Stefan Schröder - Simulating Carriers - MATSim

Simulating carriers: time-dependent vehicle routing
MATSim User Meeting 2012,
Stefan Schröder (stefan.schroeder@kit.edu)
Institut für Wirtschaftspolitik und Wirtschaftsforschung (IWW) Fachgebiet Netzwerkökonomie
KIT – Universität des Landes Baden-Württemberg und
nationales Großforschungszentrum in der Helmholtz-Gemeinschaft
www.kit.edu

Agenda
! Motivation
! Problem
! Algorithm
! Case Study
! Conclusion
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Motivation
research project: conceptual and concrete contribution to behavioral
freight modeling
concept and test-implementation of multi-tiered freight framework
(e.g. shipper, transport service provider and carrier)
streamlining of carrier layer new MATSim agent
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Motivation
Passenger traffic:
persons conduct activities (=> travel through space => traffic)
individual calculus: maximize utility, activity duration (+), travel time (-)
typical decisions: route choice, activity sequence, mode choice
Freight traffic:
carriers offer transport services (=> travel through space => traffic)
calculus: minimize costs, activity duration (-), travel time (-)
typical decisions: route choice, activity sequence, vehicle scheduling,
mode choice
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Motivation
How to model route choice, activity sequence and vehicle
scheduling decisions consistently
Consistent
given information about traffic system, decisions are made such
that total costs are minimized
Time-dependent vehicle router coupled with physical simulation
of MATSim
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Agenda
! Motivation
! Problem
! Algorithm
! Case Study
! Conclusion
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Vehicle Routing Problem
Problem
Solution
Source: http://neo.lcc.uma.es/radi-aeb/WebVRP/
Single Depot VRP with capacity constraints
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Vehicle Routing Problem - Variety
VRP type
Capacitated (CVRP)
Time Windows (VRPTW)
Pickup and Delivery (VRPPD)
Multiple Depots (VRPMD)
Heterogeneous Fleet (VRPHF)
CVRPTWPDMDHF
...
Costs
Constant costs
Time-dependent costs
Demand
Deterministic
Stochastic
Problem type
Combinatorial problem
Search space grows fast with #nodes
Solution approaches
Exact:
Branch-and-Bound, Branch-and-Cut, ...
(Meta)Heuristics:
Tabu Search, Simulated Annealing, ...
Initial solution
Search through neighborhood
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Agenda
! Motivation
! Problem
! Algorithm
! Case Study
! Conclusion
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Algorithm – Ruin-and-Recreate Principle
Schrimpf et al. (2000) ★ ,
(1) can be implemented as general framework, (2) simple operations
Initial Solution
Initial plan (vehicle routes)
Ruin
Remove customer from plan
Recreate
Re-Insert customer to plan
Threshold Accepting
Evaluate solution
Final Solution
★
Record Breaking Optimization Results Using the Ruin and Recreate Principle,
Gerhard Schrimpf,∗ Johannes Schneider,† Hermann Stamm-Wilbrandt,∗ and Gunter
Dueck∗, Journal of Computational Physics, 2000.
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Algorithm – Ruin-and-Recreate
Initial Solution
Ruin
Random Ruin (p=0.5,#customer=0.5)
Radial Ruin (p=0.5,#customer=0.3)
Recreate
Best Insertion (min. marginal cost)
Threshold Accepting
Final Solution
NewSolution.result < OldSolution.result + T
T 0
T = T 0
* exp(−ln2* x
0.1 )
Determined by random walk
€ Tolerant (1.Iteration) Greedy (last Iter.)
€
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Algorithm – Radial Ruin
Source: Schrimpf et. al (2000)
Select customer randomly
Identify neighborhood
(e.g. time, space)
Ruin neighborhood
=> List of customers not
served
Re-insert customers
subject to constraints
(where MC is minimal)
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Algorithm – Time-dependency
Time-dependent marginal costs are additional costs attributed to
inserted customer
MC(h)=c(i,h,depTime@i) + c(h,j,depTime@h) – c(i,j,depTime@i) + Δ
Δ = changes in travel time due to changes in departure times at
subsequent customers
Time-dependent travel times MATSim‘s TDSPA
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Algorithm – Implementation & Verification
Implementation in JAVA, available at contrib.freight.vrp
Verification on test instances:
Christophides, Mingozzi and Toth (CVRP)
Solomon (CVRPTW)
Li and Lim (CVRPTWPD)
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Agenda
! Motivation
! Problem
! Algorithm
! Case Study
! Conclusion
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Case – Goals
Illustrate VRP-algorithm
Several carrier vehicles can be simulated along with
passenger vehicles
Carriers can pickup congestion and adapt to changes in the
traffic system (they have plan strategies)
Carriers can score plans and have plan memory
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Case – Setup
Network:
Link-Cap: 7 Veh/h
Broadway-Link-Cap: 10 Veh/h
Outer ring: 10 Veh/h
Free-Speed: 50km/h
Depot i
W
A
W
A
Depot j
Persons:
#Persons: 400
Activities.: home, work
Locations
Departure Home: 7:00 – 10:00
Departure Work: 15:00 – 18:00
Carriers:
#Carriers: 10
Location
#Shipments: UD[10-40]
Shipment size: UD(0-10]
#Vehicles: 10; Vehicle Cap: 40
Small Delivery TW: 30 min., UD
[08:00am-12:00am]
Operation-Start: UD[6:30am
-8:30am]
Simulation:
#Iterations: 100
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Case – Simulation
Initial Plans
Vehicle routing based on empty road network (initialize routers)
Simulation
BeforeSim: Drivers are created from carrier plans
Scoring
score = −50 €/h * hours −1€/km * km −1000 €/h * hours_ tooLate
Re-Planning
−100 €/vehicle * vehicles
€
Persons:
Best-Plan (0.95)
Re-Route (0.05)
Carriers:
Best-Plan (0.9)
Re-Schedule (0.05)
Re-Route (0.05)
select best carrier-plan
transform best plan into initial solution for
ruin-and-recreate algorithm
do td-vehicle-routing on loaded network of the
last iteration
re-transform result into carrier-plan
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Case – Carrier Score
Starting with bad score; initial
plans made on empty road
network
Due to congestion, carriers
miss almost every time window
In the course of iterations,
carrier can adapt to traffic
conditions
Total score can be increased
by 78% ( costs of carriers)
Red line: sum of best scores; Green line: sum of scores of executed plan; Blue: Avg. plan score per agent
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Case – Carrier Time
Initial plan: Almost every time
window missed
Adaptations lead to a decrease
of time too late
Time on road can be reduced
by 34%
When late time decreases,
waiting time increases slightly
Red: total duty time; Green: total time on road; Blue: total waiting time; Yellow: total time too late
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Case – Verification
0
-50000
1 11 21 31 41 51 61 71 81 91 101
Green: improvements
attributed to passengers
Re-routing little better than
doing nothing
-100000
-150000
-200000
noStrat
reRoute
reSchedule
Re-scheduling is superior (30%
better than other strat.)
Re-Route: +2% computation
time
Re-Schedule: +26%
computation time
-250000
sum of best scores
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Agenda
! Motivation
! Problem
! Algorithm
! Case Study
! Conclusion
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Conclusion
VRP library that can solve a variety of vehicle routing problems
Carrier as new MATSim-Agent who can consistently consider changes in the
traffic system
MATSim-Agent that manages and employs a vehicle fleet
Optimization of the operations of the number of vehicles vs. of a single
vehicle => varying number of simulated vehicles
Decision support system in City-Logistics
From economic point of view, it is interesting for single logistics decision makers
One step to modeling freight traffic
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Conclusion
Challenges:
How to calibrate a vehicle router (an optimization problem with constraints)
empirically (here: normative model with assumption of complete
information of the modeler)
Need for tools like we have in discrete choice theory
Thank you for your attention!
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Backup
Large-scale scenarios
Computation time: very good vs. good results
Comp.Time: TD Shortest Path Algo
Memory consumption: RR requires travel times from all customers to
all customers => n*n*timeSlices (n = #customers)
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Backup – Solomon’s benchmarking (TW,100)
- Converge to best known
solution
- Marginal costs increase
- Very good solution are
expensive
- Good solutions are
affordable
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Backup – Food Retailing
Synthrade Hanno Friedrich
Closing the gap between inter-regional and intra-regional models
Evaluation of policy (city logistics) measures and impact
assessment of food retailing
Impact of E-retailing (REWE)
Connecting consumers‘ demand with freight logistics
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Backup – Broadway with more cap
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Backup – Broadway with more cap
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Vehicle Routing Problem - CarrierPlan
Problem
Solution
...
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Case – Along with passenger
CarrierAgentTracker keeping track of Drivers initiated by Carriers
CarrierAgentTracker listens to Mobsim-Events and informs
respective carriers
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Case – Bad initial solution
0
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
101
-50000
-100000
-150000
-200000
noStrat
reRoute
reSchedule
-250000
-300000
-350000
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Vehicle Routing Problem – CVRP Formal
min
∑
∑
r∈K (i, j )∈A
r
c ij
x ij
Min. costs
€
s.t.
∑
j∈N +
∑
r∈K
∑
i∈N +
∑
i∈N +
∑
i∈N +
∑
i∈N
x r ij
= y r i
, i ∈ N, r ∈K,
y i r =1, i ∈ N,
r
x ih
r
x 0i
−
r
x i(n +1)
∑
j∈N +
r
x hj
=1, r ∈K,
q i
y i r ≤ Q,
=1, r ∈K,
= 0, h ∈ N, r ∈K,
r ∈K
Every customer is served only once
Tour is consistent, flow equation
Capacity restriction
r
x ij
y i
r
c ij
Q
binary, (i, € j) ∈ A, r ∈K
binary, i ∈ N, r ∈K
transport costs from customer i to j
Vehicle − capacity
q i
K
A
N
demand of customer i
set of routes
set of arcs
set of customer
€
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