Tackling the Mess: System C onceptualization
through Cross-Impact Analysis
Nathalia Torres‘, Camilo Olaya*
"Departamento de Ingenieria Civil y Ambiental
“Departamento de Ingenieria Industrial, Grupo TESO, CeiBA-Complejidad
Universidad de los Andes
Calle 19A 1-37 Este, Bogota, Colombia
* Corresponding author: n-torres@ uniandes.edu.co
Abstract
A common first step for building a system dynamics model is the selection of
variables. This is one of the most important activities in the construction
process because they constitute the building blocks upon which the
explanations for complex patterns of behavior are proposed based on the
interrelations of those variables. This work aims to present an option to
systematically help to guide the selection of key variables integrating
quantitative and qualitative analysis. A current project in Colombia that
develops a dynamic conceptualization for Solid Waste Management policy-
making is used as an example.
Keywords: conceptualization, cross-impact method, MICMAC, variables selection, solid
waste management
1. Introduction
We develop models of systems. However, conceptualizing is still one of the least
understood steps in the modeling process. Nathaniel Mass chaired a famous plenary
session on methods of conceptualization at the 1981 International System Dynamics
Conference. The question posed by Mass were published in 1986 in an article (Mass
1986) that John Sterman wonderfully introduced as follows: “Conceptualization is
really jargon for the mysterious process of creating a new idea, a word designed to
make the creative act sound scientific, scholarly, and repeatable” (p. 76). However,
there are tools that may help to guide the conceptualization process. In this paper we
show how we used the Cross-Impact Method for building a first causal-loop
diagram in a solid-waste management project integrating both qualitative and
quantitative elements. We believe that this method provides a useful way to
systematically think and conceptualize complex issues and can support model
building processes.
The article is organized as follows. The next section briefly presents the method; the
construction of a cross-impact matrix and the importance of graphical representation
are highlighted. The third part illustrates this method as it was used in a current
project in solid-waste management; the identification of the problem, the pre-
selection of variables, the identification of stakeholders and the selection of key
variables are underlined. The final result, a first causal-loop diagram allowing for a
dynamic conceptualizing of the problematic situation is presented. The last section
summarizes the main points.
. Methods
Prior to model construction a minimal and reliable understanding of the complexity
of the matter to study is mandatory. That understanding is possible through a
selection of elements that the modeler establishes as relevant (Sterman 2000). The
ability for capturing the important variables over the less important ones is a
demanding task improved with experience and time. The selection process is ruled
by qualitative data collection of information trough an informal and intuitive way.
And yet, both quantitative and qualitative data should be collected schol (Scholz
and Tietje 2002). Cross-impact analysis involves the identification of constituent
variables of an event or a system and allows for the evaluation of the interaction
between variables (Godet 2006). The Cross-impact analysis was developed in the
60’s by Theodore Gordon and Olaf Helmer and since then it has been studied in
many fields.
The method consists of three stages. The first one is the problem identification in
which the current state of the situation is described. The second one is the
identification of variables and stakeholders where interactions between variables are
established and, finally, in the third stage the identification of key variables is done
through structural analysis.
2.1 Problem Identification
In this stage, an event is identified and should be defined in a precise way. To
ensure that goal, much information is required to support the facts that are
describing the current state of the situation (Godet 2000, 2008). This step draws a
parallels with what Sterman (2000) calls “problem articulation”.
2.2 Variables and Stakeholders Identification
Once the problem has been identified and articulated, a set of variables and
stakeholders are listed. The modeller should keep in mind the fact that they are
affecting the problem and therefore the system. It is suggested that the set should
not exceed 80 variables (Godet 2000)
2.3 Structural Analysis, Key Variables Identification with MIC MAC
It is important to select which variables are sufficient for a valid description of the
current state of the case and its dynamics (Scholz and Tietje 2002). The selection of
variables which are both influential and dependant is the first evidence of dynamics
in a system (Godet 2008), that is, the fact that an endogenous and dynamic view lie
beneath a good systemic conceptualization.
2.3.1 Cross-impact Matrix (Direct and indirect)
To determine potential interactions in a set of variables, the construction a cross-
impact matrix for scaling the most relevant direct impact variables should be
done (Table 1).
Var 1 Var 2 Var 3 Varj Influence
(ycoordenate)
Vari 0 Var2,1 Var3,1 Varj,1 Var2,1+Var
3,14+Varj1
Var 2 Var 1,2 0 Var 3,2 Varj,2 Var 1,2 +Var
3,2 +Varj,2
Var 3 Var 1,3 Var 2,3 0 Varj,3 Var1,3+Var
2,3 +Varj,3
Vari Var1,i Var2,i Var 3,i 0 Var li+Var2,i
+Var3,i
Dependence | Var1,2 + Var2,1+ Var3,1+ Varj,1+
(xcoordenate) | Var 1,3 + Var2,3 + Var 3,2 + Varj,2 +
Var 1,1 Var 2,i Var 3,i Varj,3
Table 1. Impact matrix model
If there is a direct relation between two variables, the influence could be rated in
different levels; low (1), medium (2) high (3) or potential (4) from a variable i to
a variable j. The grading in the matrix is suggested to be made by teamwork
and strong participation of experts and relevant stakeholders (Godet 2000).
Once the grading is done for all variables it is possible to observe that the row
sum for each variable will tell the influence level; similarly, the columns sum
will tell the dependency level.
Once this matrix of direct impacts is built, the indirect impacts could be
established using the Cross-Impact Matrix Multiplication Applied to
Classification (MICMAC), which was consolidated between 1972 and 1974 by
Michel Godet in collaboration with J.C. Duperin (Godet 2000). MICMAC
multiplies the graded direct impact matrix with itself several times. For each
run, it calculates the sums of columns and rows and does so until these values
show stability.
2.3.2 Graphical representation
Both direct and indirect influences can be represented in a grid (Fig. 1) where
the direct and indirect matrix impacts are used. For each variable it is possible to
locate a place into the grid from a couple of x,y coordinates obtained from the
row and column sum of the direct or indirect matrix (Table. 1). For example for
Variable 1 the (x,y) coordinates correspond to (Var 1,2+Var 1,3+...+ Var Li,
Var 2,1+Var 3,1+Varj,1)
1
Influential ! Ambivalent
Variables i
| Variables
o i
v
g
eo
5
3
= Buffer Dependent
Variables Variables
Dependence
wee eeeeeeeee Mean influence score
woven Mean dependence score
Figure 1. Impact activity scheme. Adapted from Scholz and Tietje (2002)
The grid is divided in four quadrants representing four types of variables. The
differences between the variables lie in the value for the influence and dependence.
The influential variables represent input variables; the dependent variables represent
output variables. Buffer variables are the less important variables in terms of
dependency and influence. Ambivalent variables are important because they have
both influence and dependence in the system and they could change to be input or
output variables.
2.3.3 Selection of Key variables
From the results of grading and its graphic representations, it is possible to compare
and evaluate the results from which the key variables of the system will be obtained.
These variables will be those that occur simultaneously or not simultaneously in the
upper left quadrant of influential variables or in the lower right quadrant of
dependent variables, for both direct and indirect matrices. Ambivalent variables
also must be taken into account
These results will show the key variables of the system but will not exclude the rest
of variables that work in the system. It is just telling that those “key variables” are
the variables on which greater attention should be placed.
Illustrative example. Solid Waste Management (SWM)
Environmental systems such Solid Waste Management (SWM) systems are
complex systems generated by human activities interacting with the environment
exhibiting emergent properties evidenced by their patterns of behavior (Ford 1999;
Deaton and Winegreake 2000). They can also be interpreted as embedded systems,
where one of the most relevant characteristics is that they lead to counterintuitive
results. This type of systems can be studied with system dynamic models, where
different dimensions of the system (social, financial, political, technical, etc.) can be
included.
We are currently developing a SWM project for a Colombian small municipality.
The purpose of this project is to develop sustainable policies that account for the
complexity of the interaction of people, waste, information, resources and
environmental factors. One of the first steps in this project was to develop a first
conceptualization that should drive the discussion and the construction of a solid
system dynamics model. This first step is summarized in this section.
3.1 Problem Identification
Colombian established in 1997 as a national priority to develop integral solid waste
management systems. This was a logical call since the accelarated population
growth, its massive solid waste generation through the years, and the need to handle
large quantities of residues that the country was not prepared to handle, demanded
national action.
This policy established several goals such as the reduction (or even avoiding) of
source generation and consistent and sustainable processing and treatment in order
to reduce the waste quantity going to final disposal. As a result, a concem for the
adequate and controlled final disposal in sanitary landfills emerged because they
were misused or dominated by uncontrolled open dumps. Also there were practices
of disposal in water bodies, open bumings and burials. Over time, Colombian data
has shown that integral solid waste systems have worked better for large
municipalities and cities with high density populations. It is presumed that this
sistuation occurs because environmental authorities have a better understanding of
the operation of such systems in those kinds of municipalities. For example, in
2008, Colombia had 1088 municipalities generating approximately 25 tons day of
solid waste. A 41% from the total were from 4 big cities (Bogota, Medellin, Cali
and Cartagena), an additional 19% from 28 capital cities and the remaining 40%
were from 1056 small municipalities (Superintendency 2009). The big cities and
some municipalities have been able to improve their performance in the public solid
waste management service. However, minor municipalities have technical,
institutional and financial troubles to improve their performance.
To improve the understanding of the situation, our project started a first
conceptualization to understand how waste management works in minor
municipalities in Colombia.
3.2 Pre-selection of Variables
In order to establish a first set of relevant variables primary basic information was
consulted, i.e. national laws, decrees, national and departmental policies and studies,
municipal performance reports and experience sharing of institutions, enterprises
and experts. 46 variables were identified (Table 2).
Variable Short
N° Long Title title
1 Per capita solid waste generation Var0l
2 Household users Var02
3 Household composition Var03
4 Population Var04
5 Population Density Var5
6 Source sorting Var06
7 Waste composition Var07
8 Desired waste collection (Coverage) Var08
9 Collection rate Var09
10 Waste recovery Varl0
11 Profit of waste recovery Varl1
12 Recovery rate Varl2
13 Waste treatment Varl3
14 Average distance between rural households Varl4
15 Total waste to be transported Varl5
16 Distance to final disposal site Varl6
17 Transportation cost Varl7
18 Type of transport Varl8
19 Sanitary landfill reception capacity Varl9
Area availability for solid waste final disposal in
20 sanitary landfill Var20
21 Sanitary landfill capacity Var21
22 Lecheate production Var22
23 Average employment generation Var23
24 Final disposal costs Var24
25 Fraction of waste disposal Var25
Variable Short
N° Long Title title
26 Negative Impact of waste disposal Var26
27 Hoseholds Affordability for the sanitation service Var27
28 Average charge Var28
29 Billing collection efficiency Var29
30 Financial resources availability Var30
31 Infrastructure investment Var31
32 Mortality rate Var32
33 Birth rate Var33
34 migration rate Var34
35 Population average educational level Var35
36 Environmental education Var36
37 Purchasing power Var37
38 Employment rate Var38
39 Consumption pattern Var39
40 waste generation avoidance Var40
41 Perception of solid waste management quality Var4l
42 Industrial Growth Rate Var42
43 Industry Productivity Var43
44 Industrial waste avoidance Varl4
45 Sanitation service regulation Var45
46 Life quality Var46
Table 2. Pre-selected Variables
3.3. Stakeholders identification
Various stakeholders were identified:
Households, waste generators
Municipal Government (Office of the Mayor)
Departmental Government (Office of the Governor)
National Government (Ministry of Environment, Housing and Territorial
Development, and National Planning Department
Environmental authorities (Autonomous Regional Corporations)
Institutional Regulator (Public Services Superintendency)
Economic Regulator, pricing functions (Regulatory (National Commission
for Water and Sanitation)
Local Industry
Solid waste service providers, municipal or private.
Influence
3.4 Identification of Key Variables
After the variables identification, an impact matrix was constructed and graded.
The results from the use of the MICMAC software (developed by the Strategic
Prospective and Organization Laboratory) permits to establish direct (Figure 2) and
indirect (Figure 3) relations between variables into grids. Matrices are not shown
because of their size.
[Var08
Dependence
Figure 2. Direct Impact Activity Grid
[Var10}
Influence
WW CWP) OSA To
Dependence
Figure 3. Indirect Impact Activity Grid
Once the direct and indirect activities grids were done, overlapping them was
possible to determine whether there was a displacement of the variables between the
grids. That displacement can be understood as the variation of the influence-
dependence of the variables associated to the type of impact, either direct or
indirect.
After contrasting the direct and indirect grids and determining the variables
displacement, it was possible to notice that the input variables are not very strong
compared to the output or ambivalent variables. Although the input variables are
very important they were not selected as key variables. Only 6 from the 46 pre-
identified variables were stablished as key variables for the model construction
based on their displacements between grids and their location within them. Three
variables from the six were ambivalent; the three remaining were output variables
for the system.
Ambivalent variables:
Variable 8, which is the desired waste collection in terms of public waste
collection coverage.
Variable 10, related to solid waste recovery.
Variable 41 associated to the perception of solid waste management service
quality
Output variables:
Variable 28 which is the average charge fee to households (users)
Variable 31: Infrastructure investment for the solid waste management
service
Variable 46 related to the life quality improvement in the minor
municipalities population, associated to the sanitation enhancement for
solid waste management activities
The variable 46 showed interesting properties from the indirect activity grid. This
fact was impossible to notices just with direct impacts grading in a matrix or with a
causal-loop diagram.
From the MICMAC software, direct and indirect relation graphs are optional to be
generated. In this graphs, the high influences among variables are represented. For the
direct impact the influences scored with 3, as described in section 2.3.1, are shown
(Fig. 4). For the indirect impacts the values obtained from the matrix multiplication
are use to establish the influences (Fig. 5).
x
i
x ef
ves ee
Figure 4. Direct influences graph
SAAT OS Ta
8 ~ ——
Rey rea
Figure 5. Indirect influences graph
The direct and indirect relation graphs work as a reference for Causal Loop Diagrams
(CLD) construction. In this way, the process of constructing the CLD is a task more
ordered and less intuitive. The CLD that was built based on the generated graphs is
shown in the Appendix 1. This is the base for developing further conceptualization and
refinement for building a simulation model.
. Outlook
The systemic conceptualization of a SWM system is possible to be done with the
use of system dynamics models. However, the complexity of this task can be
overwhelming. Cross-impact methods can help to guide this process. Cross-Impact
Matrix Multiplication Applied to Classification (MICMAC) is a useful tool to
establish key variables selection and it can improve the understanding of both direct
and indirect interactions.
We presented the way we have used cross-impact analysis to develop the first steps
for conceptualizing a solid waste management system for small municipalities in
Colombia. The complexity of the issue demanded a systematic method to simplify
the number of variables without loosing important elements that may help to
develop an accurate model of the situation. Although we share the view that
conceptualization is more art than science, we believe that organized methods may
also help to tackle complex issues, at least in a first step. The visualization of
variables, the quantification of relevance, and the significance of the grade of
impact of some variables over other ones, are elements that can be deal with in a
systematic way. This approach can serve as a basis for addressing further complex
issues such as feedback loop conceptualization, group model building processes and
quantification of variables for developing simulation models. This disciplined
thinking counter-balances the creative act of posing variables and relationships so as
to have a balanced approach to model building. We think that this method can be
valuable for system dynamics modelers in order to guide the complex and artistic
task of building models.
5. References
Deaton, M., and J. Winegreake. 2000. Dynamic modeling of environmental systems. New York:
Springer, 2000. New Y ork: Springer.
Ford, A. 1999. Modeling the environment. Washington D.C-.: Island Press.
Godet, M. 2000. La caja de herramientas de la prospectiva estrategica. Paris: Gerpa.
——-—. 2006. Creating futures : scenario planning as a strategic management tool. London:
Economica.
———. 2008. Strategic Foresight La Prospective. Paris: Lipsor.
Mass, N.J. 1986. Methods of Conceptualization. System Dynamics Review 2 (1):76-80.
Scholz, R., and O. Tietje. 2002. Embeded case study methods. Oaks, CA: Sage Publications.
Sterman, J. 2000. Business Dynamics: Systems Thinking and Modeling for a Complex World.
Boston, MA: McGraw-Hill.
Superintendency, Public Services. 2009. Final Disposal Report. Bogota: SSPD.
Appendix 1. SWM Causal Loop Diagram based on a MICMAC analysis
fool Growth ndustry Productivity
. eae yw
waste generation as ;
avoidance / Average employment a
cai ion snenion
Household users er
+ patterns \
4
a 4
+ \
a~ \
Per capita solid re ae oe
waste generation SEN, ae ’
as Purchasing power
~ Population —_ Ra
| a Recovery rate —— pias recovery
= Waste } i
wee — a 4 — \
Wo x: = waste = 7
/ rm As 4 a collection | (Coverag
/ jf —
(x
Ss stdnce to final
Totat-waste to be digposal site
transported —---—____ N
gration rate Population Density
Industrial waste
avoidance
. a
Birth rate
Pe
—$ Final disposal Profit of waste
Life quality~+
Sy costs recovery
=
{ + iS
SY Perception of solid waste
== Average distance management quality
~ betkeen rural households __—~
Collection— + a E
‘ 4 et
Negative Impact of _ Frequency
waste disposal —_ Billing collection ~~
Fraction of waste
efficiency
disposal. = ———
— pp Sanitary landfill
reception ca icity
— {
Area availability for solid -~
~~ waste final disposal ing
sanitary landfill -
= \
Byte .
_ Sanitation service
re regulation
Infrastructure
investment
