set VEHICLE ordered;
set WAYPNTS {VEHICLE} ordered;


param sizeWaypnts{VEHICLE};             #number of waypoints for each vehicle

set PAIRS {v in VEHICLE} := {i in WAYPNTS[v], j in WAYPNTS[v]: i!=j};


var E{v in VEHICLE, PAIRS[v]} binary;            #sweeping variable
var u{v in VEHICLE, WAYPNTS[v]}, >= 0, <= sizeWaypnts[v]-1;                            #sequence number in a tour

subject to LeaveOnce {v in VEHICLE, i in WAYPNTS[v]}:
   sum {(i,j) in PAIRS[v]} E[v,i,j] = 1;

subject to VisitOnce {v in VEHICLE, j in WAYPNTS[v]}:
   sum {(i,j) in PAIRS[v]} E[v,i,j] = 1;

# subtour elimination Miller, Tucker and Zemlin (MTZ) (1960)
subject to MTZ{v in VEHICLE,(i,j) in PAIRS[v]: i != 1}: u[v,i]-u[v,j] + (sizeWaypnts[v]-1)*E[v,i,j] <=sizeWaypnts[v]-2;