Much of the previous research on facility networks focuses on improving the network design, but a good design alone is not sufficient to ensure smooth operations against disruption risks. This study examines an underexplored question of where to invest in resilience in a facility network. Prior studies offered insights into this issue, with some scholars recommending a focus on critical nodes, while others emphasize the importance of critical paths that are sequences of adjacent nodes and edges. Yet the node and path perspectives have not been fully integrated and optimized for facility networks. Motivated by real problems from Cainiao Network, this study reconciles the debate over node versus path and solves the problem of resilience investment to maximize expected max-flow through the network. The analysis reveals that investing in high-capacity nodes is optimal under rare disruptions, whereas investing in nodes on entire paths is best under frequent disruptions. The problem of resilience investment is in general NP-hard, but we propose greedy algorithms inspired by the node and path perspectives to provide approximate solutions with performance guarantees. Empirical analysis using operational data from Cainiao Network supports our analytical findings.
AgarwalYKAnejaYPJayaswalS (2022) Directed fixed charge multicommodity network design: A cutting plane approach using polar duality. European Journal of Operational Research299(1): 118–136.
2.
AlbertRJeongHBarabásiAL (2000) Error and attack tolerance of complex networks. Nature406(6794): 378.
3.
AngEIancuDASwinneyR (2016) Disruption risk and optimal sourcing in multitier supply networks. Management Science63(8): 2397–2419.
4.
ArulselvanA (2014) A note on the set union knapsack problem. Discrete Applied Mathematics169: 214–218.
5.
BaiWBilmesJ (2018) Greed is still good: Maximizing monotone submodular+supermodular (bp) functions. In: International conference on machine learning (ICML) (Stockholm, Sweden).
BasoleRCBellamyMA (2014) Supply network structure, visibility, and risk diffusion: A computational approach. Decision Sciences45(4): 753–789.
8.
BianAABuhmannJMKrauseA, et al. (2017) Guarantees for greedy maximization of non-submodular functions with applications. In: Proceedings of the 34th International conference on machine learning-volume 70, pp.498–507. (JMLR.org).
BimpikisKFearingDTahbaz-SalehiA (2018) Multisourcing and miscoordination in supply chain networks. Operations Research66(4): 1023–1039.
11.
BirgeJRCapponiAChenPC (2023) Disruption and rerouting in supply chain networks. Operations Research71(2): 750–767.
12.
BirgeJRLouveauxF (2011) Introduction to Stochastic Programming. Springer Series in Operations Research and Financial Engineering. New York, NY: Springer.
13.
BorgattiSPMehraABrassDJ, et al. (2009) Network analysis in the social sciences. Science (New York, N.Y.)323(5916): 892–895.
14.
BrinkleyC (2018) The small world of the alternative food network. Sustainability10(8): 2921.
15.
BuLDawandeMJanakiramanG (2022) Procurement for assembly systems under disruption risk: Optimal mechanisms. Available at SSRN 4245055.
16.
CareyMHendricksonC (1984) Bounds on expected performance of networks with links subject to failure. Networks14(3): 439–456.
17.
ChaturvediAMartínez-de-AlbénizV (2011) Optimal procurement design in the presence of supply risk. Manufacturing & Service Operations Management13(2): 227–243.
18.
ChenDSunDYinY, et al. (2022a) The resilience of logistics network against node failures. International Journal of Production Economics244: 108373.
19.
ChenKLiYLindermanK (2022b) Supply network resilience learning: An exploratory data analytics study. Decision Sciences53(1): 8–27.
20.
ChopraSSodhiM (2014) Reducing the risk of supply chain disruptions. MIT Sloan Management Review55(3): 72–80.
CraigheadCWBlackhurstJRungtusanathamMJ, et al. (2007) The severity of supply chain disruptions: Design characteristics and mitigation capabilities. Decision Sciences38(1): 131–156.
DongLKouvelisPSuP (2010) Global facility network design with transshipment and responsive pricing. Manufacturing & Service Operations Management12(2): 278–298.
25.
EdrissiANourinejadMRoordaMJ (2015) Transportation network reliability in emergency response. Transportation Research Part E: Logistics and Transportation Review80: 56–73.
26.
FujishigeS (2005) Submodular functions and optimization. In: Annals of Discrete Mathematics. Vol. 58. New York, NY: Elsevier.
27.
GuptaARaviRSinhaA (2007) LP rounding approximation algorithms for stochastic network design. Mathematics of Operations Research32(2): 345–364.
28.
HandfieldRBKrauseDRScannellTV, et al. (2010) Avoid the pitfalls in supplier development. MIT Sloan Management Review41(2): 37–49.
29.
HassinRRaviRSalmanFS, et al. (2020) The approximability of multiple facility location on directed networks with random arc failures. Algorithmica82(9): 2474–2501.
30.
HeLRongYShenZJM (2020) Product sourcing and distribution strategies under supply disruption and recall risks. Production and Operations Management29(1): 9–23.
31.
HearnshawEJWilsonMM (2013) A complex network approach to supply chain network theory. International Journal of Operations & Production Management33(4): 442–469.
32.
KimYChenYSLindermanK (2015) Supply network disruption and resilience: A network structural perspective. Journal of Operations Management33: 43–59.
33.
KjeldgaardSAndersenALBrunoeTD (2023) Enabling adaptability and resilience of a global production network: A model to evaluate capital and operational expenses of reconfigurable production systems. Journal of Manufacturing Systems66: 142–162.
34.
KleindorferPRSaadGH (2005) Managing disruption risks in supply chains. Production and Operations Management14(1): 53–68.
35.
KouvelisPChambersCYuDZ (2005) Manufacturing operations manuscripts published in the first 52 issues of pom: Review, trends, and opportunities. Production and Operations Management14(4): 450–467.
36.
KouvelisPMunsonCLYangS (2013) Robust structural equations for designing and monitoring strategic international facility networks. Production and Operations Management22(3): 535–554.
LampelJGiachettiC (2013) International diversification of manufacturing operations: Performance implications and moderating forces. Journal of Operations Management31(4): 213–227.
39.
LiYChenKCollignonS, et al. (2021) Ripple effect in the supply chain network: Forward and backward disruption propagation, network health and firm vulnerability. European Journal of Operational Research291(3): 1117–1131.
40.
LikerJKChoiTY (2004) Building deep supplier relationships. Harvard Business Review82(12): 104–113.
41.
LimMKBassambooAChopraS, et al. (2013) Facility location decisions with random disruptions and imperfect estimation. Manufacturing & Service Operations Management15(2): 239–249.
42.
LuLXVan MieghemJA (2009) Multimarket facility network design with offshoring applications. Manufacturing & Service Operations Management11(1): 90–108.
43.
MagnantiTLShenZJMShuJ, et al. (2006) Inventory placement in acyclic supply chain networks. Operations Research Letters34(2): 228–238.
44.
McCullaghP (1980) Regression models for ordinal data. Journal of the Royal Statistical Society. Series B (Methodological)42(2): 109–142.
NairAVidalJM (2011) Supply network topology and robustness against disruptions—An investigation using multi-agent model. International Journal of Production Research49(5): 1391–1404.
47.
OlhagerJPashaeiSSternbergH (2015) Design of global production and distribution networks: A literature review and research agenda. International Journal of Physical Distribution & Logistics Management45(1/2): 138–158.
48.
OnagaK (1968) Bounds on the average terminal capacity of probabilistic nets. IEEE Transactions on Information Theory14(5): 766–768.
49.
PeetaSSalmanFSGunnecD, et al. (2010) Pre-disaster investment decisions for strengthening a highway network. Computers & Operations Research37(10): 1708–1719.
50.
RiopelDLangevinACampbellJF (2005) The network of logistics decisions. In: Langevin A and Riopel (eds) Logistics Systems: Design and Optimization. Boston, MA: Springer, 1–38.
51.
RoelsGTangCS (2017) Win-win capacity allocation contracts in coproduction and codistribution alliances. Management Science63(3): 861–881.
52.
SalmeronJWoodKBaldickR (2004) Analysis of electric grid security under terrorist threat. IEEE Transactions on Power Systems19(2): 905–912.
53.
SheffiYRiceJB Jr (2005) A supply chain view of the resilient enterprise. MIT Sloan Management Review47(1): 41–48.
54.
SnyderLV (2006) Facility location under uncertainty: A review. IIE Transactions38(7): 547–564.
55.
SnyderLVAtanZPengP, et al. (2016) OR/MS models for supply chain disruptions: A review. IIE Transactions48(2): 89–109.
56.
SnyderLVScaparraMPDaskinMS, et al. (2006) Planning for disruptions in supply chain networks. In: Models, methods, and applications for innovative decision making, pp.234–257. (INFORMS).
57.
SunHWuJ (2005) Scale-free characteristics of supply chain distribution networks. Modern Physics Letters B19(17): 841–848.
58.
SundarakaniBPereiraVIshizakaA (2021) Robust facility location decisions for resilient sustainable supply chain performance in the face of disruptions. The International Journal of Logistics Management32(2): 357–385.
59.
TangCS (2006) Robust strategies for mitigating supply chain disruptions. International Journal of Logistics: Research and Applications9(1): 33–45.
60.
TomlinB (2006) On the value of mitigation and contingency strategies for managing supply chain disruption risks. Management Science52(5): 639–657.
WallaceSW (1987) Investing in arcs in a network to maximize the expected max flow. Networks17(1): 87–103.
63.
WangYLiJWuD, et al. (2021) When ignorance is not bliss: An empirical analysis of subtier supply network structure on firm risk. Management Science67(4): 2029–2048.
64.
WattsDJStrogatzSH (1998) Collective dynamics of “small-world” networks. Nature393(6684): 440.
65.
WollmerRD (1991) Investments in stochastic maximum flow networks. Annals of Operations Research31(1): 457–467.
66.
YanTChoiTYKimY, et al. (2015) A theory of the nexus supplier: A critical supplier from a network perspective. Journal of Supply Chain Management51(1): 52–66.
Supplementary Material
Please find the following supplemental material available below.
For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.
For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.
