Operations Research: Method to Analyse Relations Between Variables using Enriched Loops (2006 -)


Method to Analyse Relations Between Variables using Enriched Loops (MARVEL)

Complex problems can be overwhelmingly difficult to resolve. Obtaining insight into the effects of policy interventions is often a difficult matter. In 2006, TNO started developing the Method to Analyse Relations Between Variables using Enriched Loops (MARVEL), which is an enhancement to the earlier Causal Loop Diagram (CLD) method. MARVEL is a systems-thinking approach that helps to clarify the structure of a problem and to determine effective policy interventions. It aids in the analysis of a problem by combining expert opinions and other available information sources. 

MARVEL allows groups of stakeholders to interactively model and analyse complex systems and helps to:

  • Create a shared understanding of the problem structure.
  • Explore the dynamics of the system causing the problem.
  • Uncover the effects of interventions and events over time.
  • Map and analyse an actor value network.

Why: Structure and behaviour

Complex problems are often a result of undesirable behaviour over time being created by a system. This could be e.g. a person’s rising fever, a company’s declining profits, or the progress of a military operation. Throughout our lives, we form mental models of how we think systems work. However, forming effective mental models of complex systems is difficult. This is a result of the underlying structure of variables and relations which are interconnected by feedback loops, delays and non-linearity. Studying separate parts of the system will not be enough to solve a complex problem. To understand it, we must both study the parts and the whole.

What: the model

A MARVEL model consists of variables and relations. The variables denote the tangible and intangible ‘state’ of the system, for example, ‘body temperature’ or ‘government support’. Relations between the variables describe a causal effect of one variable on the other. In addition, goal, intervention and event variables can be added to the model. In response to an intervention or event, MARVEL can simulate the propagation of this change through the model. This provides an initial insight into the expected effects of an intervention or event.

How: the process

The MARVEL approach is focused on collaboratively building and analysing the model. This is done for two reasons.: First, not one single person holds all relevant information. Second, in almost all cases, multiple people have to be involved to create support for and commitment to the results. But, vague language, misperception, defensive behaviour and prejudice are but a few factors that cause groups to be ineffective at structuring a problem. The MARVEL approach aims to overcome these deficiencies by fostering team learning and creating ownership of the model and recommendations. The process is guided by a facilitator who chauffeurs the group through process steps tailored to the specific project. The process is based on fixed principles, such as neutrality of the facilitator, equality of participants and consensus as a requirement for adjusting the model.
By combining elements of Group Model Building, Causal Mapping and Simulation, MARVEL makes modelling and analysing complex problems accessible and quick. The MARVEL tool set was continuously improved from a relatively primitive Windows-based TIM implementation (see the 2007 reference below) to a modern application suite. A touch table version named Marvelous was developed in 2012. Major improvement efforts took place in 2015.

The MARVEL toolset

The MARVEL tool set includes various tools that help the users navigate and analyse their model:

  • Radiate
    Allows the user to quickly view how a selected variable is connected to the rest of the model by displaying up to three steps of in- and outgoing connections of a variable by displaying a user-defined degree of in- and outgoing connections.
  • Path Analysis
    With path analysis, it is easy to discuss and compare different chains of effects between interventions and goals. The user can manually input a path or can automati¬cally calculate the paths between two variables and display them ranked according to relative power.
  • Loop Analysis
    Loop analysis finds and highlights the strongest feedback loops in the model. Feedback loops are powerful drivers for change that can be both a cause of problems and part of the solution. The loop analysis tool is useful to find and discuss feedback loops. By highlighting the variables included in the loop it becomes easy to distinguish it.

    The loop analysis is useful to find and discuss feedback loops. By highlighting the variables included in the loop it becomes easy to distinguish it
    The loop analysis is useful to find and discuss feedback loops. By highlighting the variables included in the loop it becomes easy to distinguish it
  • Value Network Analysis
    In addition to modelling factors, MARVEL also includes a tool to model networks of actors. Specifically, it is aimed at describing networks formed by the exchange of tangible and intangible assets between actors.
  • Effect Analysis
    Effect analysis shows the effects that interventions or events have on the selected goal variables. The user can experiment with different combinations of control settings and plot the results in time-based graphs.

    Effects of interventions over time
    Effects of interventions over time on key variables influencing diabetes type 2
  • Radar chart
    Visualisation of the effect analysis of various alternatives of several performance indicators.

    Radar chart analysis
    Radar chart analysis
  • Animation
    The animation function can be used to present large models step-by-step by gradually revealing more variables and relations.


MARVEL has been used as a tool for policy, training and operations analysis in many different domains, for example:

  • In 2008, the analysis of the complexity and comprehensive nature of the workforce recruitment and retention of personnel for Defence where “According to the TNO report, the total package of measures has the intended effect on both recruitment and retention of [Defence] personnel, and also contributes to the removal of lower “dissatisfiers” such as the reduction of the rotation schedule for military deployment, and also to the experienced justification and the improvement of the job satisfaction. The report endorses the fact that the measures are not only aimed at quick wins in the short term; a part of the measures also contribute to improved recruitment and retention of personnel in the medium and long term.” [Letter by Minister of Defence to Parliament  and Annex]
  • Operational Analysis in Afghanistan (2008-2010)
    TNO operational analysts took part as military reserve personnel in the Royal Netherlands Army activities in Afghanistan. Marvel was one of the tools they used to analyse the progress of the peace process and the need for interventions by Task Force Urozgan.
  • Effect analysis of information-based police deployment (2010) (article in Dutch)
  • Research project Stabilisation Operations
    Re-establishing stability in a conflict region is a multifaceted problem. Together with several partners, a research project for the Defence Science and Technology Laboratory (Dstl) was conducted to investigate the impact of tactical combat operations in a stabilisation context. Throughout six modelling sessions, a MARVEL model was developed together with military and civilian experts. The resulting model allows repeatable, ‘what-if’ analyses to generate a range of quantitative and qualitative outputs to inform decision-making.
  • Community resilience study
    The MARVEL RELIEF model developed in 2013 describes the interaction between the most important actors and factors contributing to citizen participation and community resilience. During model-building workshops, the practical experience and academic knowledge of a variety of TNO experts were integrated. The project has created insights into the indicators and leverage points that can help strengthen the resilience of a neighbourhood. RELIEF assists policy-makers in increasing citizen participation and directing initiatives.
  • Diabetes Type 2 behaviour interventions
    Diabetes type 2 develops through the complex dynamic interaction of physical, emotional, mental and social factors. An integrated health model was developed that describes this interaction. Specifically, the health effects of the interaction between nutrition, sleep and physical behaviour are modelled. The model aids the analyses of the combined effects of behaviour interventions on the health of a patient. The model is designed to be used by doctors and nurses to discuss with patients lifestyle changes in multiple domains. The prototype became available in 2017.

    Diabetes type 2 health model
    Diabetes type 2 health model
  • Use of MARVEL in the Intelligence Preparation of the Environment process of the Armed Forces.




MARVEL – Principles of a method for semi-qualitative system behaviour and policy analysis, E.J.A. Zijderveld (2007)

MARVEL Analyse ‘Werving en Behoud’, I. Bastings, M.P. Hasberg, S. Heesmans, rapport TNO-DV 2008 A497 bijlage bij Tweede Kamer 31243 nr. 14, 2008-2009

Operationeel analisten combineren wetenschap en praktijk, S. Heesmans, Carré (2008) V7/8 p. 28

Collaborative problem structuring using MARVEL, Veldhuis, G.A.; Scheepstal, P.G.M. van; Rouwette, E.A.J.A.; Logtens, T.W.A., Euro Journal on Decision Processes, Vol. 3, Iss. 3, (2015), pp. 249-273

Grip on health: A complex systems approach to transforming health care, H.A. van Wietmarschen, H.M. Wortelboer, J.van der Greef (2016)