Hi
Request your support here. I am trying to base this link to do my model. I do not have Viya 4.0. What i want to achieve is slightly different. i have a bunch of nodes, one of them being a depot. I know which NodeID it is. I am trying to optimize routes for each vehicle. I have unlimited supply of vehicles.
My objective function is optimize total distance travelled as is the case in the link above.
My constraints are:
(a) The total demand on a given vehicle cannot exceed 3,400 at any point of time in its journey.
(b) All vehicles should come back to depot.
(c) The total distance travelled by a vehicle cannot exceed 3,000 miles.
(d) No stop constraints. I set an arbitary 400 here.
Here is my attempt. I am getting infeasibility. I know something is not right in the way I have set up the constraints.
/*Variables*/
%let capacity = 3400;
%let num_vehicles=40;
%let dist=3000;
%let max_stops=400;
proc optmodel;
set NODES;
str ModelNode {NODES};
num ModelLat {NODES};
num ModelLong {NODES};
num Volume {NODES};
num capacity = &capacity;
num num_vehicles = &num_vehicles;
read data CASUSER.vrpdata into NODES =[NodeID] ModelNode ModelLat ModelLong Volume ;
set ARCS = {i in NODES, j in NODES: i ne j};
set VEHICLES = 1..num_vehicles;
num depot = 99999;
/* define the arc dist as the rounded Euclidean distance */
num dist {<i,j> in ARCS} = (if j ne depot then GEODIST(ModelLAt[i],ModelLong[i],ModelLat[j],ModelLong[j],'M') else 0);
/* if j=depot, this means that we want to treat the last leg to depot as 0 so that the truck goes to depot as home base free */
/* Creating an Sparse Matrix to remove any unwanted arcs*/
set LOGICAL_ARCS = {<i,j> in ARCS: dist[i,j] <= &dist};
/*print {<i,j> in LOGICAL_ARCS} dist; */
/* Flow[k] is the amount of demand carried by vehicle k */
var Flow {VEHICLES} >= 0 <= capacity;
/* UseNode[i,k] = 1, if and only if node i is serviced by vehicle k */
var UseNode {NODES, VEHICLES} binary;
/* UseArc[i,j,k] = 1, if and only if arc (i,j) is traversed by vehicle k */
var UseArc {LOGICAL_ARCS, VEHICLES} binary;
/*-----------------------OBJECTIVE FUNCTION-------------------------------*/
/* minimize the total distance traversed */
min TotalCost = sum {<i,j> in LOGICAL_ARCS, k in VEHICLES} dist[i,j] * UseArc[i,j,k];
/*----------------------------CONSTRAINTS-------------------------------------*/
/* each non-depot node must be serviced by at least one vehicle */
/*ASSIGNMENT CONSTRAINT*/
con Assignment {i in NODES diff {depot}}:
sum {k in VEHICLES} UseNode[i,k] >= 1;
/* for{k in VEHICLES} fix UseNode[depot,k] = 1; */
con VisitDepot {i in NODES diff {depot}, k in VEHICLES}:
UseNode[i,k] <= UseNode[depot,k]
suffixes=(block=k);
/* if a vehicle visits a particular node, then it has to exit via the depot */
/*DISTANCE CONSTRAINT*/
CON Distance {k in VEHICLES}:
sum {<i,j> in LOGICAL_ARCS} dist[i,j] * UseArc[i,j,k] <= &dist;
/*STOPS CONSTRAINT*/
CON Stops {k in VEHICLES}:
sum {i in NODES diff {depot}} UseNode[i,k] <= &max_stops;
/* some vehicle k traverses an arc that leaves node i if and only if UseNode[i,k] = 1 */
/* LEAVE NODE CONSTRAINT */
con LeaveNode {i in NODES, k in VEHICLES}:
sum {<(i),j> in LOGICAL_ARCS} UseArc[i,j,k] = UseNode[i,k];
/* some vehicle k traverses an arc that enters node i if and only if UseNode[i,k] = 1 */
/* ENTER NODE CONSTRAINT */
con EnterNode {i in NODES, k in VEHICLES}:
sum {<j,(i)> in LOGICAL_ARCS} UseArc[j,i,k] = UseNode[i,k];
/* the amount of Volume supplied by vehicle k to node i must equal Volume if UseNode[i,k] = 1; otherwise, it must equal 0 */
/*FLOW BALANCE CONSTRAINT*/
con FlowBalance {k in VEHICLES}:
sum {i in NODES diff {depot}} Flow[k]
= sum {i in NODES diff {depot}} Volume[i] * UseNode[i,k];
/* if UseArc[i,j,k] = 1, then the flow on arc (i,j) must be at most capacity
if UseArc[i,j,k] = 0, then no flow is allowed on arc (i,j) */
/*VEHICLE CAPACITY CONSTRAINT*/
con VehicleCapacity {k in VEHICLES}:
sum {<i,j> in LOGICAL_ARCS } Flow[k] <= sum {<i,j> in LOGICAL_ARCS} Flow[k].ub * UseArc[i,j,k];
/* decomp by vehicle *//*DECOMPOSITION*/
for {i in NODES, k in VEHICLES} do;
LeaveNode[i,k].block = k;
EnterNode[i,k].block = k;
end;
for {k in VEHICLES} Distance[k].block = k;
for {k in VEHICLES} Stops[k].block = k;
for {i in NODES diff {depot}, k in VEHICLES} FlowBalance[k].block = k;
for {k in VEHICLES} VehicleCapacity[k].block = k;
/* solve using decomp (aggregate formulation) */
solve with MILP / decomp varsel=ryanfoster presolver=basic relobjgap=0.01;
/* OUTPUT */
/* create solution data set */
create data solution_data (where=(x1<>x2 and y1<>y2)) from [i j k]=
{<i,j> in LOGICAL_ARCS, k in VEHICLES: UseArc[i,j,k].sol > 0.5}
StartNode=ModelNode[i] StartCity=ModelNode[i] x1=ModelLat[i] y1=ModelLong[i]
EndNode=ModelNode[j] EndCity=ModelNode[j] x2=ModelLat[j] y2=ModelLong[j]
flow=Flow[i,j,k] dist=dist[i,j]
function='line' drawspace='datavalue';
quit;
proc sgplot data=solution_data noautolegend;
scatter x=x1 y=y1 / datalabel=i;
vector x=x2 y=y2 / xorigin=x1 yorigin=y1 group=k noarrowheads;
xaxis display=none;
yaxis display=none;
run;
