Is there a way to insert decision variable in index range without using Constraints Programming in CPLEX?

Question

I have the following indexes:

k: index for days: k ∈ {1, ..., K=365}
i: index for tasks: i ∈ {1, ..., N=200}
j: index for the j^th time of task i: j ∈ {1, ..., Fi}

With F_i is a decision variable indicating the Number of repetitions of task i

And 2 constraints involving Fi and j: 2 constraints here

Is there a way to write this model in CPLEX? I cannot use Constraints Programming since there are float values.

Here is my sample code

int NumbDay = ...;
int NumbTask = ...;


range Day = 1 .. NumbDay;
range Task = 1 .. NumbTask;
dvar int F [Task];
range Repetition = [1..F[Task]]; //Error: Decision variable (or expression) "F" not allowed.

float TotalFH [Day]=...;
float TimeIntervalFH [Task]=...;
float TotalFC [Day]=...;
float TimeIntervalFC [Task]=...;
float TotalDY [Day]=...;
float TimeIntervalDY [Task]=...;
float Manhour [Task]=...;
float NumberOfDaysScheduled =...;
float MinimumNumberOfRepetitions [Task] =...;

dvar float r [Task][Repetition];
dvar float e [Task][Repetition];
dvar float o [Task][Repetition];
dvar float q [Task][Repetition];
dvar float n [Task][Repetition];
dvar float m [Task][Repetition];
dvar float W [Day];
dvar boolean X [Day][Task][Repetition];


execute PRE_PROCESSING {
  cplex.epgap = 0.1;
  cplex.tilim = 100;
}

// Objective: first criterion for minimize the total of the squared differences between the “Average manhour per day” and “Total manhour load of day k” 
//            second criterion for minimize the total differences of the time we execute the task and the due date of those tasks

dexpr float e1 = sum(k in Day)(((sum(k in Day, i in Task, j in Repetition) Manhour[i]*X[i][j][k])/365) - W [Day])^2; //Cannot use type range for int.

dexpr float e2 = sum(i in Task, j in Repetition)q[i][j]*n[i][j]*m[i][j];

// trying to minimize the total of the squared differences between the “Average manhour per day” and “Total manhour load of day k” first

minimize staticLex(e1, e2);
subject to {
  constraint_1:
  forall (i in Task){
    F [i] >= MinimumNumberOfRepetitions [i];
  }

  constraint_2:
  forall (k in Day){
    sum(i in Task, j in Repetition) Manhour[i]*X[i][j][k] == W [k];
  }
  
    constraint_3:
  forall (i in Task, j in Repetition){
    sum(k in Day) X[i][j][k] == 1;
  }
....

score 1 · Accepted Answer · answered May 21 '21 at 12:47

You could use a logical constraint:

constraint_2:
  forall (k in Day,j in Repetition)
     sum(i in Task ) Manhour[i]*X[k][i][j] *(j<=F[i]) == W [k];

As a start, the following model works:

int NumbDay = 1;
int NumbTask = 2;


range Day = 1 .. NumbDay;
range Task = 1 .. NumbTask;

int maxRepetition=10;
dvar int F [Task] in 0..maxRepetition;
//**range Repetition = [1..F[Task]];**

range Repetition=0..maxRepetition;

float TotalFH [d in Day]=d;
float TimeIntervalFH [Task];
float TotalFC [Day];
float TimeIntervalFC [Task];
float TotalDY [Day];
float TimeIntervalDY [Task];
float Manhour [Task];
float NumberOfDaysScheduled ;
float MinimumNumberOfRepetitions [Task] ;

dvar float r [Task][Repetition];
dvar float e [Task][Repetition];
dvar float o [Task][Repetition];
dvar float q [Task][Repetition];
dvar float n [Task][Repetition];
dvar float m [Task][Repetition];
dvar float W [Day];
dvar boolean X [Day][Task][Repetition];


execute PRE_PROCESSING {
  cplex.epgap = 0.1;
  cplex.tilim = 100;
}

// Objective: first criterion for minimize the total of the squared differences between the “Average manhour per day” and “Total manhour load of day k” 
//            second criterion for minimize the total differences of the time we execute the task and the due date of those tasks

dexpr float e1 = sum(k in Day)(((sum(k in Day, i in Task, j in Repetition) Manhour[i]*X[k][i][j])/365) - W [k])^2;

//dexpr float e2 = sum(i in Task, j in Repetition)q[i][j]*n[i][j]*m[i][j];

// trying to minimize the total of the squared differences between the “Average manhour per day” and “Total manhour load of day k” first

minimize e1;
//minimize staticLex(e1, e2);
subject to {
  constraint_1:
  forall (i in Task){
    F [i] >= MinimumNumberOfRepetitions [i];
  }

  constraint_2:
  forall (k in Day,j in Repetition)
     sum(i in Task ) Manhour[i]*X[k][i][j] *(j<=F[i]) == W [k];
  
  
    constraint_3:
  forall (i in Task, j in Repetition){
    sum(k in Day) X[k][i][j] == 1;
  }
}

Is there a way to insert decision variable in index range without using Constraints Programming in CPLEX?

1 Answers1