Dynamic Vehicle Routing in MATSim (Michał Maciejewski)

Poznan University of Technology
Department of Motor Vehicles and Road Transport
ZPSiTD
Dynamic Vehicle Routing in MATSim
Simulation and Optimization
Michal Maciejewski
michal.maciejewski@put.poznan.pl
www.michal-maciejewski.pl

Agenda
• Dynamic Vehicle Routing Problem
– Static VRP
– Dynamic VRP
• DVRP Optimizer
– Models
– Algorithms
• MATSim + DVRP Optmizer
– Recent results
– Future plans
2

CVRP
• CVRP = Capacitated Vehicle Routing Problem
• Input data
– 1 depot (node 0)
– n customers (nodes 1…n)
– k vehicles
– c ij travel cost for link i→j
– d i demand of node i
– C vehicle capacity
• Goal: minimal-cost routes
d 2
2
d 1 5 d 5 d 8
1
8
d 4
d 7
4
7
6
d 6
0
9
d 9
3
d 3
• Constraints:
– each route starts and ends at the depot
– each customer visited exactly once
– capacity of vehicles is never exceeded
3

CVRP
• CVRP = Capacitated Vehicle Routing Problem
• Input data
– 1 depot (node 0)
– n customers (nodes 1…n)
– k vehicles
– c ij travel cost for link i→j
– d i demand of node i
– C vehicle capacity
c 12 2 c 25
d 1 5 d 5 d 8
1
c 50 8
c 01 c 08
c 83
d 4
d 2
d 7
4
c 40
c 74 c 06 c 90 c 39
6
9
7 c 67 d 6
d 9
0
3
d 3
• Goal: minimal-cost routes
• Constraints:
– each route starts and ends at the depot
– each customer visited exactly once
– capacity of vehicles is never exceeded
R 1 = {1, 2, 5}
R 2 = {8, 3, 9}
R 3 = {6, 7, 4}
d 1 + d 2 + d 5 ≤ C
d 8 + d 3 + d 9 ≤ C
d 6 + d 7 + d 4 ≤ C
total cost = c 01 + c 12 + c 25 + c 50 +
+ c 08 + c 83 + c 39 + c 90 +
+ c 06 + c 67 + c 74 + c 40
4

VRP types
• Most popular types (Toth, Vigo)
• DCVRP = Distance-Constrained VRP
• VRPB = VRP with Backhauls
• VRPTW = VRP with Time Windows
• VRPPD = VRP with Pickup and Delivery
• VRPBTW = VRP with Backhauls and TW
• VRPPDTW = VRP with P&D and TW
5

Dynamic VRP
• DVRP properties (Larsen et al., 2007)
– Not all information relevant to the planning of the routes is known by the
planner before the routing process begins
– Information can change after the initial routes have been constructed
• Types of requests
– advance requests (static; known in advance)
– immediate requests (dynamic; dynamically appearing)
6

Dynamic VRP
• DVRP properties (Larsen et al., 2007)
– Not all information relevant to the planning of the routes is known by the
planner before the routing process begins
– Information can change after the initial routes have been constructed
• Types of requests
– advance requests (static; known in advance)
– immediate requests (dynamic; dynamically appearing)
diversion from
the current destination
7

Framework for DVRP
• General scheme
INITIAL DATA
OPTIMIZER
events
routes
CONCURRENT ON-LINE PROCESSES
CUSTOMER
SERVICE
TRAFFIC
MONITORING
FLEET
MANAGEMENT
9

Classification of DVRP
• Degree of dynamism vs. objective (Larsen et al., 2007)
10

Why DVRP + MATSim?
• Planning Demand Responsive Transport services
– service topology and principles
– demand modelling (market prediction)
– pricing
– algorithms
– costs
– inter-modal dependencies and sustainability
• Other services, e.g.
– taxi
– courier (demand from external data)
• Benchmarking DVRP algorithms on more realistic test cases
– real network + travel times
– demand (for transport services)
11

Agenda
• Dynamic Vehicle Routing Problem
– Static VRP
– Dynamic VRP
• DVRP Optimizer
– Models
– Algorithms
• MATSim + DVRP Optimizer
– Recent results
– Future plans
12

Current status for DVRP Optimizer
• MDDVRPTW = Multi-Depot Dynamic VRP with Time Windows and
Dynamic Travel Times/Costs
– m depots
– n customers
– k vehicles
– c ij (t d ) dynamic travel cost for link i→j
– t ij (t d ) dynamic travel time for link i→j
– d i demand of node i
i
– C k vehicle capacity
– [E k , L k ] time window of vehicle k
– [a i , b i ] time window of request i
• Missing:
– pickup & delivery (for shared many-to-many services)
– soft time windows
13

Current status for DVRP Optimizer
• Supported problems (fully/partially)
14

Request - state diagram
16

Route - state diagram
17

VRP process
Route - plan
Route - status
Request 1 - status
Request 2 - status
Request 3 - status
20

Waiting strategies
immediate
request
• Waiting strategies
– earliest departure/arrival
– latest departure/arrival
21

Routes
24

Routes
25

Routes
26

Routes
27

Routes (final results)
28

Agenda
• Dynamic Vehicle Routing Problem
– Static VRP
– Dynamic VRP
• DVRP Optimizer
– Models
– Algorithms
• MATSim + DVRP Optimizer
– Recent results
– Future plans
30

Architecture
• Data flows
• Allows for offline optimization
1. Run MATSim simulation scenario
2. Process traffic data
3. Run VRP Optimizer with external request data
31

Road network to graph mapping
• Input:
– road network
– locations (depots, customers…)
• Output
dynamic
– graph G=
– least-cost arcs
• travel distances/costs
• travel times
• sequence of visited nodes/links
(Path in MATSim)
• 100 customers + 1 depot
10,100 arcs
• 1000 customers + 10 depots
1,019,090 arcs
32

Arc (shortest path) estimation
• Data source
– LeastCostPathCalculator TravelTimeCalculator ... TravelTimeData
– TravelTimeData – contains travel times for a single link for each time slice
within the simulation
– Default precision is 15 min (the length of a time slice)
• Calculation (trivial)
– for each arc find the “shortest” path for each (15-min) time slice, i.e. (travel
time, travel distance, sequence of nodes/links)
– 100 customers + 1 depot, 24-hour simulation, 15-minute time slices
10,100 arcs * 96 s-path/arc = 969,600 shortest paths
– 1000 customers + 10 depots,...
97,832,640 shortest paths
• Calculation (more sophisticated)
– for each arc find the “shortest” path for each SENSIBLE time slice
– SENSIBLE because considering constraints (mostly time-related) of vehicles,
depots, customers and requests
33

Waiting strategies
• Earliest Departure/Arrival
– A vehicle departures at 9:00 (earliest possible departure time)
– TT_D(t): getTravelTimeOnDeparture(int departureTime)
(if (mod(t, binSize) != 0) – linear interpolation)
– The vehicle will arrive at a destination at 9:00 + TT_D(9:00)
• Latest Departure/Arrival
– A vehicle must arrive at the next stop by 10:00 (latest possible arrival time)
– TT_A(t): getTravelTimeOnArrival(int arrivalTime)
(if (mod(t, binSize) != 0) – linear interpolation)
– The vehicle must start out at 10:00 - TT_A(10:00)
• Instead of “Backward Dijkstra-like algorithms” a calculation of TT_A(t)
based on TT_D(t)
– TT_A(t+TT_D(t)) = TT_D(t)
– TT_A are not calculated with a constant time gaps have to be “normalized”
34

Network
36

Route 1
37

Route 1
38

Route 1
39

Route 1
40

Architecture
• Data flows
• Bi-directional mappings
– Person (Vehicle/Agent?) Vehicle
– Plan Schedule (Route)
– Activity/Leg Request/Trip
– ...
41

Online optimization
• Full integration of MATSim and VRP Optimizer
INITIAL DATA
OPTIMIZER
events
routes
CONCURRENT ON-LINE PROCESSES
CUSTOMER
SERVICE
TRAFFIC
MONITORING
FLEET
MANAGEMENT
42

Thank you…
43