Optimization Modelsfor

Long-haul Freight Transportation

Teodor Gabriel Crainic

Dept. Management and TechnologyUniversité du Québec à Montréal

andCentre for Research on Transportation

Université de Montréal/H.E.C./Poly

theo@crt.umontreal.ca2000

Transportation Systems

Physical (Conceptual) Infrastructure and Services

Production, Consumptionof Goods and Services

SUPPLY DEMAND

Movements of people, goods, vehicles = TrafficCosts/profits, delays, energy, emissions, …

Economic and legal environment

Transportation Systems

Physical (Conceptual) Infrastructure and Services

Production, Consumptionof Products and Services

SUPPLY DEMAND

Movements of people, goods, vehicles = TrafficCosts/profits, delays, energy, emissions, …

Economic and legal environment

Transportation Systems

Physical (Conceptual) Infrastructure and Services

Production, Consumptionof 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 FlowsPerformance 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

1

2

3

4

5

6

7

89

A

B

C

a

b

c

d e

f

Main route

Feeder routePick up and delivery route

Freight Transportation Many more actors/deciders/issues Variable planning horizons Products Terminals

Planning Levels

StrategicLong-termDesigns the system structure

TacticMedium-termDesigns the service structure

OperationalTime-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 modificationsEvolution of demandTechnology changesVariations in policy and economic environment…

Methodological Approaches

Spatial price equilibrium Route/mode choice/loading Network optimization

Sequential shipper-carrierSystem-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

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Min ( ) ( )

s.t. , , , , ( )

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and , ,

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F s v v s v v

h g o d N p P m p M

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v h a A p P

v h T p P

Nonlinear (convex) multimode multicommoditynetwork 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

1

2

3

4

5

6

7

89

A

B

C

a

b

c

d e

f

Main route

Feeder routePick up and delivery route

Consolidation TransportationCharacteristics

Regular services Consolidation terminals Frequencies and Schedules Operation efficiency = profits Service quality = customer satisfaction

Physical Network

terminal A

terminal C

terminal D

terminal E

terminal F

SERVICE: - origin terminal - destination terminal - mode - frequency

Mode 1

Mode 2

terminal B

terminal Aterminal B

terminal C

terminal D

terminal E

terminal F

ITINERARY: Path of services used to move freight from its origin to its final destination

(B, F)

(B, F)

(A, E

)

(B, F)

Physical and Service Networks

terminal A

terminal C

terminal D

terminal E

terminal F

Trade-offs: Operating costs minimisation vs.

service quality maximization

(B, F)

(B, F)

(A, E

)

Freight consolidation

BEST SERVICE AT MINIMUM COST

(A, E)+

(A, E)+

(A, E)+

terminal B

(B, F)

and

Itineraries

Cost vs. Service Trade-offs

Number of markets satisfying the service targets (%)

0 10 20 30 40 50 60 70 80 90290

440

490

590

690

390

340

740

640

540

Firm42%624000$

345000$

73%440000$

87%

M(in

100

0$)

transportation and handling costs

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 decisionsService selection:

routes, frequencies, schedulesTraffic distribution:

itineraries, flow distributionTerminal policiesEmpty balancing

Interactions and trade-offsAmong operationsBetween 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 trafficLocation of terminalsLocation-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 modelsProduction-distributionHub-network designMulticommodity location-allocation with

balancing requirements

A Container Land Distribution and Transportation System

Loaded container

Empty container

Empty vehicle

Location with Balancing

Locate depots to optimize the distribution and transportation of empty containers

MovementsCustomer to depot: return movementDepot to customer: allocation following requestBetween depots: to counter supply-demand

imbalances and reposition for future periods

Network Structure

(flows of empty containers)

customers

customers

depots

demand

supply

k

Di'

Dip

Oip

Oi

s jkp

cijp

i

j

i'

Network Structure

(flows of empty containers)

customers

customers

depots

demand

supply

k

Di'

xijp w jkp

Oi

i

j

i'

y j

xki p'

Location With Balancing Formulation

Minimise

Subject to

[Demand / Flow conservation]

Z f y

c x c x s w

x O i C p P

x D i C p P

jj D

j

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ijp ipj D

jip ipj D

{ ( ) }

,

,

Location with Balancing Formulation

,

,

[Linking / Feasibility]

[Balancing]

,

0 ,

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x D y i C j D p P

x w x w j D p P

x x i C j D p P

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y

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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

F4

A1 F1A2 F2A3 F3

A3

CX1

A4

CX2

A4

SA4

CX3

A2

CA4

CX4

A2

TITINERARIES FOR A TRAFFIC-CLASS (O-D-C)

PHYSICAL NETWORK (NODES, LINKS)

A4SERVICE LEG

SERVICE NETWORK (ROUTES, STOPS, MODES, FREQUENIES)

Model Elements

Physical network Nodes: rail yards and stations, LTL breakbulk

and end-of-line terminals, ports, …Links: tracks, roads, …Capacities and operational rules

ServiceRoute, type, costs, ...Frequency

y s Ss ,

Model Elements

Demand Market = origin, destination, commodityEmpty vehicles = product(s)VolumeCosts, service and operational rulesSet of feasible itinerariesItinerary flows

x hlp

lp, Lp

Model

Minimize “Fixed” cost of offering serviceCosts of moving the freight

through the service networkPenalties on unsatisfied service objectives or

operational rules and characteristics (e.g., capacities)

Subject toDemand satisfactionService and operation constraints

Service Frequencies as Decision Variables

Minimize

Subject to

and integer

Specific service and operation constraints

ss S

lp

l Lp P

lp

l L

p

s

lp

y y h y h

h w p P

y s S

h l L p P

p

p

( ) ( , ) ( , )

,

0

0

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 sO

sD

s sy C C E y( ) ( [ ])

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

lpO

lpD

lp lpy h C C E h( , ) ( [ ])

Itinerary Cost

Capacity considerations on service segments

C u y xpS

sk s sk(min{ , })0 2

lp

lpO

lpD p

lp lp lpy h C C H E h( , ) ( min{ , [ ] ( )) 0

Compliance with service targets

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

Holding arcEmpty repositioningLoaded movementEnd of horizon

Ter

min

als

Time

Current Period Future Periods

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

Minimise

Subject to

z h y f y k h

h w p P

h u y ij A

h u y ij A p P

h p P l L

ijij A

ij lp

l Lp Plp

lp

l L

p

lp

ijlp

l Lp Pij ij

lp

ijlp

l Lij ij

lp p

p

p

p

p

( , )

,

,

0

LINEAR PATH-BASED FORMULATION

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 designMetaheuristicsModel analysis and polyhedral characterizationBranch-and-bound (and cut, and price, …)HybridsParallel 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

TelecommunicationsElectronic 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