CIRRELT Service Network Design for Consolidation Freight Carriers Teodor Gabriel Crainic ESG UQAM & CIRRELT - CRT
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)
3© Teodor Gabriel Crainic 2006
1
2
3
4
5
6
7
89
A
B
C
a
b
c
d e
f
MainFeederPick up and delivery
Hub
Customers
Terminal
4© Teodor Gabriel Crainic 2006
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
5© Teodor Gabriel Crainic 2006
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
6© Teodor Gabriel Crainic 2006
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
7© Teodor Gabriel Crainic 2006
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…
8© Teodor Gabriel Crainic 2006
Physical Network
terminal A
terminal C
terminal D
terminal E
terminal F
terminal B
9© Teodor Gabriel Crainic 2006
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, …
10© Teodor Gabriel Crainic 2006
Services
terminal A
terminal C
terminal D
terminal E
terminal F
terminal B
Modes
S1
S7
S2
S3
S5
S5
S4
S6
11© Teodor Gabriel Crainic 2006
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
12© Teodor Gabriel Crainic 2006
Vocabulary – Demand
Market = Traffic classOrigin, destination, productQuantityPriority level – delay cost
Routing - ItinerariesOrigin, destination, route through service networkTerminal operationsQuantity and performance measures
13© Teodor Gabriel Crainic 2006
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
)
14© Teodor Gabriel Crainic 2006
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
)
15© Teodor Gabriel Crainic 2006
Itineraries : A to E (3)
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
16© Teodor Gabriel Crainic 2006
Itineraries : A to E (4)
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
17© Teodor Gabriel Crainic 2006
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)
18© Teodor Gabriel Crainic 2006
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
19© Teodor Gabriel Crainic 2006
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
20© Teodor Gabriel Crainic 2006
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
21© Teodor Gabriel Crainic 2006
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
22© Teodor Gabriel Crainic 2006
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
23© Teodor Gabriel Crainic 2006
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)
24© Teodor Gabriel Crainic 2006
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?
25© Teodor Gabriel Crainic 2006
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
26© Teodor Gabriel Crainic 2006
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
27© Teodor Gabriel Crainic 2006
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
28© Teodor Gabriel Crainic 2006
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 ≥
29© Teodor Gabriel Crainic 2006
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
30© Teodor Gabriel Crainic 2006
Service Network Design
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
31© Teodor Gabriel Crainic 2006
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
32© Teodor Gabriel Crainic 2006
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
33© Teodor Gabriel Crainic 2006
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∈
34© Teodor Gabriel Crainic 2006
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
35© Teodor Gabriel Crainic 2006
Delays and Congestion
Total traffic
Average delay (time)
Capacity
= free travel time* [1 + 0.70 total traffic +0.80 (total traffic / capacity)6]
36© Teodor Gabriel Crainic 2006
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
37© Teodor Gabriel Crainic 2006
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
38© Teodor Gabriel Crainic 2006
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
39© Teodor Gabriel Crainic 2006
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
40© Teodor Gabriel Crainic 2006
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
41© Teodor Gabriel Crainic 2006
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…
42© Teodor Gabriel Crainic 2006
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
43© Teodor Gabriel Crainic 2006
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
44© Teodor Gabriel Crainic 2006
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
45© Teodor Gabriel Crainic 2006
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
46© Teodor Gabriel Crainic 2006
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
47© Teodor Gabriel Crainic 2006
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
48© Teodor Gabriel Crainic 2006
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
49© Teodor Gabriel Crainic 2006
Service Network Design
Static: Selection and frequenciesDynamic: Schedules and dispatching
When will the service leave? (If it does…)Moving the freightRepositioning of resources (vehicles, crews, motor power)
50© Teodor Gabriel Crainic 2006
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
51© Teodor Gabriel Crainic 2006
Space-Time Network – Schedules
Inventory arcEnd of horizon
Ter
min
als
Time
Period t Periods t + …
Possible departure
Period t + 1
52© Teodor Gabriel Crainic 2006
Space-Time Network – Cyclic Schedules
53© Teodor Gabriel Crainic 2006
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
54© Teodor Gabriel Crainic 2006
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 !!
55© Teodor Gabriel Crainic 2006
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
56© Teodor Gabriel Crainic 2006
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)
57© Teodor Gabriel Crainic 2006
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
58© Teodor Gabriel Crainic 2006
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
59© Teodor Gabriel Crainic 2006
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
60© Teodor Gabriel Crainic 2006
The Polcorridor project
Hubs
Northern feeder network
Southern feeder network
SWINOUJSCIE
SZCZECIN
VIENNA
GDYNIAGDANSK
61© Teodor Gabriel Crainic 2006
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
62© Teodor Gabriel Crainic 2006
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
63© Teodor Gabriel Crainic 2006
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
64© Teodor Gabriel Crainic 2006
Common Characteristics and Issues
Cyclic schedules⇒ Cyclic Space-Time Network Representation
Node 3
Node 2
t=6t=5t=4t=3t=2t=1
Node 1
65© Teodor Gabriel Crainic 2006
Common Characteristics and Issues (2)
Need to include locomotive management“Repositioning” – Circular routes
Change of locomotive at the Czech – Polish borderNeed to synchronize/coordinate
66© Teodor Gabriel Crainic 2006
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
67© Teodor Gabriel Crainic 2006
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
68© Teodor Gabriel Crainic 2006
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
69© Teodor Gabriel Crainic 2006
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∈
70© Teodor Gabriel Crainic 2006
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
71© Teodor Gabriel Crainic 2006
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