Dealing with Multiple Models in System Dynamics: Perspectives on the Future of Copper

Dealing with Multiple Models in System Dynamics: Perspectives on the Future of Copper

Willem L. Auping (The Hague Centre for Strategic Studies, The Hague, Netherlands), Erik Pruyt (Delft University of Technology, Delft, Netherlands) and Jan H. Kwakkel (Delft University of Technology, Delft, Netherlands)
Copyright: © 2014 |Pages: 19
DOI: 10.4018/ijsda.2014100102
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This paper introduces an approach to compare simulation runs from multiple System Dynamics simulation models. Three dynamic hypotheses regarding the uncertain evolutions of long-term copper availability are introduced and used to illustrate the new approach. They correspond to three different perspectives on the copper system (global top-down, global bottom-up, and regional top-down). Although each of these models allows to generate a wealth of behavioural patterns, the focus in this paper is on the differences in trajectories caused by different models for identical values of shared parameters and identical settings of other assumptions, not on differences in behavioural patterns caused by each of the models. Hence, differences in trajectories between the three models are identified, quantified, and classified based on a quantified measure of difference. For these models, small differences between the trajectories are only found in stable runs, while the alternative perspectives are largely responsible for medium to large differences. Hence, it is concluded that multiple dynamic hypotheses may have to be modelled when dealing with uncertain issues.
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1. Introduction

More than 30 years after the first calls for multi-model work in System Dynamics (SD), there are only a few examples of explicit multi-model SD work (Moxnes 2005; Kwakkel, Auping, and Pruyt 2013; Pruyt and Kwakkel (2014); Jong, Auping, and Govers; Moorlag, Auping, and Pruyt 2014), and there are hardly any techniques and tools available for performing multi-model SD analyses. To contribute to filling this gap, this paper proposes a first method to compare runs from multiple simulation models regarding the same issue or system. Using this method to compare runs generated with three different SD models of the global copper system, we test here whether differences in trajectories generated with different models are primarily due to model uncertainty or to parametric uncertainty, and hence, whether a multi-model approach is needed in the first place. The three alternative copper models presented here correspond to different perspectives regarding the copper system. That is, they were developed from a global Bottom-up perspective, a Regional top-down perspective, and –what is mostly used in SD– a global Top-down perspective. Although the pair-wise comparison method proposed and illustrated in this paper does not offer a rationale for judging which perspective or model is more valid, it could offer a rationale for using multiple perspectives, and hence, multiple models, for policy analytical purposes. This method might help practitioners decide whether alternative competing hypotheses might have to be considered during policy analysis. Hence, this paper adopts an exploratory research agenda to test the efficacy of multi-model SD analysis in the copper industry, and does not purport to provide specific actionable solutions with regard to copper scarcity.

There is a long tradition of modelling resource depletion and scarcity in SD. The limits to growth study (Meadows et al. 1972) is probably the most well-known example. Many SD studies combine geological, technological, and economic aspects of mineral depletion (Sterman and Richardson 1985; Davidsen, Sterman, and Richardson 1987; Sterman, Richardson, and Davidsen 1988; Vuuren, Strengers, and Vries 1999; Pruyt 2010; Kwakkel and Pruyt 2013). Other SD studies focus on specific metals, like the platinum group metals (Alonso, Field, and Kirchain 2008) or magnesium (Urbance et al. 2002), and are mostly linked to specific metal uses, such as electronics (Alonso, Field, and Kirchain 2008) or the automotive industry (Urbance et al. 2002). Copper markets and their interaction with aluminium markets have also been studied by several system dynamicists (Ballmer 1961; Schlager 1961; Auping 2011).

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