service network design for consolidation freight carriers · modelling – service network àset of...

CIRRELT

Service Network Design for Consolidation Freight Carriers

Teodor Gabriel Crainic

ESG UQAM&

CIRRELT - CRT

2© Teodor Gabriel Crainic 2006

Consolidation Freight Transportation

Long distance freight transportationRailwaysLess-Than-Truckload (LTL) motor carriersShipping linesContainer transportationPostal and express couriers: Service (firm) planning perspectiveRegulatory agencies (in some countries)


1

2

3

4

5

6

7

89

A

B

C

a

b

c

d e

f

MainFeederPick up and delivery

Hub

Customers

Terminal


Consolidation Transportation (2)

The same vehicle (convoy) serves the demand of several customersRegular services ⇒Routes, frequencies, schedulesTerminals: Major and central role

Sort freight and consolidate it into vehiclesSort vehicles and group them into convoysManipulate convoys

Many types of services, equipment, and terminalsMany trade-offs among operations and among performance measures


Consolidation Transportation (3)

Reduces costs for customersReduces costs for carrier (if correctly planned and performed)Reduces the flexibility of customersAdditional operations and delays (in terminals) ⇒Reduced reliability (and costs)Operation efficiency ⇔ Carrier profitabilityService quality (delays, reliability, …) ⇔ Customer satisfactionNeed for methods to plan and manage operations


Tactical Planning

Objectives Determine the best – optimal – assignment and utilization of resources to fulfil the economic and service (customers) objectives of the carrier

Means Tactical (load, transportation, …) plan

YieldsOperation plan for normal/regular operationsScenario analysis tool


Vocabulary – Physical network

Infrastructure network on which transport services operate

Rail tracks and stationsPublic roads and terminals (motor carriers, post, express mail, …)Airports, ports, LTL breakbulk and end-of-line terminals, intermodal terminals in general, …Conceptual air, sea, river, … connections…


Physical Network

terminal A

terminal C

terminal D

terminal E

terminal F

terminal B


Vocabulary – Transport Services

For the customersPoint-to-point (city-to-city, origin to destination) service offerFrequencies and schedulesTariffsService targets: “Paris to Frankfurt in 24 hours”

For the carrierOrigin (terminal), destination (terminal), route through the physical network, stops, equipment type, …


Services

terminal A

terminal C

terminal D

terminal E

terminal F

terminal B

Modes

S1

S7

S2

S3

S5

S5

S4

S6


Transport Services – Carrier

Operations costsFrequencies and schedulesService targets: “Paris to Frankfurt in 24 hours, 80% of the time”The origin and destination as seen by a customer are generally not those of a carrier service

Pick up and deliveryFreight moved by a series of transport services and terminals

Terminals = services


Vocabulary – Demand

Market = Traffic classOrigin, destination, productQuantityPriority level – delay cost

Routing - ItinerariesOrigin, destination, route through service networkTerminal operationsQuantity and performance measures


Itineraries : A to E

terminal A

terminal C

terminal D

terminal E

terminal F

terminal B

Modes

S1

S7

S2

S3

S5

S5

S4

S6

(A, E

)


Itineraries : A to E (2)

terminal A

terminal C

terminal D

terminal E

terminal F

terminal B

Modes

S1

S7

S2

S3

S5

S5

S4

S6

(A, E

)



terminal A

terminal C

terminal D

terminal E

terminal F

terminal B

Modes

S1

S7

S2

S3

S5

S5

S4

S6(A

, E)

(A, E

)

(A, E)

Transfer at C from S3 to S5Transfer at D from S5 to S6



terminal A

terminal C

terminal D

terminal E

terminal F

terminal B

Modes

S1

S7

S2

S3

S5

S5

S4

S6

(A, E

)

(A, E

)

(A, E)

Transfer at C from S3 to S5Consolidation at D from S5 to S6


Itineraries : Extra A to E + B to F

terminal A

terminal C

terminal D

terminal E

terminal F

terminal B

Modes

S1

S7

S2

S3

S5

S5

S4

S6

(A, E

)

(B, F)

(B, F) et (A,E)+

(B, F)

(A, E

)

(A, E)


Best Itinerary (there are quite a lot of them)?

It dependsThe state of the entire system

Moving the entire demandCongestion in (in front of) terminals (lines)Frequency and utilization (loads) of services

The trade-off between operation costs (to minimize) and the service quality (to maximize)

Need to optimize the entire set of operations in an integrated way


No. of markets that satisfy quality requirements (%)

0 10 20 30 40 50 60 70 80 90290

440

490

590

690

390

340

740

640

540

Company performance42%624000$

345000$

73%440000$

87%

(in 1

000$

)Handling and transportation costs

Model results


Interrelated Decisions

Service selectionRoutes, types, frequencies, schedules, …

Freight routing (distribution)Itineraries (routes), volumes, …Empty vehicles

Terminal utilization policies Work division

Network-wide interactions and trade-offsAmong components/operations/decisions Between cost and quality objectives


Decision Environment

Interactions occur network-wide (“ripple effect”) The impact of individual decisions are difficult to forecast and rarely intuitiveTrade offs are difficult to identify


Service Network Design

Construction of tactical planAggregated modelling of the major system components, decisions, operations

“Planning, not operations”Integrates trade-offs costs versus service quality Interactions of several types of resources Network-wide level


Service Network Design (2)

Planning horizonStrategic/tacticTactic/operational

Service network design model (methodology) StaticDynamic (time-dependent)Deterministic (why not stochastic?)

Model objectiveStatic: Selection & FrequenciesDynamic: Schedules (& dispatching)


Static Service Network Design

ObjectivesStrategic/tactic planning ⇒ Transportation planInteraction and trade-off analysesScenario analyses

Typical issuesDo we operate the service?How often over the planning horizon?What service type?Terminal loads?Itineraries for demand and empty vehicles?


Static Service Network Design: Approches

Selection of servicesFrequencies as

Consequences of routing decisions (Powell et al)

Decisions (Crainic et al)

In all cases, the service network represents the decision structure on which traffic routing decisions are taken


Selecting Services

Decisions“To operate or not” each service: {0,1} variablesDemand routing: continuous flow variables

Demand for several “Products”(appropriate measures: tons, # of vehicles, …)Each service

Fixed cost to operateVariable cost to transport productsCapacity


Selecting Services (2)

2

2

2

s

s AE

s

y

x

u

1

1

1

S

s AE

s

y

x

u

terminal A

terminal C

terminal D

terminal E

terminal F

terminal B

Modes

S1

S7

S2

S3

S5

S5

S4

S6

dAE, dAF , dAD3

3

3

3

3

S

S AE

S AF

S AD

S

y

x

x

x

u


Selecting Services: Modelling

NetworkNodes: Terminals Links = services

DecisionsIs a service a, from terminal i to terminal j, to beselected (operated, offered) ? Quantity of demand of market od carried on service a

,i j T∈

( , ) ; ,a i j S i j T= ∈ ∈

{1,0}ay ∈

0aodx ≥


Selecting Services: Formulation

if at origin 0 if other terminal

if at destination

{0,1}0

ps s s sp

s S p P s S

p

sji sijs S j s S j

p

sp s sp P

s

sp

f y C x

dx x

d

x u y

xy

∈ ∈ ∈

∈ ∈

∈

+

⎧−⎪− ⎨⎪⎩

≤

∈

≥

=

∑ ∑∑

∑∑ ∑∑

∑

Minimize

Subject to

Flow conservationLinking/ capacity



Fixed-cost, capacitated, multicommodity, network design formulations (arc or path)Combinatorial and difficultAdditional constraints from operational considerationsSolved by

Exact methods (B&B, …) for small instancesHeuristics and Meta-heuristics in most cases

Frequency formulations (general integer design variables): even more complex


Frequencies as Decisions

Applications to railways, LTL motor carriers, courier, etc.Determine service frequencies Routing of demand for each market

Service and terminal work charges derived from frequencies and itineraries

More complex service routesService and terminals capacity and congestionMinimize the generalized cost of operating costs, service quality measures, delay costs, etc. Non linear formulation due to frequency/congestion impact


Modelling – Service Network

Set of services SDefined on the physical networkEach service : origin, destination, route, stops, type, capacity, …Service frequency integer (=0,1,2,3,…)Select frequencies ⇒ Determine services to be offered and the level of serviceFixed cost to operate each occurrence of a service

May depend upon the frequencies of all services

sy

s S∈

( )s yΨ


Modelling – Demand Itineraries

Defined on the service networkSeveral itineraries may exist and be used for each marketItinerary : origin, destination, service route, operations at terminals, …Quantity of demand of market p moved by itinerary l (continuous)“Variable” cost to move along each itinerary

May depend upon the service frequencies and the volumes moved on the other itineraries

pl L∈

0plh ≥

( , )pl y hΦ

p P∈


Congestion Phenomena: Average Delays

When several services / itineraries use the same facility, there is competition for the same resources

⇒ CongestionNon linear relations between facility capacity (time to go through it) and the volume that needs to use it: a small increase in volume results in a large increase in average utilization time

⇔ Congestion functions


Delays and Congestion

Total traffic

Average delay (time)

Capacity

= free travel time* [1 + 0.70 total traffic +0.80 (total traffic / capacity)6]


Operations with Congestion

Single and double rail lines: meets and overtakesCongested roadsCar classification, block and train make up (rail yards)Connection: waiting for the next service (terminals)Truck waiting at terminal doorsShip waiting at port or lock entryFreight classification and consolidation (terminals)Vehicle loading/unloading, …Functions are derived from engineering and queuing formulas, through simulation


Modelling Capacity Restrictions

For modelling & algorithmic reasons, capacity restrictions and other service quality measures are better represented as non-linear penalties in the objectiveHard constraints in actual operationHard capacity constraints: more difficult design problemOvercapacity corresponds to longer delaysThe model should be able to go over capacity and “pay the price” if it yields a better overall performance

⇒ The possibility to explore strategies and tradeoffs that strict constraints do not allow to see


Capacities as Penalties

Total volume on segment k (between two consecutive stops) of service s with current frequency ys =Sum of the volumes of all itineraries using segment k of service s Service capacity on segment (minimum of the capacities of the links making up the segment) Penalty cost for overloading the service s

skx

sku

( )2( , ) min{0, }p Pl s sk s sks k

y h C u y xΘ = −∑ ∑

PsC


Service Costs – “Fixed”

Cost to operate one occurrence of the serviceSum of unit operating costs on the lines and in the terminals of its route

Service travel timeAverage (expected value)Sum of [average] travel times and terminal handling times Cost of handling and travel time

Service total cost( ) ( [ ])O D

s s s s sy C C E yΨ = + Τ

sΤ

OsC

DsC

[ ]sE Τ


Itinerary Costs – “Variable”

Cost to use itinerary l for market pSum of unit operating cost on the lines (services) and in the terminals of the itinerary

Itinerary travel timeAverage (expected value)Sum of service travel times and terminal handling timesCost of travel and wait (delay)

Itinerary total cost( , ) ( [ ( , )])p O D p p

l lp lp l ly h C C E y h hΦ = + Τ

[ ( , )]plE y hΤ

( , )pl y hΤ

OlpC

DlpC


Operation Costs

Generally linear (proportional) with traffic volumeOperate engines or trucksHauling full and empty vehiclesSort and consolidate freightLoad / unload vehicles (trucks, wagons, barges, …)Sort wagonsBuild blocks and make up trainsTransfer blocks (wagons) between trains…


Time costs

Unit time costsDepreciation, crews, product value, priorities (how urgent it is to deliver a product), etc.

Transform time into money ⇒ coherent objective function


Delays

Total travel time, origin to destination, serves as service-quality indicator for services and itinerariesSum of travel times (delays) and terminal handling times (delays) making up the service / itineraryOften, constant average time values

Roads, maritime transport, …Load / unload / transfer vehicles, …

Non linear when congestion phenomena exist


Averages Do NOT Tell the Whole Story

Service reliability or fulfilment of targets are not well represented through average delaysPenalize (“large”) variancesIntroduce variances into the computation of total time and penalize not respecting targets

Announced target (e.g., 24 jour delivery)Target (e.g. 90% of occurrences) n

2(min{0, [ ( , )] [ ( , )]})D p p plp l p l lC h H E y h n y hσ− Τ − Τ

pH


Frequencies as Decisions

DecisionsService frequencies (integer)Routing – itineraries – of demand for each market (continuous)

Objective: Generalized cost of operating costs, service quality measures, delay costs, etc. Non linear formulation due to frequency impact (congestion)Path-based formulation


Model Idea

Minimize total generalized system cost= Fixed cost to offer the service+ Variable costs to operate full and empty vehicles

ConstraintsSatisfy demand for each market(other operational considerations)

Operational policies (e.g., capacities of vehicles, convoys, lines, terminals, …) and service targets are in the objective function


Formulation

( ) ( , ) ( , )

0 and integer 0

p

p

ps l

p Ps S l Lp p

ll L

sp

l

y y h y h

h w

yh

∈∈ ∈

∈

Ψ + Φ +Θ

=

≥≥

∑ ∑ ∑

∑

+ Particular operational constraints

Minimize

Subject to


Solving the Model

Heuristics (modify frequencies) and exact methods (itinerary generation and flow distribution)Better methods have been developed

(for the generic model; work in progress …)Applications“Many” models in the literature use the same approach with simplifications



Static: Selection and frequenciesDynamic: Schedules and dispatching

When will the service leave? (If it does…)Moving the freightRepositioning of resources (vehicles, crews, motor power)


Space-Time Network (Diagram)

Representation tool for time-dependent events (demand, activities, decisions, …) and their relations in time and spaceThe network describes the system operations during the current and the following time periodsArcs represent inter-period relations (inventories, movements, etc.) The objective function minimizes/maximizes the total cost/profit over the entire multi-period planning horizon


Space-Time Network – Schedules

Inventory arcEnd of horizon

Ter

min

als

Time

Period t Periods t + …

Possible departure

Period t + 1


Space-Time Network – Cyclic Schedules


Modelling Idea

Physical network represented at each periodArcs represent each possible departure (origins, intermediary stations) of each serviceWaiting/holding (inventory) arcs link nodes representing the same terminals in consecutive periodsDecision variables

{0,1} : The corresponding service leaves (is operated) at the specified time?Continuous: Freight flows


Modelling Idea (2)

Modelling principles and components of the static formulations applyProblem dimensions grow fast !!Network design solution approachesAdaptations of fleet management (dynamic resource allocation) methodologiesThere is a lot of work required in this field !!


An Example of “New” Challenges

Dedicated intermodal rail services to move containers & trailers

Instrument for E.U. policy Consolidation carriers with/without external servicesEfficiency and profitability of operations

Same ideas apply to the planning of services of regular navigation linesOld issues, “new” operation principles,new challenges


Rail Intermodal

Dedicated carriers (divisions)North America

Long distances – “land bridges” – linking the coast and the industrial mid-westLong trains (very long ☺)Double stackScheduled services (almost)Bookings and full-asset-utilization operations (emerging)


Rail Intermodal (2)

EuropeSeparation of infrastructure owners/managers (capacity providers) and operators (service providers)Scheduled services: network is congested !!Double stack (where possible)Bookings (contemplated)New services

Shuttle servicesE.U. expansion to Central and East Europe


Rail Intermodal – Trends

“Full asset utilization” operationsSame trains & blocks operated every day, all days (seasonal)Equipment – engines & cars – and personnel operates circular routes

BookingsAdvance reservation of space (slot) on train/day

Advanced terminals on the drawing boards⇒ Intelligent systems


Rail Intermodal – New Networks in Europe

Expansion of EUGerman network very congestedNew shuttle networks

Link Scandinavia to Central Europe and beyondUse uncongested“Eastern” rail networks: Polish, Czech, …

Andersen, Christiansen, Crainic 05


The Polcorridor project

Hubs

Northern feeder network

Southern feeder network

SWINOUJSCIE

SZCZECIN

VIENNA

GDYNIAGDANSK


The System

Vienna

Poznan

Zielona Góra

Wroclaw

Breclav

MiedzylesieChalupki

Gdansk/ Gdynia

Swinoujscie/ Szczecin

Node in external networkExternal service

Rail linesCzech/Polish border with change of locomotive

Border crossing node

Node in rail network

Intermodal hub


Swinoujscie Rail-Ferry Terminal Representation

Quay Storage area

Transhipment of rail wagons

Rail terminal

Unloading of containers& semitrailers

Loading of containers& semitrailers

TRAIN DEPARTURE

TRAIN ARRIVALDeparture of

ferry

Loading of containers& semitrailers

Unloading of containers& semitrailers

Quay Storage area

Transhipment of rail wagons

Rail terminal

Locomotives ready for new departure

Arrival of ferry


Two Models

Strategic/tactical for major design decisionsServices: types, routes, frequenciesMarket “selection” (some pricing issues) and routingFrequency service network design

Service & schedule planningWhen service depart given “ideal” frequenciesCoordination and synchronizationExternal networks (ferries, other rail services)Multi-carriers & border crossings


Common Characteristics and Issues

Cyclic schedules⇒ Cyclic Space-Time Network Representation

Node 3

Node 2

t=6t=5t=4t=3t=2t=1

Node 1


Common Characteristics and Issues (2)

Need to include locomotive management“Repositioning” – Circular routes

Change of locomotive at the Czech – Polish borderNeed to synchronize/coordinate


Scheduled Service Design + Asset Management + External Service Coordination (Model 2)

Time-space representation with repetitive service networkBorder crossings with synchronizationDesign new services interacting with existing/external services ⇒Some departure times are fixedBalancing of assets (locomotives) at nodes

Repositioning allowed to create feasible locomotive (circular) movements


Model

Minimize total time cost : travel + waiting for various terminal operations (border, connection, …)The fleet of locomotives must cover all services and repositioning in each time periodNode asset (locomotive) balance Lower and upper bounds on service frequenciesNode freight (rail car) balanceTrain capacity on internal and external services


Design-Balanced Network Design

At the core a “new” variant of multicommoditycapacitated network design problem

Design balance constraintsThe number of selected design arcs entering a node = number of selected design arcs exiting the node


Arc Formulation (DBCMND)

( , ) ( , )

( ) ( )

( ) ( )

min ( , )

( )( ) ,

0

( , )

0,

0 ( , ) ,(

p pij ij ij ij

i j A p P i j A

p

p p p pij ji i

j N i j N i

pij ij ij

p P

ij jij N i j N i

pij

ij

z X Y f y c x

w if i o px x d w if i s p i N p P

otherwise

x u y i j A

y y i N

x i j A p Ay N

+ −

+ −

∈ ∈ ∈

∈ ∈

∈

∈ ∈

= +

⎧ =⎪− = = − = ∀ ∈ ∀ ∈⎨⎪⎩

≤ ∀ ∈

− = ∀ ∈

≥ ∀ ∈ ∀ ∈∈ ∀

∑ ∑ ∑

∑ ∑

∑

∑ ∑

, )i j A∈


Design-Balanced Network Design

Exact solution methods work on very small instancesHeuristic methods for particular cases

LP relaxation & column generation + cuts + rounding Path-based generate + combine to improve

Arc-based general formulationTabu search-based method yields promising results

Interesting cycle-based formulation has been proposed


Methodological Challenges

Advance network design methodologyTransfer methodology to application areas Time-dependent design-balanced service network design

Formulations & characterizationEfficient solution methods, …

Stochastics and service network designPreliminary studies: plans are different and “better” ...Requires work on realistic formulations & efficient solution methods

service network design for consolidation freight carriers · modelling – service network àset of...

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