Integrated detection of disruption scenarios, the ripple effect dispersal and recovery paths in supply chains

Abstract

The studies on supply chain (SC) disruption management frequently assume the existence of some negative scenarios and suggest ways to proactively protect and reactively recover the SC operations and performance if such scenarios occur. Though, there is a paucity of research on how to support methodologically the detection of realistic disruption scenarios, ideally of different risk aversion degrees. The contribution of our study lies in a conceptualization of a new methodical approach to the detection of disruption scenarios, ripple effect dispersal and recovery paths in supply chains on the basis of structural genomes. The objective is to integrate and expand the existing knowledge gained isolated in robustness analysis and recovery planning into a comprehensive framework for building a theory as well as for managerial purposes. The outcomes of this research constitute a useful decision-making support tool that allows detecting disruption scenarios at different risk-aversion levels based on the quantification of the structural robustness with the use of the genome method and observing the scope of disruption propagation, i.e., the ripple effect. The advantage of using a robustness computation by the genome method is that this allows detecting both the disruption scenarios of different severity, the ripple effect dispersal, and the corresponding recovery paths. Our results can be of value for decision-makers to compare different supply chain structural designs regarding the robustness and to identify disruption scenarios that interrupt the supply chain operations to different extents. The scenario detection can be further used for identifying optimal reconfiguration paths to deploy proactive contingency and reactive recovery policies. We show a correlation between the risk aversion degree of disruption scenarios and the outcomes of the reconfiguration policies.

Appendices

Appendix 1: Computational analysis of the SC robustness with the consideration of disruptions at both nodes and arcs (i.e., both facility and transportation disruptions)

Consider the example of the genome analysis of an SC according to Fig. 1.

The grey nodes 1–7 in Fig. 5 are related to the nodes in the SC design in Fig. 1. The white nodes 8–16 are the arcs in the SC design in Fig. 1. Supplier 1 delivers to factory 3 using transportation link 8 and to factory 2 using transportation link 9. Factories 2 and 3 deliver to distribution center 4 using links 10 and 11. In addition, the distribution center 4 can source from supplier 6. In other words, plant 4 exhibits a multiple sourcing strategy from nodes 2 or 3 or 6. Customer 5 can order products either directly from factory 2 using link 13 or from distribution center 4 using link 14, or from warehouse 7, which is a subsidiary (backup warehouse) of distribution center 4, using links 15 and 16.

Fig. 5

Fuzzy-probabilistic graph of the SC design

The logical fulfillment function contains seven conjunctions:

$$ \begin{aligned} {\text{path }}6 - 12 - 4 - 15 - 7 - 16 - 5,\,{\text{path }}1 - 9 - 2 - 11 - 4 - 15 - 7 - 16 - 5,\,{\text{path }}1 - 8 - 3 - 10 - 4 - 15 - 7 - 16 - 5, \hfill \\ {\text{path }}6 - 12 - 4 - 14 - 5,\,{\text{path }}1 - 9 - 2 - 11 - 4 - 14 - 5,\,{\text{path }}1 - 8 - 3 - 10 - 4 - 14 - 5,{\text{ and path }}1 - 9 - 2 - 13 - 5. \hfill \\ \end{aligned} $$

The probability function of the robust purpose fulfillment can be written as follows:

$$ \begin{aligned} {\text{Pc}} & = {\text{P}}1{\text{ P}}2{\text{ P}}4{\text{ P}}5{\text{ P}}7{\text{ P}}9{\text{ P}}11{\text{ Q}}13{\text{ Q}}14{\text{ P}}15{\text{ P}}16 \\ & \quad + {\text{ P}}1{\text{ P}}3{\text{ P}}4{\text{ P}}5{\text{ P}}7{\text{ P}}8{\text{ P}}10{\text{ Q}}14{\text{ P}}15{\text{ P}}16 \\ & \quad + {\text{ P}}4{\text{ P}}5{\text{ P}}6{\text{ P}}7{\text{ P}}12{\text{ Q}}14{\text{ P}}15{\text{ P}}16 \\ & \quad + {\text{ P}}1{\text{ P}}2{\text{ P}}4{\text{ P}}5{\text{ P}}9{\text{ P}}11{\text{ Q}}13{\text{ P}}14 \\ & \quad + {\text{ P}}1{\text{ P}}3{\text{ P}}4{\text{ P}}5{\text{ P}}8{\text{ P}}10{\text{ P}}14 \\ & \quad + {\text{ P}}4{\text{ P}}5{\text{ P}}6{\text{ P}}12{\text{ P}}14 \\ & \quad + {\text{ P}}1{\text{ P}}2{\text{ P}}5{\text{ P}}9{\text{ P}}13 \\ & \quad - {\text{ P}}1{\text{ P}}2{\text{ P}}4{\text{ P}}5{\text{ P}}6{\text{ P}}9{\text{ P}}12{\text{ P}}13{\text{ P}}14 \\ & \quad - {\text{ P}}1{\text{ P}}3{\text{ P}}4{\text{ P}}5{\text{ P}}6{\text{ P}}8{\text{ P}}10{\text{ P}}12{\text{ P}}14 \\ & \quad - {\text{ P}}1{\text{ P}}2{\text{ P}}3{\text{ P}}4{\text{ P}}5{\text{ P}}8{\text{ P}}9{\text{ P}}10{\text{ P}}13{\text{ P}}14 \\ & \quad + {\text{ P}}1{\text{ P}}2{\text{ P}}3{\text{ P}}4{\text{ P}}5{\text{ P}}6{\text{ P}}8{\text{ P}}9{\text{ P}}10{\text{ P}}12{\text{ P}}13{\text{ P}}14 \\ & \quad - {\text{ P}}1{\text{ P}}2{\text{ P}}3{\text{ P}}4{\text{ P}}5{\text{ P}}8{\text{ P}}9{\text{ P}}10{\text{ P}}11{\text{ Q}}13{\text{ P}}14 \\ & \quad - {\text{ P}}1{\text{ P}}2{\text{ P}}4{\text{ P}}5{\text{ P}}6{\text{ P}}9{\text{ P}}11{\text{ P}}12{\text{ Q}}13{\text{ P}}14 \\ & \quad + {\text{ P}}1{\text{ P}}2{\text{ P}}3{\text{ P}}4{\text{ P}}5{\text{ P}}6{\text{ P}}8{\text{ P}}9{\text{ P}}10{\text{ P}}11{\text{ P}}12{\text{ Q}}13{\text{ P}}14 \\ & \quad - {\text{ P}}1{\text{ P}}2{\text{ P}}4{\text{ P}}5{\text{ P}}6{\text{ P}}7{\text{ P}}9{\text{ P}}12{\text{ P}}13{\text{ Q}}14{\text{ P}}15{\text{ P}}16 \\ & \quad - {\text{ P}}1{\text{ P}}3{\text{ P}}4{\text{ P}}5{\text{ P}}6{\text{ P}}7{\text{ P}}8{\text{ P}}10{\text{ P}}12{\text{ Q}}14{\text{ P}}15{\text{ P}}16 \\ & \quad - {\text{ P}}1{\text{ P}}2{\text{ P}}3{\text{ P}}4{\text{ P}}5{\text{ P}}7{\text{ P}}8{\text{ P}}9{\text{ P}}10{\text{ P}}13{\text{ Q}}14{\text{ P}}15{\text{ P}}16 \\ & \quad + {\text{ P}}1{\text{ P}}2{\text{ P}}3{\text{ P}}4{\text{ P}}5{\text{ P}}6{\text{ P}}7{\text{ P}}8{\text{ P}}9{\text{ P}}10{\text{ P}}12{\text{ P}}13{\text{ Q}}14{\text{ P}}15{\text{ P}}16 \\ & \quad - {\text{ P}}1{\text{ P}}2{\text{ P}}3{\text{ P}}4{\text{ P}}5{\text{ P}}7{\text{ P}}8{\text{ P}}9{\text{ P}}10{\text{ P}}11{\text{ Q}}13{\text{ Q}}14{\text{ P}}15{\text{ P}}16 \\ & \quad - {\text{ P}}1{\text{ P}}2{\text{ P}}4{\text{ P}}5{\text{ P}}6{\text{ P}}7{\text{ P}}9{\text{ P}}11{\text{ P}}12{\text{ Q}}13{\text{ Q}}14{\text{ P}}15{\text{ P}}16 \\ & \quad + {\text{ P}}1{\text{ P}}2{\text{ P}}3{\text{ P}}4{\text{ P}}5{\text{ P}}6{\text{ P}}7{\text{ P}}8{\text{ P}}9{\text{ P}}10{\text{ P}}11{\text{ P}}12{\text{ Q}}13{\text{ Q}}14{\text{ P}}15{\text{ P}}16 \\ \end{aligned} $$

or as

$$ {\rm P}(P) = \,2P^{5} + 3P^{7} - 2P^{8} - P^{9} - 4P^{10} - P^{11} + 4P^{12} + P^{13} + P^{14} - 3P^{15} + P^{16} , $$

or as the dual genome

$$ \eta = (0,0,0,0,0,2,0,3, - 2, - 1, - 4, - 1,4,1,1, - 3,1). $$

The SC structure failure possibility polynomial that describes all possible combinations of minimum failure edge-cuts can be written as

$$ \begin{aligned} T(Q) & = Q + 6Q^{2} + 9Q^{3} - 100Q^{4} + 173Q^{5} + 13Q^{6} - 408Q^{7} + 521Q^{8} - 74Q^{9} \\ & \quad - 535Q^{10} + 762Q^{11} - 563Q^{12} + 260Q^{13} - 76Q^{14} + 13Q^{15} - Q^{16} . \\ \end{aligned} $$

or as the genome

$\chi = (0,1,6,9, - 100,173,13, - 408,521, - 74, - 535,762, - 563,260, - 76,13, - 1)$.

Figure 6 illustrates the computation of the structural robustness, the respective disruption scenarios, and the contribution of the individual SC elements to the structural robustness.

Fig. 6

Structural robustness, respective disruption scenarios, and contribution of the individual SC elements to the structural robustness

Appendix 2: Computational analysis of the robustness of the SC with the consideration of disruptions at arcs (i.e., transportation disruptions)

Figure 7 shows a fuzzy-probabilistic graph in the event of disruptions at arcs (i.e., transportation disruptions) only.

Fig. 7

Fuzzy-probabilistic graph in the event of disruptions at arcs (i.e., transportation disruptions) only

The logical fulfillment function contains seven conjunctions:

$$ \begin{aligned} & {\text{path }}1 - 5,\,{\text{path }}1 - 3 - 6,\,{\text{path }}2 - 4 - 6,\,{\text{ path }}6 - 9, \\ & {\text{path }}1 - 3 - 7 - 8,\,{\text{path }}2 - 4 - 7 - 8,\,{\text{and}}\,{\text{ path }}7 - 8 - 9. \\ \end{aligned} $$

The probability function of the robust purpose fulfillment can be written as follows (Table 2):

Table 2 Statistical analysis

$$ \begin{aligned} {\text{Pc}} & = {\text{P}}1{\text{ P}}3{\text{ Q}}5{\text{ Q}}6{\text{ P}}7{\text{ P}}8{\text{ Q}}9 \\ & \quad + {\text{ P}}2{\text{ P}}4{\text{ Q}}6{\text{ P}}7{\text{ P}}8{\text{ Q}}9 \\ & \quad + {\text{ P}}1{\text{ P}}3{\text{ Q}}5{\text{ P}}6{\text{ Q}}9 \\ & \quad + {\text{ P}}2{\text{ P}}4{\text{ P}}6{\text{ Q}}9 \\ & \quad + {\text{ Q}}6{\text{ P}}7{\text{ P}}8{\text{ P}}9 \\ & \quad + {\text{ P}}1{\text{ P}}5 \\ & \quad + {\text{ P}}6{\text{ P}}9 \\ & \quad - {\text{ P}}1{\text{ P}}5{\text{ P}}6{\text{ P}}9 \\ & \quad - {\text{ P}}1{\text{ P}}5{\text{ Q}}6{\text{ P}}7{\text{ P}}8{\text{ P}}9 \\ & \quad - {\text{ P}}1{\text{ P}}2{\text{ P}}4{\text{ P}}5{\text{ P}}6{\text{ Q}}9 \\ & \quad - {\text{ P}}1{\text{ P}}2{\text{ P}}3{\text{ P}}4{\text{ Q}}5{\text{ P}}6{\text{ Q}}9 \\ & \quad - {\text{ P}}1{\text{ P}}2{\text{ P}}4{\text{ P}}5{\text{ Q}}6{\text{ P}}7{\text{ P}}8{\text{ Q}}9 \\ & \quad - {\text{ P}}1{\text{ P}}2{\text{ P}}3{\text{ P}}4{\text{ Q}}5{\text{ Q}}6{\text{ P}}7{\text{ P}}8{\text{ Q}}9 = 0.572265625000 \, \left( {{\text{probability}}\,{\text{of}}\,{\text{purpose}}\,{\text{fulfillment}}} \right) \\ \end{aligned} $$

Figure 8 illustrates the computation of the structural robustness, the respective disruption scenarios, and the contribution of the individual SC elements to the structural robustness.

Fig. 8

Structural robustness, respective disruption scenarios, and contribution of the individual SC elements to the structural robustness