Le design de réseaux logistiques robustes : la prise en compte des aléas et des périls Alain...
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Transcript of Le design de réseaux logistiques robustes : la prise en compte des aléas et des périls Alain...
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 ?