Discussion :

[Guerlain]

Bonsoir

Je dois résoudre le problème IRP avec Cplex mais je suis novice % a ce logiciel

j'ai commencé a codé mais je ne sais pas comment inclure une instance de donnée

Ci joint le modèle mathématique le code que j'ai fait et l'instance de donnée

S'il y a qq chose pas clair merci de me laisser vos commentaire.

Code :

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int n=...;// nombre des sommets 
int T=...;// Horizon de planification 
 
tuple arc { 
int i; int j;
} 
setof (arc) arcs = {<i,j> | ordered i,j in 0..n : i!=j};// l'ensemble des arcs 
float A[arcs] = ...; 
 
int q[i in 1..n][t in 1..T] = 1;// la quantité de produit livré a un sommet
 
int I[i in 1..n][t in 1..T] = 2; // niveau de stock a un sommet 
 
float Q = ...; // la capacité du fournisseur 
 
int c =...;// la capacité de véhicule 
 
int t [1..T]=...;// periode temps 
 
tuple Position {
    key int id;
    int x;
    int y;
  };
 
  tuple Demand {
    key int id;
    int q;
  };
 
  {Position} Positions = ...;
  {Demand} Demands = ...;
 
  {int} Customers = { p.id | p in Positions };
 
  tuple triplet { 
  int c1; 
  int c2; 
  int d; 
  };
 
  {triplet} Dist = { <p1.id,p2.id,(sqrt(pow(p2.x-p1.x,2)+pow(p2.y-p1.y,2)))> | p1, p2 in Positions };
 
  execute {
     writeln(Dist);
  };
 
 
// Decision variables
 
dvar boolean y[0..n][0..n][1..T];/* = 1 if the arc (i,j)*/
 
dvar boolean x[0..n]; /* = 1 if the node j*/
 
dexpr float Cobj= 
sum(ordered i,j in 0..n : i!=j)sum(t in 1..T) A[<i,j>]*y[i][j][t]+sum(i in 1..n)sum(t in 1..T) w[i]*x[i][t]+
sum(i in 1..n)sum(t in 1..T) h[i]*I[i][t]+
sum(t in 1..T) h[0]*I[0][t] ;
 
 
//objective function 
 
minimize Cobj;
 
//constraints 
 
subject to{ 
 
forall (t in 1..T )
I[0][t]=I[0][t-1]+r[0][t]-sum(i in 1..n)q[i][t]; //Inventory definition at the supplier
 
forall (t in 1..T )forall (i in 1..n )
I[i][t]=I[i][t-1]-r[i][t]+q[i][t]; //Inventory definition at the retailers
 
forall (t in 1..T )forall (i in 1..n )
I[i][t]>=0; // Stockout constraints at the retailers
 
forall (t in 1..T )forall (i in 1..n )
I[i][t]<=U[i]; // Born Sup
 
forall (t in 1..T )forall (i in 1..n )
I[i][t]>=L[i]; // Born Inf
 
forall (t in 1..T )forall (i in 1..n )
q[i][t]>=U[i]*x[i][t]-I[i][t-1]; // Order-up-to level constraints
 
forall (t in 1..T )forall (i in 1..n )
q[i][t]<=U[i]-I[i][t-1]; // Order-up-to level constraints
 
forall (t in 1..T )forall (i in 1..n )
q[i][t]<=U[i]x[i][t]; // Order-up-to level constraints
 
forall (t in 1..T )
sum(i in 1..n)q[i][t]<=Q; // Capacity constraints
 
 
forall (t in 1..T )
sum(i in 1..n)q[i][t]<=Q*x[0][t]; // Routing constraints
 
 
forall (t in 1..T )forall (i in 1..n )
sum(j in 1..n : j<i)y[i][j][t]+sum(j in 1..n : j>i)y[j][i][t]=2*x[i][t]; // Routing constraints
 
forall (t in 1..T )forall (s in 1..n)
sum(i in 1..n)sum(j in 1..n : j<i)y[i][j][t]<=sum(i in 1..n)x[i][t]-x[s][t]; // Subtours elimination constraints
 
forall (t in 1..T )forall (i in 1..n )
q[i][t]<=1; // Nonnegativity and integrality constraints
 
forall (t in 1..T )forall (i in 1..n )forall (j in 1..n )
y[i][j][t]<=1;
 
forall (t in 1..T )forall (i in 1..n )forall (j in 1..n )
y[i][j][t]>=0;
 
forall (t in 1..T )forall (i in 1..n )
x[i][t]<=1;
 
forall (t in 1..T )forall (i in 1..n )
x[i][t]>=0;
 
forall (t in 1..T )forall (j in 1..n )
y[0][j][t]<=2;
 
forall (t in 1..T )forall (j in 1..n )
y[0][j][t]>=0;
 
};
execute { 
writeln ("objectif=", Cobj) 
}

les données :

Code :

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  TYPE:	ORDER-UP-TO-LEVEL-TSP
 COMMENT: NODE 1 REPRESENTS THE SUPPLIER
 COMMENT: THE QUANTITY ABSORBED BY RETAILER AND THE
          QUANTITY MADE AVAILABLE AT THE SUPPLIER 
          ARE CONSTANT OVER TIME
 TRANSPORTATION-COST-TYPE: EUC_2 (T(i,j)=
  T(J,I)=INT((SQRT((X(I)-X(J))**2+(Y(I)-Y(J))**2))+.5)
 
 DIMENSION:        6
 HORIZON:          3
 CAPACITY:       600
 id_SUPPLIER    x_COORD_STARTING    y_COORD_STARTING    STARTING LEVEL   QUANTITY MADE AVAILABLE    COST
   1                 436.0               498.0               1120                 2628              .30
  id    x_COORD_STARTING  y_COORD_STARTING   LEVEL  LEVEL_MAX LEVEL_MIN  QUANTITY_ABSORBED    COST
   2       391.0                96.0          84       168        0              84           .23
   3       268.0               146.0         166       249        0              83           .32
   4       358.0               133.0         112       168        0              56           .33
   5        12.0               256.0         170       255        0              85           .23
   6       165.0               108.0          98       147        0              49           .18