Le design de réseaux logistiques robustes : la prise en compte des aléas et des périls

1. 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 Klibi Étudiant au doctorat, CIRRELT Consortium de recherche FOR@C Centre interuniversitaire de recherche sur les réseaux d’entreprise, la logistique et le transport (CIRRELT)

2. Outline • Supply Chain Network (SCN) Design Problem • Design Methodology • SCN risk analysis • Decision-making framework • Conceptual design model • Solution Approach • Scenario building • Sample average design generation model • Design evaluation model • Ongoing Research

3. ... ... 1-Supply Chain Network Design Problem Raw material sources Deployed SupplyChain Network ManufacturingProcess Finished Products DistributionChannels Markets

4. Inventory 2 Potential Facilities Bucking 3 Chipping Drying 6 5 Planing Grading 7 Production-distribution site Sales Market Supply Market 1 9 Distribution site Inventory 8 Sawing 4

5. OptimalSupply Network DOMTAR CASE

6. Design Objective Maximize Economic Value Added Design Discounted Cost (Value) Total Revenue Value added (Profit) Total Cost Robustness ? Design Response Time Large MIP model

7. Second planning cycle First planning cycle Possible environments (w) • User • Decisions • Demand management • Supply • Production • Inventory • Transportation… • y1 • User • Decisions • Demand management • Supply • Production • Inventory • Transportation y2 • … … Must beanticipated 4 Planning horizon Deployment Adapted network availablefor operations Structural adaptation decision point x2 2- Design Methodology • Design • Decisions • Location • Capacity • Technology • Markets • Mission • x1 2 Planning horizon SCN Risk Analysis 1 Deployment 3 Network availablefor operations Network designdecision point …

8. SCN’s Environment • Aleatory events (A) • Hazardous events (H) • Totally uncertain events (T) Deterministic Models Stochastic Programming Models Catastrophe Models Min Max Regret

9. SCN’s Environment Evolutionary Paths Leads to the definition of a set K of evolutionary paths with probabilities

10. 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

11. Scenarios Tree for the Planning Horizon (Fan of individual scenarios) … Aleatory scenarios Hazardousscenarios Totally uncertain scenarios Planning horizon

12. SCN Hazard Risk Analysis • What can go wrong? • Vulnerability sources identification and filtering • Multihazard zones exposure index • What are the consequences? • Hazardous incidents damage on SCN resources • What is the likelihood of that happening? • Stochastic multihazard arrival processes • Attenuation probabilities Haimes (2004), Grossi & Kunreuther (2005), Banks (2006)

13. Natural Accidental Willful X Hazards => Vulnerability Sources Set {1, 2, 3, 4, 5} S SCN Risk Analysis: What can go wrong? 1 2 3 4, 5

14. What can go wrong? SCN Risk Modeling Exposure level of network node locations ?

15. Fund for Peace Failed State Index Foreign Policy

16. Seismic Hazard Exposure Map

17. SCN Risk Modeling

18. SCN Risk Analysis: What are the consequences? • Multihazard Incidents Severity Profile SCN Vulnerability Sources (S = {1, 2, 3, 4, 5}) (1) Suppliers (2) Plants (3) Warehouses (4) Demand source 1 (5) Demand source 2 Impact intensity Capacity loss rate Capacity loss rate Demand inflation rate Demand deflation rate Unfilled supply rate Severity dimensions metrics Time to recovery Time to restoring supplies Time to restarting production Time to restarting distribution Surge duration Drop duration

19. SCN Risk Analysis: What are the consequences? Recovery Function Examples Capacity loss recovery function Demand surge recovery function

20. SCN Risk Analysis: What is the likelihood of that happening? • Multihazard Likelihood Assessment • Distinct multihazard non-stationaryarrival process per exposure level • Poisson arrival process • Exponential inter-arrival time Exp(mgkt) with an expected time between multihazard mgkt • Time pattern for an evolutionary path k superimposed on process using a mean shaping function • Attenuation probability (azl) per network node based on hazard zone granularity

21. Design methodology: Decision-making framework Design Level • Investment • Policy making Anticipationof expected revenues and costs Design User Level Synchronization of supply and demandto minimize operations costs and maximize revenues

22. Structural adaptation decision Deployment lead time Usage period Design methodology: Decision time hierarchy for two planning cycles Design decision Design level Deployment lead time Usage period User level

23. Illustrative Case: Multi-depot location-routing problem • Daily stochastic orders from customers • Depots vulnerable to extreme events • How many warehouses and where ? Compound Stochastic Hazard Process DC Compound Poisson Demand Process

24. Design methodology: Decision-making framework (Rolling Horizon)

25. 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: Conditional return measure Conditional dispersion measure Conditional expected value measure Robustness criterion Multiparametric program

26. 3- Solution Approach Design generation 2 … Small samples replications Modeling approaches ( Anticipation; Resilience) Monte Carlo scenario generation 1 Status quo Design evaluation 3 … Large sample Solution methods Worst Case Scenarios

27. A1 A1 A1 A1 A1 A1 A1 A1 A1 A1 A1 A1 A2 A2 A2 A2 A2 A2 A2 A2 A2 A2 A2 A2 H1 H2 (A) Scenarios T1 (H) Scenarios (T) Scenarios Scenario building 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 Scenarios Evolutionary paths Aleatory events (A) Hazardous events (H) Totally uncertain events (T) 1 Environments

28. Monte Carlo : Scenario generation Monte-Carlo : • For all, • Generate the random number • Compute End For • For all ( , , andare random numbers) • Repeat : compute Until • For all , • Compute • Compute End For End For

29. Solution Approach: Sample statistics design generation model • 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) The complexity of the problem depends on the nature of

30. Solution Approach: Design evaluation model • Generate one large sample of scenarios partitioned into , and scenarios • For a given , solve the sample statistics design evaluation model: The most Effective and Robust SCN design is

31. 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)

32. Thank you for your attention Questions ?