! A Fleet Routing and Assignment model in LINGO.
Given a number of flights, each with a number of passengers to carry,
and a set of vehicle types, each with a capacity, how should
vehicles be assigned to flights, and vehicles be routed,
to carry the passengers at minimum cost;
! Keywords: Aircraft scheduling, Airline, Assignment, Fleet assignment,
 Fleet routing, FTL routing, Load assignment, Routing, Trucking, Vehicle routing;
  LOCN;                    ! List of locations or cities;
  VTYPE: CAP, CLEG, NVAIL; ! Vehicle types & attributes/fields;
  PERIOD;                  ! Period or Event index set;
  FLIGHT( LOCN, PERIOD, LOCN, PERIOD): NUMPASS; ! Flight demand info;
  V2F( VTYPE, FLIGHT): XVF; ! Vehicle flight combinations;
  VxL( VTYPE, LOCN): IDLEB; ! Vehicle locaton combinations;
  VxLxP( VTYPE, LOCN, PERIOD): IDLE; ! V, L, P combinations;
DATA: ! The cities in today's problem; LOCN = CHI MNN, KC_; ! The periods or event points in today's problem; PERIOD = P0600 P0630 P0700 P0730 P0800 P0830 P0900 P0930; ! Vehicles and their attribues; VTYPE, CAP, CLEG, NVAIL = B737 162 20 2 A320 150 19 4; ! Start and end point and passengers, each flight; FLIGHT, NUMPASS = CHI P0600 KC_ P0730 145 MNN P0600 CHI P0730 100 KC_ P0630 MNN P0930 130 CHI P0700 MNN P0830 120 MNN P0730 KC_ P0930 130 KC_ P0730 CHI P0900 135; ENDDATA ! To see the scalar version, click on Solver | Generate | Display model; ! Variables: XVF( v, i, p1, j, p2) = number vehicle of type v departing locn i in period p1, arriving at j in p2, IDLE( v, i, p) = number vehicles of type v idle on ground at i, just after period/event p IDLEB( v, i) = number vehicles of type v idle on ground at i, just before 1st period/event. ! Objective: Minimize cost; MIN = @SUM( V2F( v, i, p1, j, p2) : CLEG( v) * XVF( v, i, p1, j, p2)); ! Flow balance, Begin on ground + arrivals = ending on ground + departures; ! Begining period, vehicle v, city i; @FOR( VxL( v, i): [BAL0] IDLEB( v, i) = IDLE( v, i, 1) + @SUM( V2F( v, i, p1, j, p2) | p1 #EQ# 1: XVF( v, i, p1, j, p2)); ); ! Subsequent periods, flow into v, j, p = flow out of v, j, p; @FOR( VxLxP( v, j, p) | p #GT# 1: [BAL] IDLE( v, j, p-1) + @SUM( V2F( v, i, p1, j, p) : XVF( v, i, p1, j, p)) = IDLE( v, j, p) + @SUM( V2F( v, j, p, i, p2): XVF( v, j, p, i, p2)); ); ! Cannot use more planes than have in fleet; @FOR( VTYPE( v): [VAVAIL] @SUM( LOCN( i): IDLEB( v, i)) <= NVAIL( v); ); ! Capacity on leg i, p1, j, p2 must cover demand on leg; @FOR( FLIGHT( i, p1, j, p2): [FCOV] @SUM( V2F( v, i, p1, j, p2) : CAP( v) * XVF( v, i, p1, j, p2)) >= NUMPASS( i, p1, j, p2) ; ); ! The XVF variables must be general integer; @FOR( V2F( v, i, p1, j, p2): @GIN( XVF( v, i, p1, j, p2)) ); ! Optional features not included: Deadheading/Repositioning/RedEye flights, Cyclic schedule that repeat daily or weekly. Specified initial position of vehicles, Revenue/flight to allow selection of most profitable legs to fly in face of limited capacity. Random demand with safety capacity;