Originally posted by: zab.a

Hi,

I have the following scenario: variable x[i] is an integer variable. Assume that i =5 , x[i] may have values of [1 1 1 2 3] // x[i] represent arrival time of customers . I need to strict the number of customers they will arrive at the same time. for example x[i]=1  shall occur  only 2 times. so that x[i] will be [ 1 1 2 2 3] instead of [ 1 1 1 2 3] . another example same case in x=[ 1 5 5 5 5 3], the four "5" shall be only thee "fives" for example. means only three customers shall arrive on time 5.

I need to formulate a constraint the counts the number of equal values in x array and put a limit on it e.g z <= cap. //maybe z will be the number of equal values in the variable array x[i], or another way.

this is my trial,

int n=...; // number of customers

range costm=1..n; 

int P[costm]=...; // preferable customer arrival time

int cap=...;  // limit on how may customer shall arrive each time

dvar int+ x[costm]; // customer arrival time --> integer 
dvar boolean z[costm][costm];    // if customer i will arrive at the same time of cutomer j 

minimize sum (i in costm) abs(x[i]-P[i]);

subject to {

C3:forall ( i,j in costm:i!=j) z[i][j]==(x[i]==x[j]); // defining z:  z=1 if customer i will arrive at the same time of cutomer j 
C4: sum (i,j in costm:i) z[i][j] <=cap; // to limit the number of customers arriving at the same time 

but the above code did not work properly. since sum (i,j in costm:i) z[i][j] is not the number of customers arrive at the same time.

Thanks In Advance;

Hi,

let me share a small example to help you do the count:

int n=4;
range r=1..4;

dvar int x[r] in r;
dvar boolean xx[i in r][j in r]; // true if x[i]==j
dvar int count[v in r]; // number of value v in x

subject to
{

// example

x[1]==2;
x[3]==2;
x[2]==4;
x[4]==1;

// end of example

forall(i in r,j in r) xx[i][j]==(x[i]==j);
forall(i in r) count[i]==sum(j in r) xx[j][i];

}

execute
{
writeln(count);
}

gives

[1 2 0 1]

NB:

if you were using CPO then you could use count:

using CP;

int n=4;
range r=1..4;

dvar int x[r] in r;

dvar int countv[v in r]; // number of value v in x

subject to
{

// example

x[1]==2;
x[3]==2;
x[2]==4;
x[4]==1;

// end of example

forall(i in r) countv[i]==count(x,i);
}

execute
{
writeln(countv);
}

regards

Originally posted by: zab.a

Thank you Alex for your reply,

it is very helpful since I now know about count function in cplex, btw, I am using CPLEX Studio IDE 12.9.0 .

however, I would like to count any value in the array of variable x regardless of the value of index j in x. 

e.g. x[i] = [15 20 20 20 14] , here i=1..5 . so that this line of code you proposed: forall(i in r,j in r) xx[i][j]==(x[i]==j);  unfortunately , will not work with this case .

May be my explanation was not that clear, but now I want to count and constrain the number of times a variable x[i] has the same value. in other words:

 scenario 1 (simpler): if variable x[i] will have similar values in its array, I want to constrain the number of those equal values. e,.g limiting the number of having equal values in array x[i] to be only two times. 

  scenario 2 (more detailed level): to constrain how many times a certain value ex. 20 shall be obtained in array x[i] . e.g. the value of 20 obtained only one time, the value of 3 obtained only 2 times, value x if 7 obtained only 2 times and so on.

Thank you for your support,

Hi,

Let me adapt my example to your values.

With your values

int n=5;
    range r=1..n;
    range r2=1..20;

    dvar int x[r] in r2;
    dvar boolean xx[i in r][j in r2]; // true if x[i]==j
    dvar int count[v in r2]; // number of value v in x

    subject to
    {

    // example

    x[1]==15;
    x[2]==20;
    x[3]==20;
    x[4]==20;
    x[5]==14;

    // end of example

    forall(i in r,j in r2) xx[i][j]==(x[i]==j);
    forall(i in r2) count[i]==sum(j in r) xx[j][i];

    }

    execute
    {
    writeln(count);
    for(var i in r2) if (count[i]!=0) writeln(count[i]," times ",i);
    }

gives

 [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 3]
1 times 14
1 times 15
3 times 20

with regards to scenario 2 once you have the count decision variables you may use them in a constraint.

regards

Originally posted by: minayekta

hi; 

i'm a  student from iran. i need cplex academic version But unfortunately they do not accept my email. can you help me please to download it??

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