Quantifying supply chain vulnerability using a multilayered complex network perspective

Abstract

Today's supply chains face increasing volatility on many fronts. From the shop-floor where machines break and suppliers fail to the boardrooms where unanticipated price inflation erodes profi tability. Turbulence is the new normal.

To remain competitive and weather these (daily) storms, supply chains need to move away from an effi ciency mindset towards a resilience mindset. For over a little more than a decade industry and academia have awakened to this reality. Academic literature and case studies show that there is no longer a shortage of resilience strategies and designs. Unfortunately, industry still lacks the tools with which to assess and evaluate the effectiveness of such strategies and designs. Without the ability to quantify the benefi t it is impossible to motivate the cost.

This thesis adds one piece to the puzzle of quantifying supply chain vulnerability. Speci fically, it focussed on supply chains within urban areas. It addresses the question: "How does a supply chain's network design (internal con figuration) and its dependence on the underlying road network (external circumstances) make it more or less vulnerable to disruptions of the road network?"

Multilayered Complex Network Theory (CNT) held promise as a modelling approach that could capture the complexity of the dependence between a logical supply chain network and the physical road network that underpins it. This approach addressed two research gaps in complex network theory applications. In the supply chain arena CNT applications have reaped many benefi ts but the majority of studies regarded single-layer networks that model only supply chain relations. There were no studies found where the dependence of supply chain layers on underlying physical infrastructure was modelled in a multilayered manner. Road network applications offered many more multilayered applications but these primarily focussed on passenger transport, not freight transport.

The first artefact developed in the thesis was a multilayered complex network formulation representing a logical (supply chain) layer placed on a physical (road infrastructure) layer. The individual layers had predefi ned network characteristics and on their own could not hint at the inherent vulnerability that the system as a whole might have. From the multilayered formulation, the collection of shortest paths emerged. This is the collection of all shortest path alternatives within a network. The collection of shortest paths is the unique fingerprint of each multilayered network instance. The key to understanding vulnerability lies within the characteristics of the collection of shortest paths.

Three standard supply chain network archetypes were de fined namely the Fully Connected (FC), Single Hub (SH) and Double Hub (DH) archetypes. A sample of 500 theoretical multilayered network instances was generated for each archetype. These theoretical instances were subjected to three link-based progressive targeted disruption simulations to study the vulnerability characteristics of the collection of shortest paths. Two of the simulations used relative link betweenness to prioritise the disruptions while the third used the concept of network skeletons as captured by link salience. The results from these simulations showed that the link betweenness strategies were far more effective than the link salience strategy.

From these results three aspects of vulnerability were identifi ed. Redundancy quantifi es the number of alternative shortest paths available to an instance. Overlap measures to what degree the shortest path sets of an instance overlap and have road segments in common. Effi ciency step-change is a measure of the magnitude of the "shock" absorbed by the shortest paths of an instance during a disruption. For each of these aspects one or more metrics were defi ned. This suite of vulnerability metrics is the second artefact produced by the thesis.

The design of the artefacts itself, although novel, was not considered research. It is the insights derived during analysis of the artefacts' performance that contributes to the body of knowledge. Link-based progressive random disturbance simulations were used to assess the ability of the vulnerability metrics to quantify supply chain vulnerability. It was found that none of the de fined vulnerability aspects are good stand-alone predictors of vulnerability. The multilayered nature and random disturbance protocol result in vulnerability being more multi-faceted than initially imagined. Nonetheless, the formulation of the multilayered network proved useful and intuitive and even though the vulnerability metrics fail as predictors they still succeed in capturing shortest path phenomena that would lead to vulnerability under non-random protocols.

To validate the fi ndings from the theoretical instances, link-based random disturbance simulations were executed on 191 case study instances. These instances were extracted from real-life data in three urban areas in South Africa, namely Gauteng Province (GT), City of Cape Town (CoCT) and eThekwini Metropolitan Municipality (ET). The case study instances showed marked deviations from the assumptions underlying the theoretical instances. Despite these differences, the multilayered formulation still enables the quanti fication of the relationship between supply chain structure and road infrastructure. The performance of the vulnerability metrics in the case study corroborates the findings from the theoretical instances.

Although the suite of vulnerability metrics was unsuccessful in quantifying or predicting vulnerability in both the theoretical and case study instances, the rationale behind their development is sound. Future work that will result in more effective metrics is outlined in this thesis. On the one hand the development of a more realistic disruption strategy is suggested. Road network disruptions are neither completely random nor specifi cally targeted. Important segments with greater tra ffic loads are more likely to be disrupted, but the reality is that disruptions such as accidents, equipment failure or road maintenance could really occur anywhere on the network. A more realistic disruption strategy would lie somewhere on the continuum between targeted and random disruptions. Other future work suggests the refi nement of both artefacts by incorporating link weights in both the logical and physical layers.

An unanticipated fi nding from this thesis is that future research in the fi eld may be expedited if theory-building emanates from real-life empirical networks as opposed to theoretically generated networks. Expanding the scope of the case study, characterising the true network archetypes found in practice and increasing the number of case study samples is a high priority for future work.