Hello everyone,

I have a problem with a model for a single depot vehicle routing problem. Every time I run the model I get the solution 0E0. Can you tell me what's wrong with the model and why it doesn't work?

{int} V = ...; //Set of nodes Customers + Depots

{int} K = ...; //set of vehicles k

float Distance [V][V]= ...;

float Capacity [K] = ...;

float Demand [V] = ...;

dvar boolean X [V][V][K];

dvar float u[V];

int n = ...;

minimize

sum (i in V, j in V, k in K )

X[i][j][k] * Distance[i][j];

subject to {

// 16

forall(j in V)

sum (i in V, k in K)

X[i][j][k] == 1;

// 17

forall (i in V)

sum (j in V, k in K)

X[i][j][k] == 1;

// 18

forall (k in K, h in V)

sum (i in V) X[i][h][k] - sum (j in V) X[h][j][k] == 0;

//19

forall (k in K)

sum (i in V, j in V)

Demand[i] * X[i][j][k] <= Capacity[k];

//21 -24

forall(k in K)

sum (j in V)

X[1][j][k] <= 1;

//Subtour elimination

forall (k in K, i in 1..n, j in 1..n: i!=j)

u[i] - u[j] + n*X[i][j][k] <= n-1;

}

This is the dat file I am using.

V = {1, 2, 3, 4}; //set of all nodes

K = {1, 2}; // set of trucks

n= 4;

Distance = [

[0, 15, 10, 30],

[15, 0, 24, 23],

[10, 24, 0, 36],

[30, 23, 36, 0]

];

Capacity = [100, 120]; // capacity of vehicle k

Demand = [0, 30, 50, 40]; // demand for product of customer i

If you are expecting a different objective, add a constraint to reflect your expectation and see whether the model is still feasible. If the model becomes infeasible, conflict refiner should tell you which constraints are conflicting with your expectation.