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 
pP  aA
tT

s.t.

lLmod( 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   lLp  al hl , a  A, p  P
vtp   lLp  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}
pP 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)   

pP lL
sS
p
 l ( y, h)   ( y, h)
p
Subject to

lL
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
pP l Lp
p P
l Lp
p
l
 uij yij
ij  A
pP 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