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Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic...

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Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic [email protected] Colloque Logistique Urbaine et Interdisciplinarité, Paris
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Page 1: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning

Teodor Gabriel [email protected]

Colloque Logistique Urbaine et Interdisciplinarité, ParisLe 27 novembre 2014

Page 2: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 20142

City Logistics Ideas

“New” organizational strategies/models Reduce & control freight vehicle flows & types Improve efficiency of freight transportation

Higher loads, less empty vehicle-km Reduce environmental footprint & congestion &

interference with people impact Without penalizing its economic activities To foster an efficient transportation system To make the city a better place to experience: live, work,

visit, move within and through … Work on demand & supply sides + behaviour, policy,

regulation, law, …

Page 3: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 20143

Move Freight Differently, “Out of the Way”

Underground automated systems: new supply systems Conveyor belts or adapted vehicles on particular

infrastructure Particular packing Loading/unloading stations Huge investments required

Night deliveries: Move the demand out in time Successful pilot in New York city – much interest

elsewhere Requires particular city regulations Does not necessarily decrease number of vehicles

Page 4: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 20144

Move Freight Differently (2)

Most actual systems, past projects and proposals are based somehow on the principle of

Consolidation and coordination Coordination of shippers and carriers (& consignees) Consolidation of several shipments of different

shippers & carriers into, and delivery by the same (improved, more energy efficient, “green”) vehicle

Makes use of one or a series of terminals Consolidation facilities, Urban / city distribution /

logistics centers, of various sizes and roles

Page 5: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 20145

The City Logistics (Supply) Fundamental Idea

An integrated logistics system = Shippers, shipments Carriers (all modes including passenger and

interurban, e.g., rail, navigation), vehicles Service providers, consignees/customers, …

Optimize this logistics system “Public system” view (not ownership!) operated as best

fits the local culture, laws and regulations

Page 6: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 20146

Single-Tier Single-CDC City Logistics

Customerzone

Urban vehicle

CityDistributionCenter

Page 7: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 20147

City Logistics for Large or Sensitive Urban Areas

Most display a two-tier structure Loads consolidated at CDC into “large” vehicles Moved to CDC-like facilities – satellites – “close” to

customers Transferred to “small” vehicles appropriate for city

center Delivered to final destinations

Page 8: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 2014

SS S

SS

SP

P

P

Center 1Center 2

Origin-node

AirportRailway station

Navigation Terminals

Platforms

Depots

Satellites

Multi-Tiered City Logistics

SRailway station

Page 9: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 20149

Two-Tier City Logistics

CDC

Satellite CDC

Page 10: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201410

City freighter - route

Urban vehicle - route

Empty vehicle

Two-Tier City Logistics

Page 11: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201411

2T-CL with Rail & Transit (Public Transport)

Navigation

Long-Haul Trucks

Rail

City Freighter

Urban Vehicle

Satellite Crossdock

Customer

Distribution center

City route

City Distribution Center

Page 12: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201412

City Logistics for Large Cities

Several not necessarily integrated sub-systems Many have access to some public infrastructure (light rail

lines, parking lots, …) even for private initiatives A few initiatives to use dynamically available

transportation & storage capacity An implicit idea: Disconnect the actual mean of

transportation / delivery from the carrier/shipper/3PL originally contracted

Private inititive implementing CL operating principles Multimodal systems that aim for intermodality

Page 13: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201413

Modular & Standard Physical Internet -Containers

Page 14: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 2014

Ship

Long-distancevehicle

Train

City freighter

Plane

Bicycle

Urban vehicle

Urban hub

Interconnected, Multi-tiered City Logistics

Page 15: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201415

Challenges & Opportunities

CL = complex consolidation-based transport system Multiple “layers”, facilities, fleets, modes Time restrictions, dependencies, synchronization

Goal of sustainable efficiency for stakeholders & city Operations Research & Transportation Science

“New” problems New models, algorithms, instruments

Methods for the system and its components Appropriate for the decision-level concerned

Page 16: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201416

Challenges & Opportunities (2)

Culturally and socially-aware organization and business models, e.g.,

Cultural (government ↔ people & business, business models, taxation, etc.) impact and need for somewhat tailored solutions

Stakeholder behaviour modelling Demand identification and modelling Partnerships & collaborations → Supply modelling Public policy Materials (“boxes”), law, regulation, land use, …

Page 17: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201417

An illustration of O.R. development:Uncertainty and tactical planning

Nicoletta Ricciardi (Sapienza U. di Roma)Walter Rei (UQAM)

Fausto Errico (CIRRELT)

Page 18: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201418

Tactical (Medium-term) Planning

season

day

• Tactical planning = Plan regular operations, based on a (point) forecast, for efficient resource allocation & utilization, customer satisfaction, profitable operations

• Day-to-day situation generally different from forecast

XBuild

the plan

Adjust the plan

X

Page 19: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201419

Accounting for Uncertainty

season

day

Tactical medium-term planning accounting for uncertainty = Integrate into the tactical planning model/method the possible “adjustments” and their costs

XBuild a more flexible and robust plan

Adjust the plan “less”

X

System dataForecast demand

Observed demand

Page 20: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201420

Sources of Uncertainty in City Logistics

Time Work at facilities & service at customers Travel through the city

Demand (regularity of activities within customer zones) Volume (including no show; volume = 0) Unexpected

Rare but predictable events (e.g., vehicle or infrastructure incidents)

Rare, “catastrophic” events

Page 21: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201421

Demand Uncertainty & Planning

Robust plans (flexible operations) versus managerial concerns

Build a season plan based on available/forecast data Each “day”, once the uncertain demand data is resolved

Keep part/most of the plan External and satellite facility utilization Urban-vehicle service network

Adjust using a recourse policy Routing city freighters and extra vehicles

Two-stage modelling

Page 22: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201422

Two-Stage Modelling Framework

Two-stage recourse formulation First stage

Selection of first-tier services (& departure times) Allocation of customers to services & satellites

Second stage Routing of second-tier city freighters Service adjustment (eventually) Customer-to-satellite allocation (eventually) Calling on extra vehicles (when required)

Page 23: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201423

Two-Stage Stochastic Programming

A priori optimization

First-stage decisions: the a priori plan x : Realization of demand for : Cost of “optimal” operation plan using

the a priori plan for demand given a recourse policy RP

DMinimize ( ) E ( ( , ( ))

Subject to ,

RPDf x Q x D

x X

( )D ( , ( ))RPQ x D

( )D

Page 24: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201424

Problem Elements: Facilities & Customers

d

External zone

, , ,z zz

: , , , ,[ , ], ( )d p vol e c a b d

e

Satellite

Customer demand

Page 25: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201425

Scheduled Urban-Vehicle Services

r’: t(r’)=t

r: t(r)=t+1

Decision: Whichservice to run?(When?)

e

s

(r) {1,0}

r’: t(r’)=t; (r)={z}

Page 26: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 2014

st

s’t+

c4

gt- g’t++

e’t’

e’’’t’’’e’’t’’

c2

c3

c4

c1c5

c6

c7

c8

c8

c3

c2

c1

c5

c7

c6

City-Freighter Work Segment & Assignment

(h) {1,0}

Decision: Whichc-f work assignment to operate?

Page 27: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201427

Demand Itineraries

m:{e,r(m),t(m) < t(r),z(m)=z(m) (r(m)),(p(d)), l(h(m)), c(d)}

d

z’

z

Select itinerary to deliver cargo on time:(m) {1,0}

ed: e,c,p,t,[a,b],vol

Page 28: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201428

First Stage

Information considered System data Estimation of future demand

Defining an a priori plan Aggregated service network design model with

approximate routing costs (Tr. Sc. 2009) Decision variables

Page 29: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201429

First Stage FormulationGeneralized costfirst-tier services

Generalized cost second-tier work assignments – forecast demand Recourse cost

U. Vehicle capacityLinking

Single itinerary

Satellite capacityU. Vehicles

C. Freighters

Page 30: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201430

First Stage Output – The Plan

Page 31: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201431

Second Stage – Observing the Demand

All demands Forecasts Determine routing =

Synchronized, scheduled, multi-depot, multiple-tour, heterogeneous VRPTW

Attempt to improve system response =Apply a recourse policy + routing

Adjust plan + routing, otherwise Straightforward to determine which customers need

extra capacity to be serviced

Page 32: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201432

2nd Stage Recourse Policies

Routing (R) Routing & possible customer re-assignment (RA) Service Dispatch and Routing (SR) Service Dispatch, Routing & possible customer re-

assignment (SRA) Increased latitude in the recourse actions Extra city freighters with high cost for the demand that

cannot be moved by regular vehicles A single city-freighter fleet to service the “regular”

and the “extra” demand Direct-shipment policy

Page 33: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201433

3-Leg City Freighter Work Segment

zt

z’t++

i ’’

k’’

j ’’

h’’

i

k

j

h

gt-

g’t+++

et+

i ’

k’

j’

h’

Direct shipment

Page 34: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201434

2nd Stage Routing Recourse

Keep Selected first-tier services (routes and schedules) Customer-to-satellite assignments Bounds on

second-tier vehicle departures at each rendez-vous point (satellite, period)

Optimize the routing & demand itineraries

Page 35: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201437

2nd Stage Route & Reassign Recourse

Keep Selected first-tier services (routes and schedules)

Relax the customer-to-satellite rendez-vous assignments Optimize the routing & demand itineraries without pre-

assignment of customers to satellites Same formulation, larger set of itineraries, simpler

stochastic formulation

Page 36: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201438

2nd Stage Service Dispatch and Routing Recourse

Keep Selected first-tier services (routes and schedules) Customer demands to be served from each (satellite,

period) point Identify satellite opportunity windows and urban-vehicle

compatible services

Page 37: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 2014

Output of Service Network Design

zt

i

j

k

et’

or

ztC

[ ( ), ( )]a k b k[ ( ), ( )]a j b j

[ ( ), ( )]a i b i( )id

( )jd ( )kd

Page 38: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 2014

Opportunity Windows and Compatible Services

zt

i

j

k

et’

ztC

or

[ ( ), ( )]o oa r b r

[ ( ), ( )]a k b k

[ ( ), ( )]a i b i

[ ( ), ( )]a j b j

[ ( ), ( )]a zt b zt

( )jd

( )id

( )kd

( )oR r

Page 39: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201441

2nd Stage Service Dispatch and Routing Recourse

Optimize the restricted selection of services, the routing of regular and extra city freighters & demand itineraries: restricted tactical model With and without fixed customer-to-rendez-point

assignment

Page 40: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201444

Experimental Study of Recourse Alternatives

System performance & management issues Monte Carlo-like simulation

Not an evaluation of the value of stochastic model

Page 41: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201445

Experimental Setup

The four recourse strategies No tactical plan but daily plan = “the day before” A simplified setting: single product & vehicle type, fixed

travel times, no split Data sets randomly generated – “small” dimensions

(including with realistic geographical settings) 1-2 external zones, 2-3 satellites, 15 & 25 customer

zones, 6 periods of 25 minutes (2.5 hours) 2 demand-size distributions, 2 prediction values

Page 42: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201448

Experimental Setup (2)

Analyses based on Traffic intensity: numbers of vehicles, vehicle-km Vehicle (capacity) utilization System cost Impact & social cost Managerial concerns

Page 43: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201449

Cost Analysis

No-planning = Lower bound on costs & no direct deliveries (extra vehicles); Management (e.g., labor)?

Cost of planning ≈15% and but extra vehicles More flexibility = less direct services (60%, lower

variance) & costs (2% - 3.5%) Direct services: ↑nb. Customers, ↓nb. of CDC Do not use the “average” forecast

Recourse 1s2l 2s2l 2s2l_std DirectDel avg#DD R 20941 22900,4 10% 7878,2 2,8RA 20938,9 22087,1 11% 366,9 1,3NO 18311,7 18506,2 13% -3265,8 0 SR 20947,5 23041,5 10% 7871,7 2,8

SRA 20899,9 22538,8 11% 91,3 1,2

Page 44: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201450

Route Length Analysis

More flexibility = shorter city-freighter routes (4,8%) and less empty travel (6%)

Higher empty travel with # of customers Lower empty travel with # of external zones / satellites Modifying – sliding – the urban-vehicle departures

appears beneficial

Recourse 2s1l 2s2l 2s2l_std Empty c-f R 64.8 318.6 37.6 156.4RA 64.8 298.4 36.2 147.0NO 80.4 233.4 29.3 118.6 SR 64.8 321.8 38.8 157.2

SRA 65.2 303.3 36.7 149.6

Page 45: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201451

Vehicle Capacity Utilization

No planning = few more vehicles 1st level, less on 2nd

Planning yields very good loading factors More flexibility yields better vehicle loadings (≈ 15%) Most city freighters operate a single leg, a few two

Need to investigate “waiting” strategies (synchronization is hard)

Recourse Urban vehs. City freighters avg#DD C-f WSeg U-v load C-f load R 4,5 10,2 2,8 11,4 77% 79,30%RA 4,5 10,2 1,3 11,1 88,40% 81,10%NO 4,6 9,2 0 9,5 85,60% 82,60% SR 4,5 10,2 2,8 11,5 77% 78,80%

SRA 4,5 10,4 1,2 11,3 88,40% 79,40%

Page 46: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201452

Satellite Utilization

System appears stable Increasing flexibility, increases the “volatility” of using

the satellites Trade off to find between operation flexibility and

management concerns Need of ITS

Recourse veh1l veh2l custAssR 0 0,1 0,1

RA 0 0,1 0,2NO 0,3 0,7 1,1SR 0,2 0,4 0,8

SRA 0,3 0,6 1,1

Standard deviations

Page 47: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201453

Conclusions and Perspectives

Flexibility in adjusting the plan is beneficial on all counts: costs, km performed, capacity utilization …

It might come with higher requirements for management (& labor relations and work rules) flexibility

Needs advanced IT and decision-support systems NOW: Address the stochastic models (and the deterministic ;-) Large dimensions City Logistics systems design, policies, financing, …

Page 48: Two-Tiered City Logistics Modelling Demand Uncertainty in Tactical Planning Teodor Gabriel Crainic TeodorGabriel.Crainic@CIRRELT.ca Colloque Logistique.

© Teodor Gabriel Crainic 201454


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