Working SD

vrp.mod

/*********************************************
 * OPL 12.5 Model
 * Author: crash
 * Creation Date: Mar 6, 2013 at 3:33:35 PM
 *********************************************/

using CP;

// Nodes
tuple node { string name; float lat; float lon; int x; int y; int tmin; int tmax; }
{node} AllNodes = ...;
int N = card(AllNodes);
range nodes = 0..N-1;

// Edges
tuple edge {int i; int j;}
setof(edge) AllEdges = { <i,j> | i,j in nodes : i != j }; // not filtered!
setof(edge) OrderedEdges = { <i,j> | ordered i,j in nodes};
int Dist[OrderedEdges] = ...;
 
// Deliveries
tuple delivery {int destination; int from; int numpalettes;}
{delivery} Deliveries = ...;

// Remove superfluous thingies
sorted {int} clients = { d.from | d in Deliveries : d.numpalettes > 0 } union { d.destination | d in Deliveries : d.numpalettes > 0 };
sorted {int} cities = {0} union clients;
int numCities = card(cities);

int demand[t in cities] = sum (d in Deliveries : d.destination == t) d.numpalettes;
int outgoing[t in cities] = sum (d in Deliveries : d.from == t) d.numpalettes;
int orders[from in cities, dest in cities] = sum (d in Deliveries : d.from == from && d.destination == dest) d.numpalettes;

int tmin[t in cities] = item(AllNodes, t).tmin;
int tmax[t in cities] = item(AllNodes, t).tmax;

setof(edge) Edges = { <i,j> | i,j in cities : i != j }; // filtered! :)
//
//execute {
// writeln(AllEdges);
// writeln(tmin);
// writeln(tmax);
//}  

// Camions
tuple camion {key int id;int capacity; int maxweight; int maxtime;}
{camion} Camions = ...;
 
// Travel time
int vitesse = 65; // km/h
int tempstrajet[<i,j> in OrderedEdges] = ftoi(round(Dist[<i,j>]/vitesse*60));
int tempsservice = 30;
 
// Decision variables
dvar boolean x[Edges,Camions];
dvar boolean y[Camions,cities];
dvar boolean takenby[Deliveries][Camions];

dvar int arrival[Camions][cities] in 1..numCities-1;
dvar int+ tarrival[Camions][cities];
dvar int+ quantity[cities][Camions];
//dexpr int r[w in cities][k in Camions] = sum (i in cities, j in cities : i!=j) ((y[k][i] + y[k][j] == 2 && arrival[k][i] <= arrival[k][w]) ? (orders[i][j] + orders[j][i]) : 0);


//sum(i in cities) (y[k][i] == 1 ? ((arrival[k][i] < arrival[k][j]) ? quantity[i][k] : 0) : 0);
//dvar interval timeofdelivery[i in clients][m] in i.tmin..i.tmax size 30;

edge E = <0,1>; // intermediary object
execute {
//  cp.param.NoOverlapInferenceLevel = "Medium";
//  cp.param.ElementInferenceLevel   = "Low";
  //cp.param.TemporalRelaxation      = "Off";
  cp.param.TimeMode                = "ElapsedTime";
  cp.param.TimeLimit               = 20;
};

//tuple Subtour { 
//  int ssize;
//	camion truck;
//	int subtour[cities];
//};
//{Subtour} subtours = ...;
 
minimize sum (<i,j> in Edges, m in Camions) Dist[<minl(i,j), maxl(i,j)>]*x[<i,j>,m];

subject to {
  	forall (k in Camions, i in cities)
  	  	y[k][i] == (((sum(<i,j> in Edges) x[<i,j>][k]) + (sum(<j,i> in Edges) x[<j,i>][k])) > 0);
  
	forall (k in Camions, j in cities)
	  	(sum(i in cities : j!=i) x[<i,j>][k]) == y[k][j];
	  	
  	forall (k in Camions, j in cities)
		(sum(i in cities : j!=i) x[<j,i>][k]) == y[k][j]; 
		
	forall (d in Deliveries)
	  	sum (k in Camions) takenby[d][k] >= 1;

	forall (d in Deliveries, k in Camions)
	  	(takenby[d][k] == 1) => (y[k][d.from] == 1 && y[k][d.destination] == 1);

//	forall (i in clients, k in Camions)
//		(quantity[i][k] >= 1) => y[k][i] == 1;
//
// 	forall (i in clients)
// 	  	((demand[i] + outgoing[i]) >= 1) == (sum(k in Camions) y[k][i] >= 1);

	// continuité  	
  	forall (p in cities, k in Camions)
  	  	((sum(i in cities : i!=p) x[<i,p>][k]) - (sum(j in cities : j!=p) x[<p,j>][k])) == 0;
	  	  	
  	forall (k in Camions, <i,j> in Edges : i!=0)
  	  	(x[<i,j>][k] == 1) => (arrival[k][i] + 1 == arrival[k][j]);
	  	  	
	// For each client, the aggregated quantity of all trucks must match the demand
	forall (i in cities)
	  	sum (k in Camions, d in Deliveries : d.destination == i) takenby[d][k] * d.numpalettes == demand[i];
	
	forall (d in Deliveries)
	  	sum (k in Camions) takenby[d][k]*k.capacity >= d.numpalettes;

	
//	forall (i in cities)
//	  	sum(k in Camions) quantity[i][k] == demand[i];	
//  	  		  	
//  	// The amount of palettes the truck is going to deliver must be inferior|equal to his capacity
//  	// (perhaps include dvar (c12)
//  	forall (k in Camions)
//  	  	sum(i in cities) quantity[i][k] <= k.capacity;
  	  	
	// respect timewindows
//	forall(j in clients, k in Camions)
//	  	(x[<0,j>][k] == 1) => (tarrival[k][j] >= (tempstrajet[<0,j>] + tmin[0]));
//
//  	forall (<i,j> in Edges : i!=0, k in Camions)
//  		(x[<i,j>][k] == 1) => ((tarrival[k][i] + tempstrajet[<minl(i,j), maxl(i,j)>] + (15 + 3*(quantity[i][k]))) <= tarrival[k][j]);
//  	
  	// min max timeframe for entry at client
//  	forall(i in cities, k in Camions)
//  		(y[k][i] ==1) => ((tmin[i] <= tarrival[k][i]) && (tarrival[k][i] <= tmax[i]));

  	// truck can't be longer than e.g. 12h on route
  	forall (m in Camions)
		m.maxtime >= ((sum (<i,j> in Edges) x[<i,j>,m]*(tempstrajet[<minl(i,j),maxl(i,j)>]+tempsservice))-tempsservice);
	
	// pickup is before delivery, by same truck
	forall (d in Deliveries, m in Camions)
	  	(takenby[d][m] == 1) => (arrival[m][d.from] <= arrival[m][d.destination]);
};

execute {
  	var unused = "We didn't use the following trucks: ";
  	var nUnused = 0;
	for (var k in arrival) {
		var num = 0;
		var last = 0;
		var timetotal = 0;
		var str = "- Camion "+k.id+": 0 -> ";
		for (var f = 1; f <= numCities-1; f++) {
			for (var i in y[k]) {
				if (y[k][i] == 1 && arrival[k][i] == f) {
				  	if (!(last == 0 && i == 0)) {
				  	  	E.i = Math.min(last, i);
				  	  	E.j = Math.max(i, last);
				  		timetotal += tempstrajet[E] + tempsservice;
				  		last = i;
				  		if (i!=0) {
				  			str += i+" -> ";
      					}				  		
       				}
					num++;
	   			}			    
	  		}
  		}
  		timetotal -= tempsservice;
  		if (num > 0) {
	  		writeln(str + "0 (total time: "+timetotal+")");
  		} else {
  		  	nUnused++;
  		  	unused += "c"+k.id + " ";
    	}  		    		  		  		  
 	}
 	if (nUnused > 0) {
 		writeln(unused); 
  	} 	     
}