Networked consumption systems:
Influence of structure on sustainability
Namy Espinoza-Orias and Paul N. Sharratt
Environmental Technology Centre, School of Chemical Engineering and Analytical Science
The University of Manchester
PO Box 88, Manchester M60 1QD, England
[email protected]
Keywords: network structure, life-cycle, life-cycle management, sustainability
ABSTRACT
The life cycle of any given product or service can be represented by a set of stakeholder networks
structured around activities that make up the life cycle. A need has been identified for the understanding of the
mechanisms that drive the organization of stakeholders into networks within consumption systems, as well as of
the resulting network structure. This work presents a model that explains network structuring on the basis of a
mechanism of exchange of complementary resources along the activities of the life cycle of a product or service.
Fuzzy factors intrinsic to stakeholders, such as availability of resources and willingness to exchange those
resources determine the propensity of stakeholders to establish links and thus create networks exhibiting
characteristic structures. In turn, the structure of the self-assembled stakeholder networks provides valuable
information for the development of life cycle management strategies that have an effect on the sustainability of
the consumption system.
Introduction
Any network can be viewed as consisting of sets of nodes and links. An autonomous entity performing
functions and operations that contribute to larger processes is denoted as a node. In turn, a group of nodes
connected by multiple links through which resources are transferred forms a network. The life cycle of any given
product or service can be represented by a set of stakeholder networks structured around activities that make up
the life cycle.
A need has been identified for the understanding of the mechanisms that drive the organization of
stakeholders into networks within consumption systems, as well as of the resulting network structure. Clearly the
nature of the network strongly influences the life-cycle efficiency and sustainability of the consumption system.
This work presents a model that explains network structuring on the basis of a mechanism of exchange of
complementary resources along the activities of the life cycle of a product or service. Fuzzy factors intrinsic to
stakeholders, such as availability of resources and willingness to exchange those resources determine the
propensity of stakeholders to establish links and thus create networks exhibiting characteristic structures. In turn,
the structure of the stakeholder networks provides valuable information for the development and implementation
of life cycle management strategies that have an effect on the sustainability of the consumption system.
The initial results provided by the model show that stakeholders assemble into scale-free1 networks, a
configuration observed in real-world networks of varied nature. The introduction into the model of additional
factors such as the efficiency of the resource exchange, the distance between stakeholders and the capacity for
resource exchange exhibited by stakeholders, opens avenues for further investigation of the behaviour of real
consumption systems.
Life cycle thinking
The consumption system of a given product or service can be described as an entity containing a
number of interacting parts (consumers and providers), so that if a part fails or is removed, the system ceases to
1
In graph theory, the number of incident links with a given node is called the degree of the node [1]. Power-law
distributions have no natural scale; consequently, the term scale-free is fitting. Networks that exhibit a powerlaw degree distribution are called scale-free networks [2].
behave as such, i.e. consumption of the product or service is halted. In a broader sense, consumers and providers
of the product or the service, as well as other entities (individuals, organizations and the environment) are
stakeholders of the consumption system, for they can affect or are affected by its inherent activities.
By applying a life cycle perspective (“from cradle to grave”) to a consumption system, it is possible to
envision it as the interaction of a set of stakeholders and the interconnection of a number of activities and
subsystems – either sequentially or concurrently – expanding across different time and geographic scales.
Functions, operations, processes and flows of resources become integrated at different levels. If, according to
Soft Systems Methodology [3], the consumption system is considered a purposeful human activity system2, then
it is reasonable to propose that the consumption system of a product or a service will follow various life cycles
depending on the purpose being pursued. Consequently, any observable and structured set of sequential activities
constitutes a life cycle of a product or a service. Life cycles are actually emergent properties of consumption
systems.
Model assumptions
Networks are assumed to be self-organizing and decentralized systems, where multiple actors exchange
resources, perform a variety of roles and exhibit decision-making capabilities. Since consumption takes place
through the exchange of complementary resources among stakeholders, networks provide a sound representation
of consumption systems.
In the present work, it is proposed that the overall structure of a networked consumption system
emerges from the local activity of resource exchange between stakeholders who exert control over
complementary resources. In network terminology, stakeholders are nodes and the exchange of resources
between them represents a link. The elementary mechanism that drives the creation of potential links between
nodes is based upon the following assumptions. Figure 1describes the mechanism in a graphic way.
Node X
Node Y
Resource A
Fitness of
resource A
Fitness of
resource A
Link
Fitness of
resource B
Willingness to
exchange
resources
Fitness of
resource B
Resource B
Willingness to
exchange
resources
Figure 1. Mechanism of exchange of complementary resources.
a)
Complementariness of resources implies that resource A is exchanged in order to obtain resource B.
The following are viable pairs of complementary resources in a consumption system: materialsmaterials, materials-financial capital, labour-financial capital, labour-materials, labour-information,
information-financial capital, information-materials, time-financial capital, water-financial capital,
energy-financial capital. Materials include both raw and processed ones.
b) The link between stakeholders resolves the lack of a resource; consequently, the link creates a mutual
benefit [4].
c) The propensity A(X,Y) of stakeholder X to establish a link with stakeholder Y in order to obtain
resource A is directly proportional to its current availability of resource B (designated as “fitness” of
resource B) and the willingness to exchange it for resource A; and it is inversely proportional to its
current availability of resource A (designated as “fitness” of resource A). Equation 1 summarizes this
assumption:
2
A human activity system is a conceptual system serving a purpose which expresses some willed` human
activity. Such systems do not necessarily exist in the real world; rather, they assist observers and analysts by
providing an ideal framework for debate [3].
Propensity of stakeholder X to establish
a link with stakeholder Y to gain
resource A in exchange for resource B
(ρA(X,Y))

Willingness of
stakeholder X to
exchange resource
B for resource A

Fitness of resource B
Fitness of resource A
(1)
X
d) Stakeholders act wilfully; consequently, the stakeholder that reveals a larger propensity for link creation
will be the one that initiates the respective process.
Network generation algorithm
Stakeholders of an activity in the life cycle of a product or service can be identified within their
respective consumption systems. A set of such stakeholders self-assembles into a network when they decide to
engage in the activity in question following the mechanism of exchange of complementary resources. Here a
model is proposed so that given a set of N stakeholders of types X (provider) and Y (consumer) in a proportion
of Nx/Ny (where stakeholders of type X command control over resource A and reach out to stakeholders of type
Y who in turn command control over resource B and vice-versa), the probabilities Px(k) and Py(k) that a
stakeholder of one type has established k links with stakeholders of the other type follow power laws Px(k) k-
and Py(k) k-. This result shows that the proposed mechanism organizes the stakeholders into scale-free
networks. Indeed, the scale-free structure has been observed in various real-world networks of different nature;
to name a few: the World Wide Web, movie actor collaborations, power grids, citation patterns of scientific
papers and genetic networks [5].
The algorithm used in the model is repeated for each of the stakeholders in the set. It is detailed here:
1.
2.
3.
4.
Each stakeholder in the set is assigned values comprised in the interval [0,1] for the following
parameters: Fitness of resource A, fitness of resource B, willingness to exchange resource A for
resource B and willingness to exchange resource B for resource A. The values are randomly chosen
from a given probability distribution.
For each stakeholder and each type of resource, the propensity to establish links A (X,Y) and B (Y,X)
are calculated using Equation (1).
A pair-wise comparison is made between A (X,Y) of every stakeholder i of type X and B (Y,X) of
every other stakeholder j of type Y. The larger value (ρ = max (A (X,Y), B (Y,X))) implies that the
respective stakeholder will initiate the link creation process.
The resulting larger values i,j from step 3 are summed over all j and normalized to obtain initial
probability values Pi,j using Equation 2. Pi,j represents the probability that stakeholder i will establish
the link with stakeholder k. Then, the probabilities are summed giving the overall cumulative
probability of linkage.
Pi , j 
i, j
 i, j
(2)
j
5.
A random variable is generated in the interval [0,1]. Depending on which of the subintervals of the
cumulative probability of linkage contains the random value, it will be decided which stakeholder j will
be connected to stakeholder i. Therefore, each run of pair-wise comparisons between stakeholder i of
type X and the entire sub-set of stakeholders of type Y (and vice-versa), generates the possibility for the
creation of one link between a stakeholder of type X and another stakeholder of type Y.
When steps 3 to 5 of the algorithm are repeated for every stakeholder of each type (X and Y) in the set,
the final number of links of any stakeholder will correspond to either of the following cases: a) single link (k = 1),
or b) multiple links (k > 1).
Structure of a networked consumption system
The application of the model algorithm produces a static network. On the basis of the overall number of
links established per stakeholder it is possible to calculate the features that characterize the created network: a)
degree distribution P(k), b) average degree <k>, c) exponents of the power laws ( and ) in the region of linear
behaviour when the degree distribution is plotted in a log-log graph d) size of the network M measured by the
number of links, e) sparseness of the network  measured as the size of the network compared to the size of a
fully connected network with a similar number of nodes. Table 1 and Figure 2 summarize a typical outcome of
the model.
Table 1. Characteristics of networked consumption systems (N = 100).
Network
1
2
3
Nx
0.25
0.60
0.85
Ny
0.75
0.40
0.15
<k>
1.98
1.98
1.98
(a)
M
98.79
98.79
98.82

0.05
0.04
0.08


2.32
2.35
2.86
2.66
2.31
2.41
(b)
Figure 2. Degree distribution of networked stakeholders in a consumption system. N = 100. a) PX(k), b) PY(k).
Implications of the network structuring model
The results of the network structuring model show that the degree distribution follows a power law
irrespectively of the proportion of stakeholders of each type (X or Y). From Table 1, it can be seen that the
exponents of the power laws ( and ) are comparable to the exponents obtained for real-world networks, for
example: the protein network of S. Cerevisiae ( = 2.4) [6], the network of internet routers ( = 2.48) [7] and the
network of co-authors in mathematics papers ( = 2.5)[8].
Low values of sparseness of the networks reflect the fact that not all the individuals or organizations
identified as stakeholders of an activity participate in it more than once. This behaviour might reflect a range of
underlying features of the real system, such as:
a)
Visibility of stakeholders: The effective chances of acknowledging the existence of other stakeholders
and receiving information about the availability of complementary resources under their control are
reduced when stakeholders are not visible to each other. Factors such as geographical location, lack of
access to social networks, inefficient or non-existing communication networks, the cost of becoming a
visible stakeholder and the ability of stakeholders to scan and comprehend their environment as well as
the information coming from it affect the visibility of stakeholders.
b) Stakeholder idiosyncrasy: Each stakeholder bestows different priorities to resources and degrees of
criticality to resource exchange, depending on their circumstances and points of view.
c) Timing: The model describes how the consumption system structured itself into a network when an
opportunity for choice emerged. According to the reasoning of the “garbage can” model of
organizational choice [9], when such opportunities emerge, the system is expected to produce an
observable behaviour; in this particular case, the exchange of complementary resources. It is likely that
the stakeholders were not aware that the opportunity for choice had emerged; if they were indeed aware,
their behaviour was procrastinated or they decided to exchange a different type of resources instead.
d) Efficiency of exchange: When the efficiency of exchange is deemed intolerable by the standards set by
the consumption system or the stakeholders, the potential link between stakeholders goes unaccounted
for by the model. Inefficiencies originate, among other causes, from asynchrony in the availability and
demand of resources, large distances between stakeholders, differences in the protocols used for
resource exchange by each stakeholder, or misunderstanding of the exchange process.
The power law degree distribution implies that a large proportion of stakeholders establish few links (1
or 2), whereas very few establish themselves as “hubs” capable of linking with almost all of the stakeholders of
the other type (Figure 3 shows the emergence of hubs in a network’s structure). The mechanism for exchange of
complementary resources provides alternative explanations for this behaviour:
a)
In the model, the willingness to exchange resources parameter captures the stakeholder idiosyncrasy
elegantly. The value of the parameter reveals the scale of resource priority of a given stakeholder as
well as his or her degree of detachment from resources in order to meet the need for or requirement of a
certain resource. It can be argued that a high value of the parameter entails the predisposition of the
stakeholder to engage in multiple linkages with other stakeholders.
b) A stakeholder that perceives a high deficiency of a resource initiates the process of linkage creation.
The demand for the resource is more likely to be met effectively if multiple linkages are sought with
stakeholders that are in the position of delivering the required resource.
c) Considerable and ready availability of a resource to a stakeholder provides the opportunity for
complementary resource exchange in order to gain access to another resource. In this case, multiple
linkages are deemed advantageous, for they are seen as a “means to an end”, as well as a business
opportunity.
(a)
(b)
(c)
Figure 3. Representation of a network structure showing the affiliation networks generated by stakeholders
interacting in similar contexts. a) Affiliation network for stakeholders of type X ( ); b) bi-partite representation;
c) affiliation network for stakeholders of type Y ( ). N = 30, Nx = Ny = 15.
Strategies for Life Cycle Management in networked consumption systems
The model provides information about the structure of a networked consumption system. Equipped with
this insight, it will be possible to devise and develop life cycle management strategies aimed at introducing,
encouraging and implementing sustainability in the consumption system.
a)
Improvement of conditions so that when resource exchange is performed, assurance is given that
measures have been taken to reduce its environmental impact.
b) Inclusion of marginal stakeholders or non-benefiting stakeholders to the life cycle activities of a
consumption system through empowerment of their fitness for resources and provision or creation of
means of access to ancillary networks (transportation, communication, education, training). In this way,
it is possible to address social sustainability issues related to the consumption system.
c) Identification of the characteristics of the hubs that emerge in networked systems. If these are local hubs
connected to local stakeholders, it is possible to promote them as preferred stakeholders for resource
exchange in that area. On the other hand, if the hubs are connected to distant stakeholders, it is possible
to analyze the viability of alternative schemes for local resource exchange. By addressing the
implications of physical transportation of resources, it is possible to improve both the economic and
environmental sustainability of activities within the consumption system.
d) The willingness to exchange of resources can be adjusted directly or indirectly. Directly, it is possible to
create environmental regulation that discourages the exchange of certain resources (for example
taxation of certain resources or goods based on the polluter pays principle). Indirectly, it is possible to
inform and educate stakeholders about the sustainability issues inherent to resource exchange. If the
perceptions of stakeholders in relation to certain exchanges of resources change and as a result
perceptions converge unto the acceptability of alternative sustainable exchanges, then the consumption
system will self-organize into a more sustainable structure.
e) Creation of opportunities for choice: Opportunities for choice originate in changes in values,
perceptions, needs and the Weltanshcauung3 of the system’s stakeholders or the external environment,
internal and external pressures, climatic and natural events, scarcity of resources, physical constraints,
and timing. The stakeholder can develop capacity and skills that enable it to generate opportunities for
sustainable choices and take advantage of them.
Conclusions and future work
In the present work, a model based on the mechanism of exchange of complementary resources has
been proposed to generate stakeholder networks that exhibit structural features characteristic of real-world
complex networks of varied nature. Despite the simplicity of the model, it has the prospect of bringing
significant insight into the effects that network structure has upon the sustainability of a consumption system as
well as in the development of effective life cycle management strategies.
The model captures the fact that decisions taken locally by stakeholders in relation to resource exchange
and selection of stakeholders with which to interact drives the self-organization of networks exhibiting scale-free
characteristics [5]. The introduction into the model of additional factors such as the efficiency of the resource
exchange, the distance between stakeholders and the capacity for resource exchange exhibited by stakeholders
will open avenues for further investigation of the behaviour of real consumption systems.
References
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[6] H. Jeong et al. Lethality and centrality in protein networks. Nature, Vol. 411, No. 6833 (2001), pp. 41-42.
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3
Weltanschauung means perspective of the world. In SSM it encompasses the beliefs and values that shape a
particular perspective and explains why the transformation processes in a conceptual model are meaningful.