FREIGHT TRANSPORTATION SYSTEMS Producers who own or
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Transcript FREIGHT TRANSPORTATION SYSTEMS Producers who own or
Optimization Models
for
Long-haul Freight Transportation
Teodor Gabriel Crainic
Dept. Management and Technology
Université du Québec à Montréal
and
Centre for Research on Transportation
Université de Montréal/H.E.C./Poly
[email protected]
2000
Transportation Systems
Physical (Conceptual)
Infrastructure and Services
SUPPLY
Production, Consumption
of Goods and Services
DEMAND
Economic and legal environment
Movements of people, goods, vehicles = Traffic
Costs/profits, delays, energy, emissions, …
Transportation Systems
Physical (Conceptual)
Infrastructure and Services
SUPPLY
Production, Consumption
of Products and Services
DEMAND
Economic and legal environment
Movements of people, goods, vehicles = Traffic
Costs/profits, delays, energy, emissions, …
Transportation Systems
Physical (Conceptual)
Infrastructure and Services
Production, Consumption
of Products and Services
Modes and Services
Stations and Terminals
Vehicles and Convoys
Routes and Frequencies
Costs and Tariffs
Economic Criteria
Service Quality Criteria
Mode Choice
Multimodal Multicommodity Flows
Performance measures
Transportation Systems
Passengers
vs. Freight
User/Shipper vs. Carrier
Urban vs. Interurban/“Regional”
Uni- vs. Multi/Inter-modal
Integration ?
Intelligent Transportation Systems - ITS
Passenger Transportation
Customized
(door-to-door) services:
private cars, walking, other modes vs.
Consolidation transportation: transit
Urban
Multimodal
Short planning horizons (hours)
dependent upon time-of-day, day-of-week,
week-of-year, …
“authorities plan, users decide”
Freight Transportation
Producers
who own or operate the
transportation fleet (and infrastructure) vs.
“For hire” carriers
Long-haul (intercity) transportation vs.
“Local” vehicle routing and distribution
Multimodal transportation system of a
region vs. Carrier network and services
Consolidation transportation vs.
Customized (door-to-door) services
b
2
1
d
e
c
3
f
a
4
A
5
6
B
7
C
9
Main route
8
Feeder route
Pick up and delivery
route
Freight Transportation
Many
more actors/deciders/issues
Variable planning horizons
Products
Terminals
Planning Levels
Strategic
Long-term
Designs the system structure
Tactic
Medium-term
Designs the service structure
Operational
Time-dependent
Makes happen: dynamic management and
control of resources, routes, schedules, ...
Strategic System Analysis and Planning
International,
national, regional planning
All (most) products
All (most) transportation modes
(infrastructure networks and services)
Scenario analysis (“what if ?”)
Infrastructure modifications
Evolution of demand
Technology changes
Variations in policy and economic environment
…
Methodological Approaches
Spatial
price equilibrium
Route/mode choice/loading
Network optimization
Sequential shipper-carrier
System-wide representation
System-wide Modelling
Zones: origins and destination of freight
Modes: transportation means/services
Nodes and modal links
Intermodal transfers
Products: commodity groups
Demand: origin-destination matrices by
product (and mode choice)
Output:product flows and costs on links
(modes), transfers, and paths
Model
p
p
p
p
Min F sa (v)va st (v)vt
pP aA
tT
s.t.
lLmod( p )
hl g
hl 0, l L
m( p )
od
m( p )
od
, o, d N , p P, m( p ) M
, o, d N , p P , m ( p ) M
and vap lLp al hl , a A, p P
vtp lLp tl hl , t T , p P
Nonlinear (convex) multimode multicommodity
network flow formulation
Technological Transfer
Computer-based
decision support systems
Custom-made vs. “tool box”
Example: STAN, Strategic Transportation
Analysis, software for multimodal,
multiproduct transportation systems
Consolidation Transportation
Long
distance freight carriers
One vehicle/convoy serves many customers
Railways
Less-than-truckload motor carriers
Intermodal container transportation
Express package services
Control agencies, ...
Consolidation Transportation
Accounts
for a huge proportion of the
freight moved both in volume and value
Vital component of transportation and
economic systems
Less studied
(compare to VRP, location, pure design)
Fewer, more “remote” players
Messier problems and formulations
b
2
1
d
e
c
3
f
a
4
A
5
6
B
7
C
9
Main route
8
Feeder route
Pick up and delivery
route
Consolidation Transportation
Characteristics
Regular
services
Consolidation
Frequencies
Operation
Service
terminals
and Schedules
efficiency = profits
quality = customer satisfaction
Physical Network
terminal B
terminal A
terminal C
Mode 1
Mode 2
terminal D
terminal F
SERVICE: - origin terminal
terminal E
- destination terminal
- mode
- frequency
Physical and Service Networks
terminal B
terminal A
(B, F)
(A, E)
terminal C
(B, F)
terminal D
(B, F)
terminal F
ITINERARY: Path of services used
terminal E
to move freight from
its origin to its final
destination
Itineraries
terminal A
(A, E)+
terminal B
(B, F)
terminal C
Freight consolidation
(A, E)
(B, F) and (A, E)+
terminal D
(A, E)+
terminal E
(B, F)
terminal F
Trade-offs: Operating costs minimisation vs.
service quality maximization
BEST SERVICE AT MINIMUM COST
Cost vs. Service Trade-offs
740
690
transportation and
handling costs
(in 1000$)
87%
Firm
42%
624000$
640
590
540
490
M
440
73%
440000$
390
345000$
Number of markets satisfying
the service targets (%)
340
290
0
10
20
30
40
50
60
70
80
90
Carrier Tactical Planning
Goal:
optimal allocation and utilisation of
resources to achieve the economic and
customer service objectives of the company
Means: tactical plan
(load, transportation, … plan)
Evaluation tool of strategic alternatives
Carrier Tactical Planning
Interrelated
decisions
Service selection:
routes, frequencies, schedules
Traffic distribution:
itineraries, flow distribution
Terminal policies
Empty balancing
Interactions
and trade-offs
Among operations
Between cost and service quality (time) measures
Tactical planning issues for freight carriers
generally addressed through
Service Network Design
formulations and methods
Service Network Design
It’s planning => Network view
Planning horizon
Strategic/Tactical
Tactical/Operational
Generally
several interacting resources
Usually several interacting objectives
Certainly many “decisions”
Static or dynamic (deterministic) formulations
Service Network Design:
Model Classes
Location
Frequency
Schedules/Dispatching
(Dynamic)
Location Design
Strategic
“long term” design of infrastructure
considering impact on services and traffic
Location of terminals
Location-routing
Not
many models specific for long-haul
consolidation freight transportation
Deterministic
service network design models
used to simulate scenarios
Location Design
A few
discrete location models
Production-distribution
Hub-network design
Multicommodity location-allocation with
balancing requirements
A Container Land Distribution and
Transportation System
Empty vehicle
Loaded container
Empty container
Location with Balancing
Locate
depots to optimize the distribution and
transportation of empty containers
Movements
Customer to depot: return movement
Depot to customer: allocation following request
Between depots: to counter supply-demand
imbalances and reposition for future periods
Network Structure
Oi
supply Oip
i
customers
cijp
s jkp
j
k
depots
customers
i'
demand
D i'
(flows of empty containers)
Dip
Network Structure
Oi
supply
i
customers
x ijp
yj
wjkp
j
k
depots
x ki' p
customers
i'
demand
D i'
(flows of empty containers)
Location With Balancing Formulation
Minimise Z f j y j
j D
{ (cijp xijp c jip x jip ) s jkp w jkp}
pP i C j D
Subject to
j D k D
xijp Oip
j D
i C, p P
x jip Dip
j D
i C, p P
[Demand / Flow conservation]
Location with Balancing Formulation
xijp Oip y j
i C, j D, p P
x jip Dip y j
i C, j D, p P
[Linking / Feasibility]
x w x
ijp
i C
kjp
k D
jip
i C
w jkp 0
j D, p P
k D
[Balancing]
xijp , x jip 0
i C, j D, p P
w jkp 0
j D, k D, p P
y j {0,1}
j D
Frequency Service Network Design
Objectives
Strategic planning and scenario analysis
Study of interactions and trade-offs among
subsystems, decisions, objectives
Typical
issues
What type of service?
How often over the planning horizon?
Terminal workloads
Traffic itineraries (includes empties)
Two Major Approaches
Service
levels as Decisions
Service levels as Output
Service Frequencies: Decisions
Integer frequencies
Continuous flows
Nonlinear Mixed Integer formulations:
frequency-related measures
(costs, delays-congestion, etc.)
Physical network: given infrastructure
Service network: decision structure
Traffic itineraries: on service network
PHYSICAL NETWORK (NODES, LINKS)
A1
A2
A3
A4
F1
F2
F3
SERVICE LEG
F4
SERVICE NETWORK (ROUTES, STOPS, MODES, FREQUENIES)
A3
C
C
C
C
X1
A4
A4
A4
A4
S
C
A2
A2
T
ITINERARIES FOR A TRAFFIC-CLASS (O-D-C)
X2
X3
X4
Model Elements
Physical
network
Nodes: rail yards and stations, LTL breakbulk
and end-of-line terminals, ports, …
Links: tracks, roads, …
Capacities and operational rules
Service
Route, type, costs, ...
Frequency
ys , s S
Model Elements
Demand
Market = origin, destination, commodity
Empty vehicles = product(s)
Volume
Costs, service and operational rules
Set of feasible itineraries
Itinerary flows
x lp , hlp Lp
Model
Minimize
“Fixed” cost of offering service
Costs of moving the freight
through the service network
Penalties on unsatisfied service objectives or
operational rules and characteristics
(e.g., capacities)
Subject
to
Demand satisfaction
Service and operation constraints
Service Frequencies as
Decision Variables
Minimize
s ( y)
pP lL
sS
p
l ( y, h) ( y, h)
p
Subject to
lL
p
p
hl
ys 0
p
hl 0
w
p
and integer
p P
s S
l L, p P
Specific service and operation constraints
Service Cost
Determined
by system characteristics and
(potentially) all other services
Cost of operations in terminals and en-route
Cost of time (average delay) spent in
terminals and en-route
s ( y) (C C E[ s ]) ys
O
s
D
s
Itinerary Cost
Determined
by system characteristics and
(potentially) all services and itinerary flows
for all markets
Cost of operations in terminals and en-route
Cost of time (delay) spent in terminals and
en-route
lp ( y, h) (ClpO ClpD E[ lp ])hlp
Itinerary Cost
Capacity
considerations on service segments
C (min{0, usk ys xsk})
S
p
2
Compliance with service targets
( y, h) (C C min{0, H E[ lp ] ( lp ))h
p
l
O
lp
D
lp
p
p
l
Delays - A Few Examples
Rail
yard operations: car classification and
blocking, train formation, …
Consolidation of freight in vehicles
Waiting at terminal “gates” before admission
Train delays due to meetings and overtakes on
the lines of the network.
Departure/connection delays in terminals:
the waiting time for the designated service
to be available
Delays
Representation:
Congestion functions
Models: Engineering procedures + queuing
models
Dynamic Service Network Design
Objectives
Planning of “schedules”
If or when services depart
Traffic itineraries
Space-time
graphs
Space-time Diagram
Terminals
Time
Current Period
Future Periods
Holding arc
Empty repositioning
Loaded movement
End of horizon
Dynamic Service Network Design
“To
operate or not” a given service at a given
moment (0,1) variables
Continuous flows (usually)
Capacity constraints/considerations
Special operational constraints (often)
MIP formulations: the previous formulations
in a time-dependent framework
Deterministic (for now)
Most service network design and related issues yield
Fixed Cost, Capacitated, Multicommodity Network
Design Formulations
LINEAR PATH-BASED FORMULATION
Minimise
z(h, y) fij yij klp hlp
ij A
Subject to
h
w
p
h
lp
ij
p
l
pP l Lp
p P
l Lp
p
l
uij yij
ij A
pP l Lp
p lp
h
l ij uij yij
ij A, p P
hlp 0
p P, l Lp
l Lp
SERVICE NET.DES. SOLUTION METHODS
Network
design formulations are difficult
(even in simple cases)
Problem instances are very large
(time dependencies)
Mainly heuristics and metaheuristics
A few MIP (+ heuristics) methods
Some models integrated in decision support
systems
SOLUTION METHODS
Work
in progress on network design
Metaheuristics
Model analysis and polyhedral characterization
Branch-and-bound (and cut, and price, …)
Hybrids
Parallel optimization
CONCLUSIONS
Transportation
offers many challenges and
opportunities: planning, operations
management, control (dynamic, real-time)
Operations Research and Mathematical
Programming models and methods offer good
analysis framework and solution approaches
Need to develop efficient implementations and
user-friendly decision support systems
Many challenges yet
Models
(more realistic, more real-time)
Math. analysis of formulations
Computing efficiency
Integration with
Telecommunications
Electronic commerce
Operational Planning and Management
Crew
scheduling
Terminal and Line-haul operations
Empty vehicle distribution and
repositioning
Dynamic allocation and dispatching of
resources
Issues
Time-dependent
elements (e.g., demand)
and decisions
Stochastic variations in demands, supplies,
travel times, …
Network interactions still strong
Impact of real-time information and ITS
Decision support systems