Identifying dynamical instabilities in supply networks using generalized modeling

• Date: 01 March 2019
• Published date: 01 March 2019
• Author: Thilo Gross,Bart L. MacCarthy,Daniel Ritterskamp,Güven Demirel,Alan R. Champneys
• DOI: http://doi.org/10.1002/joom.1005

ORIGINAL ARTICLE

Identifying dynamical instabilities in supply networks using

generalized modeling

Güven Demirel

1

| Bart L. MacCarthy

2

| Daniel Ritterskamp

3

| Alan R. Champneys

3

|

Thilo Gross

3

1

Management Science & Entrepreneurship

Group, Essex Business School, University

of Essex, Southend-on-Sea, UK

2

Operations Management & Information

Systems, Business School, University of

Nottingham, Nottingham, UK

3

Department of Engineering Mathematics,

University of Bristol, Bristol, UK

Correspondence

Bart L. MacCarthy, Operations

Management & Information Systems,

Business School, University of Nottingham,

Nottingham NG7 2RD, UK.

Email: bart.maccarthy@nottingham.ac.uk

Handling Editors: Anand Nair and Felix

Reed-Tsochas

Funding information

Engineering and Physical Sciences Research

Council, UK, Grant/Award Number:

EP/K031686/1

Abstract

Supply networksneed to exhibit stability in order to remainfunctional. Here, we apply

a generalizedmodeling (GM) approach, which has a strong pedigree in theanalysis of

dynamicalsystems, to study the stability of real-worldsupply networks. It goes beyond

purely structural network analysis approaches by incorporating material flows, which

are definingcharacteristics of supply networks.The analysis focuses on the networkof

interactions between material flows, providing new conceptualizations to capture key

aspects of production and inventory policies. We provide stability analyses of two

contrasting real-world networks—that of an industrial engine manufacturer and an

industry-levelnetwork in the luxury goods sector. We highlight the criticality of links

with suppliers that involve the dispatch, processing, and return of parts or sub-assem-

blies, cyclic motifs that involve separate paths from a common supplier to a common

firm downstream,and competing demands of differentend products at specific nodes.

Based on a critical discussion of our findings in the context of the supply chain man-

agement literature, we generate five propositions to advance knowledge and under-

standing of supply network stability. We discuss the implications of the propositions

for the effectivemanagement, control, and development of supply networks. The GM

approach enables fast screening to identify hidden vulnerabilities in extensive supply

networks.

KEYWORDS

complex networks, nonlinear dynamics, stability, supply chain

1|INTRODUCTION

Supply networks need to remain functional in the presence of

disturbances and disruptions (Tang, 2006). The capability of a

network to withstand disturbances anddisruptions is related to

the concept of stability. This is a term commonly used in a

number of disciplines to refer to the capability of a system to

remain closeor converge back to a steady statefollowing a trig-

gering event (Guckenheimer & Holmes, 1983). In the absence

of stability, even small disturbances may drive a supply net-

work away from a desired or planned state (Venkateswaran &

Son, 2007; Wei,Wang, & Qi, 2013). Here, we are interested in

the stabilityof material flows in supply networks,where its loss

manifests itselfby divergence from an equilibrium state and by

oscillations,leading to uncontrolled inventory build-upsand/or

stock-outs, production overtime and/or production shutdowns,

all of which will typically have very costly consequences

(Venkateswaran& Son, 2007). Although firms thatconstitute a

DOI: 10.1002/joom.1005

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original

work is properly cited.

© 2019 The Authors. Journal of Operations Management published by Wiley Periodicals, Inc. on behalf of The Association for Supply Chain Management Inc.

136 wileyonlinelibrary.com/journal/joom J Oper Manag. 2019;65:136–159.

supply network would be expected to react to such undesired and

costly consequences by revising their policies over time, for

instance by changing the replenishment period or shifting orders

to other suppliers, costs will still be incurred until these measures

show their effect. Worse still, such reactive measures may not lead

to the intended outcomes, because individual firms are embedded

in complex supply networks, which need to be understood in their

entirety (Pathak, Day, Nair, Sawaya, & Kristal, 2007; Surana,

Kumar, Greaves, & Raghavan, 2005). It is therefore imperative to

understand the stability properties of supply networks.

Supply network stability has been investigated in previous

studies, particularly in the context of inventorycontrol policies

(Sarimveis, Patrinos, Tarantilis, & Kiranoudis, 2008; Wang &

Disney, 2016). Many studies in the literature on supply net-

work dynamics have focused on isolated parts of largersupply

networks such as buyer–supplier dyads or retailer-wholesaler-

manufacturer triads (Sarimveis et al., 2008; Wang & Disney,

2016). Some recentstudies in the context of the bullwhipeffect

have consideredlarger networks (Chatfield, 2013;Dominguez,

Framinan,& Cannella, 2014), showing thatinsights from small

networks cannot be directly transferred to the larger networks

to which they belong. Complex network analysis approaches

developed in other disciplines (Newman, 2003) have been

applied in supply chain management. However, knowledge

and understandingof the stability of large dynamic supply net-

works is still limited.This may be explained to some extent by

the size and nontrivialnetwork structure of large dynamic sup-

ply networks, aswell as the low visibility that pertainsin many

such networks (Choi, Dooley, & Rungtusanatham, 2001). An

extensive supply network may incorporate hundreds of suppliers,

of which only a small fraction are tier-one suppliers directly visi-

ble to a focal or prime organization in a network. Even if a focal

organization invests resources to analyze the structure of its entire

supply network, there are a multitude of operational details that

cannot be captured, for example, different suppliers may use dif-

ferent modes of production and different inventory management

policies. The problem is further complicated by the intractability

of models that seek to capture the dynamics of large networks,

especially when nonlinearities are considered.

Supply chain management is not the only field that faces

the challenge of modeling and analyzing large dynamic net-

works. Systems of equal or greater complexity are studied in

ecology, which has a long history of mathematical modeling

and places substantial emphasis on the study of stability

(Grimm & Wissel, 1997; May, 2013). Generalized modeling

(GM) is an important approach that has been used in ecology

and other domains to address the challenge of network

modeling when there is uncertainty about the precise mathe-

matical forms of relationships that define a system (Gross &

Feudel, 2006; Gross, Rudolf, Levin, & Dieckmann, 2009).

In this article, we apply generalized models to manufactur-

ing supply networks to investigate instabilities emerging from

the pattern of interactions between firms, that is, the network

topology. In contrastto the conventional modeling approaches

for supply chain dynamics such as control theory, agent-based

models, and discrete-event simulation, the GM approach

enables the stability of a network to be investigated in the absence

of detailed information on operational policies, using information

primarily derived from the network structure, that is, who is con-

nected with whom. We take a high-level network view and con-

sider supply as being continuous and instantaneous. This lean

modeling approach does not seek to capture instabilities such as

the bullwhip effect that may arise at a finer level of granularity,

due to the effects of discreteness, delays, and stochasticity.

The article makes four significant contributions to the sup-

ply chain management literature. First, we provide stability

analyses of two contrasting real-world supply networks—the

inbound supply network of an industrial engine manufacturer

and an industry-level supply network in the luxury goods sec-

tor. Second, we presenta set of five propositions on the stabil-

ity of supply networks. The propositions relate to both the

network structure and the material flows on the network and

seek to advance the extant knowledge on the stability of sup-

ply networks. Cyclic motifs and competition from different

product streams in a supply network are identified as having

destabilizing effects. Links with suppliers that have bi-

directional flows, performing operations such as painting and

machining, have a high influence on the rest of the network at

the onset of instability but a lower sensitivity to disturbances

occurring elsewhe re in a network. Limited product a vailability

may have a stabilizing impact in small inbound networks

serving a single prime entity but can become destabilizing in

industry-level networks formed from the intertwining of sepa-

rate networks. The more quickly the production rate is

adjusted to account for changes in the inventory level, the

more likely the supply network is to be stable.

The third contribution of the study is the insights and guid-

ance provided for organizations to manage critical suppliers.

Prime entitiesin supply networks that have the requiredvisibil-

ity and power can consider strategic development activities

with influentialsuppliers in their supply networks.Investing in

extra buffersis recommended, if organizationsare highly sensi-

tive to disturbances elsewhere in the network. Investment in

capacity is recommended for suppliers that are at the apex of

cycles and/or supply directly or indirectly to multiple prime

entities. The fourth contribution is the introduction and devel-

opment of new conceptualizationsfor generalized turnover and

elasticity parameters, which capture crucial aspects of material

flows, inventory management, and production policies in sup-

ply networks. These conceptualizations allow the GM

approach to be applied in a computationally efficient way that

can be automated for fast screening of extensive supply net-

works. This enables the stability implications of a perceived

change in some part of the system to be quickly investigated,

DEMIREL ET AL.137