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Importance measures in strategic-level supply chain risk management Anssi Käki Ahti Salo Department of Mathematics and Systems Analysis School of Science, Aalto University, Finland

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Introduction Diagnosis of risks and evaluation of risk mitigation strategies is difficult in large supply networks: – Numerous nodes (suppliers, tiers) – Many uncertainties (demand, quality, lead time) – High level of dependency (disruptions at supplier’s supplier’s supplier) We present how supply network disruptions can be evaluated with Probabilistic Risk Analysis (PRA) and Bayesian networks : – How to recognize, group, and prioritize risk factors? – How to visualize risks?

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Executive summary Material supplier network for Honda Accord center console 1 Risk importance of each supplier illustrated 1 Network adapted from Choi and Hong (2002), Kim et al. (2011)

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Supply chain risks can be captured with optimization models: – Stochastic optimization for minimizing expect cost under known probability distributions – Robust optimization for a guaranteed outcome without much assumptions of uncertainty – Tailored for specific decision situations: e.g, facility location or supplier selection Probability based diagnostic analysis serves different purposes: – Not focused on particular decisions; increases visibility and understanding of the whole – Allows modeling substantially large networks – Models are not ”black boxes” Comprehensible for management Why Probabilistic Risk Analysis (PRA) for Supply Networks? Review of optimization models for disruption management: Snyder et al. (2010)

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PRA importance measures for prioritization: A Fussell-Vesely example Probability of disruption at supplier i: Pr(F i )= 10.0% Probability for network disruption: Pr(F s )≈ 2.2% Supplier S 3 is the most important, then S 4 and S 5, then S 1 and S 2 S3S3 S1S1 S2S2 S4S4 S5S5 10% Lower branch Upper branch 2.2% 2.0% Fussell-Vesely measures the decrease in network disruption probability, if a supplier is not disrupted

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Different importance measures are used to support different decisions There are many importance measures for various purposes; we consider Fussell-Vesely (FV) & Risk-Achievement-Worth (RAW): The direct effect of supplier i for the network disruption F s ”Defence in depth” - the capability of the network to resist a disruption at supplier i FVRAWPotential for improvementPotential for degrading High Supplier, networkNo HighLowSupplierNo LowHigh”Avoid disruptions”, networkNo Low NoSupplier, network Source of table: van der Borst & Schoonakker (2001)

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Typical PRA methods use logic gates to describe a system; this can be too rigorous for supply chains Bayesian network consists of a causality graph and conditional probability tables Bayesian networks can be used to model probabilistic reliability networks Logic or-gate Bayesian network Pr(JFC OK | J3 and CVTWood OK)100%95% Pr(JFC OK | J3 or CVTWood OK)100%50% Pr(JFC OK | J3 and CVTWood disrupted)0%5% Logic diagram Bayesian network Pr( CVTWood OK)95%

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The Accord net is translated into a Bayesian net Assumptions: – A leaf supplier has 5% disruption probability – Disruption at a parent supplier leaves a 50% ”survival probability” (due to backup suppliers, inventories) – The disruption probability of suppliers with multiple parents is proportional to amount of parents disrupted Importance measures are calculated for two scenarios: – As above – As above, but with supplier J3 turning risky Disruption probability is updated from 5% to 50% The Honda Accord center console network

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Fussell-Vesely (no disruption at supplier): First tier suppliers are critical Scenario: J3 becomes risky Size and color indicate the importance measure value For example: FV(JFC)=32.86% FV(Emhart)=1.01%

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Size and color indicate the importance measure value Risk Achievemet Worth (certain disruption): Parent supplier CVT is critical For example: RAW(JFC)=3.37 RAW(Emhart)=1.11 Scenario: J3 becomes risky

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Fussell-Vesely guides the prioritization of improvement actions at individual suppliers 1.Improvements at 1st tier suppliers CVTAss and JFC increase reliability the most 2.When J3 has reliability issues, improvements at JFC and J3 become a key priority Risk Achievement Worth can be used when improving network (design, other suppliers) 3.A disruption at CVT (parent of three CVT-sub- suppliers) harms reliability the most Decreasing dependency on CVT is recommended Key takeways from different measures

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Estimation of probabilities: – Expert judgment, estimation from statistical data, discrete-event simulation Dynamic modeling: – Inventory and delays work as supply chain buffers; they are dynamic in nature – Once-in-ten-years disruption that lasts 6 months vs. Once-a-year disruption that lasts 18 days Both have (yearly) disruption probability of 5% – Dynamic Bayesian nets and simulation can capture such dynamics Multi-stage models: e.g., ”Full disruption” – ”50% capacity” – ”Full capacity” Other importance measures, such as joint-importance Extensions of the approach

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Importance measures can be used for various purposes… – Fussell-Vesely when planning improvements at individual suppliers – Risk Achievement Worth for changes in network design …and the results can be illustrated in an intuitive risk map The approach is next validated in real applications Conclusions

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Thank you! Choi, T. Y. and Hong, Y. (2002). Unveiling the structure of supply networks: case studies in Honda, Acura, and DaimlerChrysler. Journal of Operations Management, 20:469–493. Deleris, L. and Erhun, F. (2011). Quantitative risk assessment in supply chains: a case study based on engineering risk analysis concepts. In Planning production and inventories in the extended enterprise. Springer Science+Business Media. Kim, Y., Choi, T. Y., Yan, T., and Dooley, K. (2011). Structural investigation of supply networks: A social network analysis approach. Journal of Operations Management, 29:194–211. Schmitt, A. and Singh, M. (2011). A Quantitative Analysis of Disruption Risk in a Multi-Echelon Supply Chain. Working paper. Center for Transportation and Logistics. Massachusetts Institute of Technology. Snyder, L, Atan, Z., Peng, P., Rong, Y., Schmitt, A. and Sinsoyal, B. (2010). OR/MS Models for Supply Chain Disruptions: A Review. Working Paper. Van der Borst, M. and Schoonakker, H. (2001). An overview of PSA importance measures. Reliability Engineering and System Safety, 72: Zio, E. (2011). Risk Importance Measures. In Safety and Risk Modeling and Its Applications. Springer-Verlag London. References

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Appendix: Tabular results

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