Importance measures in strategic-level supply chain risk management

Anssi Käki

Ahti Salo

Department of Mathematics and Systems AnalysisSchool of Science, Aalto University, Finland

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?

Executive summary

Material supplier network for Honda Accord center console1

Risk importance of each supplier illustrated

1 Network adapted from Choi and Hong (2002), Kim et al. (2011)

• 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)

PRA importance measures for prioritization: A Fussell-Vesely example• Probability of disruption at supplier i: Pr(Fi)= 10.0%

Probability for network disruption: Pr(Fs)≈ 2.2%

Supplier S3 is the most important, then S4 and S5, then S1 and S2

Supplier S3 is the most important, then S4 and S5, then S1 and S2

S3

S1

S2

S4

S5

10%

10%

10%

10% 10%

Lower branch Upper branch

2.2%2.0%

• Fussell-Vesely measures the decrease in network

disruption probability, if a supplier is not disrupted 2.2%SS(SS5(SPr 3214 ))()

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):

)Pr(FOK)S|Pr(F)Pr(F

FV(SS

iSSi

)

)Pr(FDISRUPTED)S|Pr(F

)RAW(SS

iSi

The direct effect of supplier i for the network disruption Fs

The direct effect of supplier i for the network disruption Fs

”Defence in depth” - the capability of the network to resist a disruption at supplier i

”Defence in depth” - the capability of the network to resist a disruption at supplier i

FV RAW Potential for

improvementPotential for degrading

High High Supplier, network No

High Low Supplier No

Low High ”Avoid disruptions”, network

No

Low Low No Supplier, networkSource of table: van der Borst & Schoonakker (2001)

• 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% 95%

• 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

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%

Size and color indicate the importance measure value

Risk Achievemet Worth (certain disruption): Parent supplier CVT is critical

For example:RAW(JFC)=3.37RAW(Emhart)=1.11

Scenario: J3 becomes risky

• 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

1.

2.

3.

• 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

• 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

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: 241-245.

Zio, E. (2011). Risk Importance Measures. In Safety and Risk Modeling and Its Applications. Springer-Verlag London.

References

Appendix: Tabular results