I am writing code based on a mathematical model. This is my math model and my code. i don't know what are error in constraint 9. please help me debug it

my .mod: 

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Trần Phúc
------------------------------

Hello Trần,

        Could you send us a data file ?

Best regards,

------------------------------
Thierry Sola
------------------------------

Original Message:
Sent: Sat May 10, 2025 12:58 PM
From: Trần Phúc
Subject: debug cplex code

I am writing code based on a mathematical model. This is my math model and my code. i don't know what are error in constraint 9. please help me debug it

my .mod: 

/*********************************************

 * OPL 12.9.0.0 Model

 * Author: Hiep

 * Creation Date: May 7, 2025 at 6:06:42 AM

 *********************************************/

int NumJ=...;

int NumW =...;

int NumM =...;

range J =1.. NumJ ;

range WS =1.. NumW ;

range M =1..NumM;

tuple JS{

int job;

int station;

}

tuple JSS {

int job ;

int station1 ;

int station2 ;

} ; 

tuple Fin{

int Job;

int Station;

}

tuple JM{

JS job;

int machine;

}

tuple MS{

int machine;

int station;

}

tuple JJM{

JS job1;

JS Job2;

int machine;

}

setof(JJM)JJMSet=...;

setof(MS)MSSet=...;

setof(JM)JMSet=...;

setof(JS)JSSet=...;

setof(JSS)JSSSet=...;

setof(Fin)FinSet=...;

int p[JMSet]=...; //processing time of job i in machine m

int k[JJMSet]=...; //set up time of job i in machine m

int d[FinSet]=...; //due date of job i

float BigM= 10000;

dvar boolean X[JMSet]; //1 if job i is assigned to machine m

dvar int+ S[JSSet]; //Startiing time of job i on station s

dvar int+ C[JSSet]; //completing time of job i on station s (operation)

dvar boolean Z[JJMSet]; //if Job j is processed before job i

dvar int+ F[j in J]; //Completion time of job j

dvar int+ Cmax; //makespan

//objective function

minimize Cmax;

subject to {

// (1) makespan covers every job

constraint1: //Total compeletion time

forall(j in J) Cmax >= F[j];

constraint2: //Completion time of each operation

forall(<<j,s>,m> in JMSet) 

F[j] >= C[<j,s>];

constraint3:

forall(<j,s> in JSSet){

 F[j] <= d[<j,s>];

} 

constraint4: //every job at one station assigned only once

forall(<j,s> in JSSet){

sum(<m,s1> in MSSet: s1==s) X[<<j,s>,m>] == 1;

}

constraint5:

forall (<j,s> in JSSet){

S[<j,s+1>] >= C[<j,s>];

}

constraint6:

forall (<j,s> in JSSet){

C[<j,s>] >= S[<j,s>] + (sum(<m,s> in MSSet) X[<<j,s>,m>]*p[<<j,s>,m>]);

}

constraint7:

forall(<<j,s>,m> in JMSet){

X[<<j,s>,m>]*BigM >= C[<j,s>];

X[<<j,s>,m>]*BigM >= S[<j,s>];

}

constraint8:

forall(<i,j,m> in JJMSet){

Z[<i,j,m>]  <= X[<j,m>];

Z[<i,j,m>]  <= X[<j,m>];

Z[<i,j,m>] + Z[<j,i,m>] ==1;

}

constraint_9:

        forall(<i, j, m> in JJMSet, s in JSSet) {

            C[<j,s>] + k[<i, j, m>] <= S[<i,s>] + BigM * (1 - Z[<i, j, m>]);

        }

}

execute WRITE_RESULT{

    var ofile = new IloOplOutputFile("Result.txt");

    ofile.writeln("The objective value: ", Cmax); // Changed to Cmax

    for (var js in JSSet){ // Iterate through JSSet to get Job and Station

      ofile.writeln("Time of job--", js.job, "--Station--", js.station, "--BTime--", S[js], "--FTime--", C[js]); // Use S and C which are the correct start and finish times

    }

    ofile.writeln("-------------------------------");

    for (var jm in JMSet){ // Iterate through JMSet to get Job and Machine assignment

      ofile.writeln("Enable of job--", jm.job, "--Machine--", jm.machine, "--X--", X[jm]); // Access job from JM tuple

    }

    ofile.writeln("-------------------------------");

    for (var jjm in JJMSet){ // Iterate through JJMSet for job sequences on machines

      ofile.writeln("Sequence of job--", jjm.job1.job, "--", jjm.job2.job, "--Machine--", jjm.machine, "--Y--", Z[jjm]); // Access job1 and job2

    }

    ofile.writeln("-------------------------------");

    ofile.close();

  }

------------------------------
Trần Phúc
------------------------------

Hello Trần,

 There is a problem within the "MILP model.dat" file. The "Machine Station" table (MMSet) is defined up to B28 instead of B29.

MSSet from SheetRead(TupleData,"testdata!A21:B28");

Station 1 of Job 3 must be executed on one of the machines 1, 2 or 3. The respective processing times are equal to 8, 9 and 10 (constraint_3).

Station 2 of Job 3 must be executed on one of the machines 4, 5 or 6. The respective processing times are equal to 4, 3 and 2 (constraint_3).

Station 3 of Job 3 must be executed on one of the machines 7 or 8. The respective processing times are equal to 6 and 2 (constraint_3).

Due to the sequence constraint (constraint_6) related to job 3, the sum of the minimum durations for each station is equal to 12 (= 8 + 2 + 2).

The due date for job 3 must be less than or equal to 10 (constraint_2).

12 is strictly greater than 10.

How I found this infeasibility? I added the constraints incrementally and examined the conflicts.

Regarding the last two constraints (constraint_7_8_9 and constraint_10), it might be easier to use indicators initially.

The constraint Z[<i,j,m>] + Z[<j,i,m>] ==1; enforce that the jobs i and j are processed on the same machine m.

Best regards,

------------------------------
Thierry Sola
------------------------------

Original Message:
Sent: Thu May 15, 2025 03:37 AM
From: Thierry Sola
Subject: debug cplex code

Hello Trần,

        Could you send us a data file ?

Best regards,

------------------------------
Thierry Sola

Original Message:
Sent: Sat May 10, 2025 12:58 PM
From: Trần Phúc
Subject: debug cplex code

I am writing code based on a mathematical model. This is my math model and my code. i don't know what are error in constraint 9. please help me debug it

my .mod: 

/*********************************************

 * OPL 12.9.0.0 Model

 * Author: Hiep

 * Creation Date: May 7, 2025 at 6:06:42 AM

 *********************************************/

int NumJ=...;

int NumW =...;

int NumM =...;

range J =1.. NumJ ;

range WS =1.. NumW ;

range M =1..NumM;

tuple JS{

int job;

int station;

}

tuple JSS {

int job ;

int station1 ;

int station2 ;

} ; 

tuple Fin{

int Job;

int Station;

}

tuple JM{

JS job;

int machine;

}

tuple MS{

int machine;

int station;

}

tuple JJM{

JS job1;

JS Job2;

int machine;

}

setof(JJM)JJMSet=...;

setof(MS)MSSet=...;

setof(JM)JMSet=...;

setof(JS)JSSet=...;

setof(JSS)JSSSet=...;

setof(Fin)FinSet=...;

int p[JMSet]=...; //processing time of job i in machine m

int k[JJMSet]=...; //set up time of job i in machine m

int d[FinSet]=...; //due date of job i

float BigM= 10000;

dvar boolean X[JMSet]; //1 if job i is assigned to machine m

dvar int+ S[JSSet]; //Startiing time of job i on station s

dvar int+ C[JSSet]; //completing time of job i on station s (operation)

dvar boolean Z[JJMSet]; //if Job j is processed before job i

dvar int+ F[j in J]; //Completion time of job j

dvar int+ Cmax; //makespan

//objective function

minimize Cmax;

subject to {

// (1) makespan covers every job

constraint1: //Total compeletion time

forall(j in J) Cmax >= F[j];

constraint2: //Completion time of each operation

forall(<<j,s>,m> in JMSet) 

F[j] >= C[<j,s>];

constraint3:

forall(<j,s> in JSSet){

 F[j] <= d[<j,s>];

} 

constraint4: //every job at one station assigned only once

forall(<j,s> in JSSet){

sum(<m,s1> in MSSet: s1==s) X[<<j,s>,m>] == 1;

}

constraint5:

forall (<j,s> in JSSet){

S[<j,s+1>] >= C[<j,s>];

}

constraint6:

forall (<j,s> in JSSet){

C[<j,s>] >= S[<j,s>] + (sum(<m,s> in MSSet) X[<<j,s>,m>]*p[<<j,s>,m>]);

}

constraint7:

forall(<<j,s>,m> in JMSet){

X[<<j,s>,m>]*BigM >= C[<j,s>];

X[<<j,s>,m>]*BigM >= S[<j,s>];

}

constraint8:

forall(<i,j,m> in JJMSet){

Z[<i,j,m>]  <= X[<j,m>];

Z[<i,j,m>]  <= X[<j,m>];

Z[<i,j,m>] + Z[<j,i,m>] ==1;

}

constraint_9:

        forall(<i, j, m> in JJMSet, s in JSSet) {

            C[<j,s>] + k[<i, j, m>] <= S[<i,s>] + BigM * (1 - Z[<i, j, m>]);

        }

}

execute WRITE_RESULT{

    var ofile = new IloOplOutputFile("Result.txt");

    ofile.writeln("The objective value: ", Cmax); // Changed to Cmax

    for (var js in JSSet){ // Iterate through JSSet to get Job and Station

      ofile.writeln("Time of job--", js.job, "--Station--", js.station, "--BTime--", S[js], "--FTime--", C[js]); // Use S and C which are the correct start and finish times

    }

    ofile.writeln("-------------------------------");

    for (var jm in JMSet){ // Iterate through JMSet to get Job and Machine assignment

      ofile.writeln("Enable of job--", jm.job, "--Machine--", jm.machine, "--X--", X[jm]); // Access job from JM tuple

    }

    ofile.writeln("-------------------------------");

    for (var jjm in JJMSet){ // Iterate through JJMSet for job sequences on machines

      ofile.writeln("Sequence of job--", jjm.job1.job, "--", jjm.job2.job, "--Machine--", jjm.machine, "--Y--", Z[jjm]); // Access job1 and job2

    }

    ofile.writeln("-------------------------------");

    ofile.close();

  }

------------------------------
Trần Phúc
------------------------------