Le design de réseaux logistiques robustes : la

prise en compte desaléas et des périls

Alain Martel Codirecteur, CIRRELT, et

Professeur titulaire, Operations et systèmes de décision

Walid KlibiÉtudiant au doctorat, CIRRELT

Consortium de recherche FOR@CCentre interuniversitaire de recherche sur les réseaux d’entreprise, la logistique et le transport (CIRRELT)

Outline

1. Supply Chain Network (SCN) Design Problem

2. Design Methodology• SCN risk analysis

• Decision-making framework

• Conceptual design model

3. Solution Approach• Scenario building

• Sample average design generation model

• Design evaluation model

4. Ongoing Research

1-Supply Chain Network Design Problem

Raw material sources

Markets

Finished Products

ManufacturingProcess

DistributionChannels

Deployed SupplyChain Network

...

...

SalesMarket

9

SupplyMarket

1

v V

d D

Sawing 4

Inventory

2

Inventory

8

pds S

Potential Facilities

Production-distribution site

Distribution site

ds S

s S

PlaningGrading

7

Optimal Supply Network

DOMTAR CASE

Design Objective

DesignDiscounted

Cost(Value)

Total Revenue

ValueValueaddedadded

(Profit)(Profit)

Total Cost

Design Response Time

MaximizeEconomic

ValueAdded

Large MIP model

Robustness ?

DesignDecisions

• Location• Capacity• Technology• Markets• Mission

x1

SCN Risk Analysis

Deployment

2

1 3

Network designdecision point

Network availablefor operations

2- Design Methodology

Possible environments

UserDecisions

• Demand management• Supply• Production• Inventory• Transportation…

y1 4

…

First planning cycle

Structural adaptation

decision point

x2

Deployment

Adapted network available

for operations

Must beanticipated

Planning horizon

Second planning cycle

…

UserDecisions

• Demand management• Supply• Production• Inventory

• Transportation y2

• …

Planning horizon

Info

rmat

ion

Impact

Imperfect

Very low probability

Nil

Perfect

probable

NormalNone Moderate

SeriousCatastrophic

Info

rmat

ion

Impact

Imperfect

Very low probability

Nil

Perfect

probable

NormalNone Moderate

SeriousCatastrophic

SCN’s Environment Aleatory events (A) Hazardous events (H) Totally uncertain events (T)

Deterministic Models

Stochastic ProgrammingModels

Catastrophe Models

Min Max Regret

SCN’s Environment Evolutionary Paths

Leads to the definition

of a set K of

evolutionary paths with

probabilities, kp k K

Design Methodology: Concept definitions

• Environment: Compound events defined over a planning period

• Scenario: A set of environments for a planning horizon

• = Set of all possible scenarios over horizon

• = Probability of occurrence of scenario

• K = Set of all possible evolutionary paths over horizon

Ω is divided in 3 mutually exclusives and collectively exhaustive subsets:

• Scenarios including only aleatory events

• Scenarios including aleatory and hazardous events

• Scenarios including, in addition, totally uncertain events

( )p

AHT

t T ˆ

T

T

T

Scenarios Tree for the Planning Horizon (Fan of individual scenarios)

1

A

Planning horizon

Aleatory scenarios

t T

2x

1x

N x…

Hazardousscenarios

Totally uncertain scenarios

H

T

Ak Hk Tk

k K

•What can go wrong? • Vulnerability sources identification and filtering

• Multihazard zones exposure index

•What is the likelihood of that happening?

• Stochastic multihazard arrival processes

• Attenuation probabilities

•What are the consequences? • Hazardous incidents damage on SCN resources

SCN Hazard Risk Analysis

Haimes (2004), Grossi & Kunreuther (2005), Banks (2006)

SCN Risk Analysis:What can go wrong?

Hazards

Natural

Accidental

WillfulX

=>Vulnerability Sources Set {1, 2, 3, 4, 5} S

1

2

3

4, 5

SCN Risk Modeling What can go wrong?

Exposure level of network node locations ?

Fund for Peace Failed State Index

Foreign Policy

Seismic Hazard Exposure Map

SCN Risk Modeling

What are the consequences?

Multihazard Incidents Severity Profile

SCN Risk Analysis:

( ) ( )~F (.) ( )l l s l g l sgl L s g S G ,, , ,

( )

Severity dimensions

metrics

(1)Suppliers

(2)Plants

(3)Warehouses

(4) Demand source 1

Impact intensity Unfilled

supply rate

Capacity lossrate

Capacity lossrate

Demand inflation rate

Time to recovery

Time to restoring supplies

Time to restarting production

Time to restarting distribution

Surge duration

SCN Vulnerability Sources (S = {1, 2, 3, 4, 5})

(5) Demand source 2

Demand deflation rate

Dropduration

What are the consequences?SCN Risk Analysis:

Demandlevel

Capacityavailable

tt

Capacity when hit

Demand when hit

sb t , ; sb t , ;

Recovery Function Examples

Capacity loss recovery function

Demand surge recovery function

What is the likelihood of that happening?

SCN Risk Analysis:

• Distinct multihazard non-stationary arrival process per exposure level

• Poisson arrival process

• Exponential inter-arrival time Exp(gkt) with an expected time between multihazard gkt

• Time pattern for an evolutionary path k superimposed on process using a mean shaping function

• Attenuation probability (zl) per network node based on hazard zone granularity

Multihazard Likelihood Assessment

1( , )gkt k g t

Design Level

User Level

Design

• Investment• Policy making

Synchronization of supply and demandto minimize operations costs andmaximize revenues

Anticipation of expected

revenues and costs

Design methodology: Decision-making framework

Design decision

Deployment lead time

1 1

1uT

Usage period

Designlevel

User level

1T

1x1 1y Yˆ

Design methodology: Decision time hierarchy for two planning

cycles

1 1 1( )x X I

*x

y Y n uI

2uT

2T

Structural adaptationdecision

2 2 2( )x X I

2x2 2y Y ˆˆˆ

Usage period

2 Deployment lead time

1 2ˆ ˆ ˆT T T

12 2 xx Xˆ

Demand zones

(d D)Ship to locations

Potential DClocations

lx

ax

ryry ryDemand zones

(d D)Ship-topoints

lx

ax

ryry ry

Plant

l L

p P

Demand zones

(d D)Ship to locations

Potential DClocations

lx lx

axax

ry ryry ry ry ryDemand zones

(d D)Ship-topoints

lx lx

axax

ry ryry ry ry ry

Plant

l L

p P

Illustrative Case: Multi-depot location-routing problem • Daily stochastic orders from customers• Depots vulnerable to extreme events• How many warehouses and where ?

DC

Compound Stochastic

Hazard Process

Compound Poisson Demand Process

Design methodology: Decision-making framework (Rolling Horizon)

Design Model

User Level Decisions

1 1 1

1 11 1max d duC C CC I

x Xx x xxR ˆ, , , ,, . ,

uI

1I

1x

y Y

opt yn

u uC I

x

R*

uT

1 , duC xˆ ,

2 1

1

11

opt N n

T

du u d ut n t

nt T t T

C C C C

x x

y y

x y x y

ˆ

ˆ ˆ. ,..., . ˆ ˆˆ ˆ. ,..., .

ˆ ˆ ˆ ˆˆ ˆ ˆ,

*1x

1s.t 1 n tnn n t tn t xxx X y Y ( )ˆ ˆˆ ˆ,

Anticipated Adaptation-Usage Model

Design Methodology: Design

model Using Stochastic Programming (Shapiro, 2007), Robust Optimization (Kouvelis et al., 1997) and Risk Analysis (Haimes,

2004) concepts, the design problem can be formulated as follows:

1 11 1 1max A H TA H T

C C C x X

x x xR R R, . , , . , , .

1 1 1 0 1A A AA AA A AC C C

x x xR E D, . , . , . , ,

1 1 1 0 1, . , . , . , ,H H HH HH H HC C C

x x xR E D

1 1TT TT C Min C

x xR D, . ,

Conditional dispersion measure

Conditional return measure

Conditional expected value measure

1 1

1 1 1max A H TA H TA H Tw C w C w C

x Xx x x, . , . , .R R R

Multiparametric program

Robustness criterion

3- Solution Approach

1Monte Carloscenario

generation

2

3

Status quo

1, , ...,mi i I

1 1j j Jx , , ...

M

01x

*1x

Large sample

Small samples replications

Design evaluation

Design generation

Solution methods

…

Modeling approaches

( Anticipation; Resilience)

…

,miSSA i

1M jSSA j x, ,

Worst Case ScenariosTm

Evolutionary pathsScenarios

Scenario building

Aleatory events

Hazardous events

Totally uncertain

events

(A)

(H)

(T)

(T) Scenarios

(H) Scenarios

(A) Scenarios

Environments1 Tˆt T

Tt ˆH1 H2

T1

A1

A2

A1

A2

A1

A2

A1

A2

A1

A2

A1

A2

A1

A2

A1

A2

A1

A2

A1

A2

A1

A2

A1

A2

A scenario is a compound event defined over all the environments of the planning horizon

It is the juxtaposition of aleatory, hazardous and totally uncertain events

mn

Monte Carlo : Scenario generation

, ˆe t T

etu1( )ekt etF u

Monte-Carlo :

1) For all,

a) Generate the random number

b) Compute

End For

2) For all ( , , and are random numbers)

a) Repeat : compute

Until

b) For all ,

i. Compute

ii. Compute End For

End For

z Z u

,l s l g l u lF -1

( ) ( ) ( ( ))

-1( ) ( ( , ))ez g z ktt F u z t

ˆ

ezt T( )z zlu ll L

1l l s lf F u l

ezt

u u

,k

u

,k

Solution Approach: Sample statistics design generation model

The complexity of the problem depends on the nature of 1xC ,

• Generate samples of scenarios

partitioned into , and A, H and T-scenarios,

with associated weights , and

(Importance Sampling)

• Define to take resilience opportunities into account

• For a given I, solve the design problem (for the case of a

dispersion neutral decision-maker)

1, , ...,mi i I

Am

1X

1 1

1 1 1x X

max x x xTmA Hm m

HAT TA H

ww

m mC C w Min C

, , ,D

I mH

mT

m

Aw Hw Tw

Solution Approach: Design evaluation model

• For a given , solve the sample statistics design

evaluation model:

The most Effective and Robust SCN design is

1 11 max * *x Z(x ) {Z(x ), }j j J

• Generate one large sample of scenarios partitioned into , and scenarios

M

1

jx

2

1

1 1 1 1x x

y y

x = x x xZ max A H T

N

T

A H T

j j j jC C C

ˆ

ˆ ˆ. ,..., .ˆ ˆ. ,..., .

, . , , . , , .R R R

MA

MH

MT

M

1s.t 1 n tnn n t tn t xxx X y Y ( )ˆ ˆˆ ˆ,

4- Ongoing Research• Evaluate several anticipation types to explore the

complexity of models and the quality of related solutions

• Propose a modeling approach based on flexibility to

improve the SCN resilience under disruptions

• Redundancy

• Dual sources

• Operational flexibility

• Strategic emergency buffers (insurance inventories)

• Propose a general solution method for large scale problems

(heuristic approach)

Thank you for your attention

Questions ?