7>,
  <44,4,8>,
  <45,4,9>,
  <46,4,10>,
  <47,4,11>,
  <48,4,12>,
  <49,4,13>,
  <50,5,0>
  };
 
  Modes = {
  <1,3,13>,
  <1,7,12>,
  <2,8,9>,
  <2,9,17>,
  <3,7,16>,
  <3,5,5>,
  <4,1,8>,
  <5,10,18>,
  <5,7,14>,
  <6,4,15>,
  <6,9,20>,
  <7,2,11>,
  <8,8,3>,
  <9,5,5>,
  <9,6,17>,
  <10,3,5>,
  <11,7,10>,
  <12,9,15>,
  <12,6,18>,
  <13,4,7>,
  <13,1,7>,
  <14,8,17>,
  <15,10,10>,
  <16,8,16>,
  <16,4,8>,
  <17,2,3>,
  <18,7,14>,
  <19,8,3>,
  <20,10,17>,
  <20,6,2>,
  <21,2,19>,
  <22,10,5>,
  <23,3,2>,
  <23,7,16>,
  <24,1,16>,
  <25,3,17>,
  <25,7,20>,
  <26,2,15>,
  <27,7,1>,
  <28,7,18>,
  <28,6,18>,
  <29,8,2>,
  <30,3,20>,
  <30,4,17>,
  <31,7,5>,
  <32,3,13>,
  <33,5,13>,
  <34,4,5>,
  <35,5,19>,
  <36,1,18>,
  <36,6,7>,
  <37,5,4>,
  <37,3,16>,
  <38,8,1>,
  <39,3,12>,
  <40,2,18>,
  <41,4,20>,
  <42,7,10>,
  <42,9,15>,
  <43,6,13>,
  <44,4,2>,
  <44,7,6>,
  <45,6,12>,
  <46,8,20>,
  <46,2,10>,
  <47,7,20>,
  <47,1,3>,
  <48,6,7>,
  <49,8,20>,
  <50,2,10>
  };

I had to use a smaller .dat because otherwise MIP is too slow. Of course MIP and CPO find the same objective.

And again CPO is the way to go : https://www.slideshare.net/PhilippeLaborie/introduction-to-cp-optimizer-for-scheduling

regards

Originally posted by: bobby76

Dear Mr. Fleischer,

I want to write a manuscript to a reputable journal paper. It is about scheduling and I think it is interesting to use CP. Can I collaborate with you or any other IBM staff regarding this matter? 

Best regards, 

Bobby Kurniawan

Hi,

then you should try to contact our research experts : https://researcher.watson.ibm.com/researcher/view.php?person=fr-laborie

You could have a look at https://link.springer.com/epdf/10.1007/s10601-018-9281-x?author_access_token=PvQi2dcbGAy4BzM-mewXmve4RwlQNchNByi7wbcMAY4nHcDNzBIAxP9-qcxkT9nuYdU8nXJOl1k7alaTXN5sqp9XmmnnNJ6ICV9jSnbqGccmnqkClre4b2TTJXn2jwjhdh1oR1DBzW1uOxOO8XYofA%3D%3D

regards