Originally posted by: quawarty

Hi,

I would like to know how to write the condition below using OPL.

Thank you for your help.

/*Parameters*/

int a;
int c = 2;
{int} I = {1,2};
{int} K = {1, 2, 3};

/*Decision variable*/

dvar int+ T[I][K];
//objective function
Min Z = a * ( c * (sum (i in I, k in K) (T[i][k] - l[i]));

/*Condition*/

a = 1 if T[i][k] >= l[i] forall (i in I, k in K)

a = 0 otherwise,
#DecisionOptimization
#OPLusingCPLEXOptimizer

Originally posted by: SystemAdmin

You could solve your model with CP Optimizer with a constraint like

a == prod(i in I, k in K) (T[i][k] >= l[i]);

I believe a is a decision variable, right?

Here is a code sample that may help:

using CP;
 
/*Parameters*/
int  c = 2;
{int} I = {1,2};
{int} K = {1, 2, 3};
int l[I] = [2,4];
 
/*Decision variable*/
dvar boolean a;
dvar int+ T[I][K]; 
dexpr int Z = a * ( c * (sum (i in I, k in K) (T[i][k] - l[i])));
 
 //objective function
minimize Z;
subject to {
  a == prod(i in I, k in K) (T[i][k] >= l[i]);
  // other constraints
}

#DecisionOptimization
#OPLusingCPLEXOptimizer

Originally posted by: quawarty

> Thank you for your reply.

I would like to use condition instruction.

g = 0 

if  ei =< Ti <= li g = 1 

if Ti >= li:

Could you please tell me if what I did is correct or not?
Thank you for your help.

//Notation// 
//----------------------------------// 

int n = 3; range V = 1..1; range P = 1..2; range N = 0..n+1;
/* set of customers and   depots (N.B. depot is represented by the two vertices )*/ 
//Parameters// 
//------------------------------------//   

int q[N0][P] =...;   ;  
/* amount of a product p provided or required by customer */ 

int d[N][N] = ...;
/* travel distance between customer*/ 

int e[N] = [0, 0, 0, 0, 0]; 
/* lower bound of the time windows*/ 

int l[N] = [5, 2, 6, 5, 18];
/* upper bound of the time windows*/ 

int cs = 2; 

int E= -1; 

int g = 0; 
//--------------------------------------------------// 
//Decision variables// 
//--------------------------------------------------// dvar int+   f[N][N][P]; 
/* load of the vehicle  by product p passing through the arc (i,j)*/ dvar int+   T[N];     
/*continous variable indicationg the time at which the vehicle strats serving pickup customer*/ dvar 

boolean  x[N][N][P];
/* = 1 if the arc (i,j)*/ dvar int+    h;   
//--------------------------------------------------// 
//Objective fucntion// 
//--------------------------------------------------// minimize sum (i in N, j in N, p in P) (d[i][j] * x[i][j][p]) +  cs * h + g * E* (sum (i in N)(T[i] - l[i])); 
/* Minimize the total distance */   
/* Constraint: customer is  visited exactly once*/ subject to 
{   forall(i in N) 

if (g == 1) (T[i] >= l[i]); 

else (e[i] <= T[i] <= l[i]);

#DecisionOptimization
#OPLusingCPLEXOptimizer