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R. SCHEUMANN A. FÜGENSCHUH S. SCHENKER I. VIERHAUSR. BORNDÖRFER M. FINKBEINER

Global Manufacturing: How to UseMathematical Optimisation Methods to

Transform to Sustainable Value Creation

Supported by the DFG Collaborative Research Center CRC 1026 “Sustainable Manufacturing -‚Äì Shaping Global Value Creation”.

ZIB-Report 12-28 (August 2012)

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Global Manufacturing: How to Use MathematicalOptimisation Methods to Transform to

Sustainable Value Creation§

R. Scheumann∗ A. Fügenschuh∗∗ S. Schenker∗∗

I. Vierhaus∗∗ R. Borndörfer∗∗ M. Finkbeiner∗

Abstract

It is clear that a transformation to sustainable value creation is needed,because business as usual is not an option for preserving competitive advan-tages of leading industries. What does that mean? This contribution pro-poses possible approaches for a shift in existing manufacturing paradigms.In a first step, sustainability aspects from the German Sustainability Strat-egy and from the tools of life cycle sustainability assessment are chosen tomatch areas of a value creation process. Within these aspects are indicators,which can be measured within a manufacturing process. Once these data areobtained they can be used to set up a mathematical linear pulse model ofmanufacturing in order to analyse the evolution of the system over time, thatis the transition process, by using a system dynamics approach. An increaseof technology development by a factor of 2 leads to an increase of manufac-turing but also to an increase of climate change. Compensation measuresneed to be taken. This can be done by e.g. taking money from the GDP (asan indicator of the aspect “macroeconomic performance”). The value of thearc from that building block towards climate change must then be increasedby a factor of 10. The choice of independent and representative indicatorsor aspects shall be validated and double-checked for their significance withthe help of multi-criteria mixed-integer programming optimisation methods.

§Supported by the DFG Collaborative Research Center CRC 1026 “Sustainable Manufac-turing -‚Äì Shaping Global Value Creation”∗Department of Environmental Technology, Technische Universität Berlin, Germany; Email

rene.scheumann@tu-berlin.de, matthias.finkbeiner@tu-berlin.de∗∗Zuse Institute Berlin, Takustr. 7, 14195 Berlin, Germany; Email borndoerfer@zib.de,

fuegenschuh@zib.de, schenker@zib.de, vierhaus@zib.de

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1 BACKGROUND

In face of the challenges interwoven withthe development of emerging countries,growing human population, resource avail-ability, energy consumption, and climatechange it is essential to change the valuecreation process to preserve also competi-tive advantages of leading industries. In ad-dition the unequal distribution of wealth indifferent regions of the globe must be over-come. A step into that direction can betaken by shaping sustainable value creationof global manufacturing due to creating sta-ble, socially, economically, and environmen-tally acceptable living and working condi-tions. One option to measure the impact ofproducts is to use the life cycle sustainabil-ity assessment (LCSA) approach [1].

Today we face those manufacturing pro-cesses with different, sometimes dramaticlocal impacts in many parts of the world.The lifestyle of people in modern, highly in-dustrialised civilizations with the consump-tion driven economy forces companies totransfer part of their production into re-gions with low requirements concerning en-vironmental and societal regulations. Thepower, skills, and willingness to change cur-rent production and management processesat the level of enterprises and governmentscan help to achieve a higher level of eq-uity. Nevertheless, the term sustainabil-ity is widely used on different levels, e.g.companies, institutions, and governments,but mostly only as a synonym for envi-ronmental activities [2]. It is now time togo beyond the focus of environmental is-sues alone and therefore include the socio-economic aspects in a so called triple bot-tom line approach by rising the followingquestions:1. Which indicators are scientifically valid

to assess the environmental, economicaland social dimensions of a sustainablevalue creation process?

2. How should these indicators be mea-sured and aggregated to sub-themes,themes, and/or aspects?

3. How can the time-scale as well as themulti-criteria dimension of sustainabil-ity be optimised for decision making?

4. Which data are necessary for the imple-mentation and is that data available?

Although this paper cannot give satisfyinganswers at this time to all these questions,it still holds some interesting points on howto gain more knowledge and how to usemathematical optimisation tools to analysethe effects of decision taking in favour of oneor the other process option. This top-downorientated methodology shall be seen as afirst step. The proof of a suitable as wellas comprehensive set of indicators and as-pects concerning the integrated sustainabil-ity assessment can be done with the helpof multi-criteria mixed-integer optimisationmethods. The evolution of the system overtime, that is, the transition process, can beassessed using a system dynamics approach.

1.1 The Concept of Sustain-ability Indicators

Sustainability indicators consider all threedimensions of sustainability and do not fo-cus on the environmental issues alone, al-though indicators have been widely em-ployed for many years [3]. The first indi-cators were developed at the early 1970 bybiologists to describe the health status ofan ecosystem. As an early example, thestudy of Learner et al. [4] followed an ap-proach to assess the environmental impactof pollution on fish and macro-invertebratesin a river. In 1972 the report “Limits to

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Growth” of the Club of Rome pointed outthat continued growth creates stress theboundaries of our system earth [5], whichcan be seen as a first step to think aboutsustainability. Nevertheless, the most com-mon interpretations of sustainability nowa-days are still based on the environmentalaspects only. This has its origin partlyin political debates starting in the late80s and the resulting environmental regu-lations. Take the aspect climate change asan example: More or less, the whole dis-cussion is on environmental issues and itseffect on human kind. Nevertheless, thistopic has the potential to include the socialand economic dimensions as well by askingthe questions how to pay for the changesas well as by whom, and what are the so-cial consequence, if e.g. coastal areas areincreasingly under the stress by flood andrising sea level.

Sustainability Indicators

Environmental Indicators, e.g.

emission of greenhouse

gases

Economical Indicators, e.g. gross saving

Social Indicators, e.g.

suicide rate

USE

Aggregation to Themes & Aspects;

Interpretation

System

Figure 1: Description of the functional-ity of sustainability indicators.

As depicted in Figure 1, for a systemanalysis, the first step is the collection ofrelevant information and data, before thevalues can be interpreted. In the end,one should make reasonable use of the ob-tained results. The problem is, that there

are too many indicators to use them allat once without ballooning the costs andpushing the time frame over the limit. TheUnited Nations Department of Economicand Social Affairs (UN-DESA) came upwith a total number of 132 indicators, ag-gregated to 46 key themes divided into thefour aspects: Social, Environmental, Eco-nomic, and Institutional in their first pub-lication [6]. During the third revision bythe Commission on Sustainable Develop-ment (CSD), the indicators were reducedto 96 with now only 14 themes or 44 sub-themes [7]. The German Strategy on Sus-tainability displays 21 themes associatedwith partly more than one indicator [8].

How many indicators for global sustain-able value creation should be used and cho-sen? Simplifying the handling and max-imising the outcome and relevance of infor-mation can be useful. One possibility is togroup the indicators, as done e.g. by theUnited Nations with the proposal of threetypes of indicators: (i) driving force or pres-sure indicators, (ii) state indicators, and(iii) response indicators. The driving forceindicators mark a process that influences astate indicator, which describes the condi-tions of a variable, whereas the responseindicators gauge required progress in re-sponse of governments. Parris and Kates [9]made a review on existing measuring ini-tiatives of sustainable development indica-tors and proposed a 2x3 taxonomy of goals.On the one hand there are the three majorcategories, which should be sustained: na-ture, life support systems, and community.On the other hand there are the three cate-gories, which should be developed: people,economy, and society:

• What is to be sustained

– Nature: (i) Earth, (ii) Biodiversity,(iii) Ecosystem

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– Life Support Systems: (i) Ecosys-tem services, (ii) Resources,(iii) Environment

– Community : (i) Cultures,(ii) Groups, (iii) Places

• What is to be developed

– People: (i) Child survival,(ii) Life expectancy, (iii) Education,(iv) Equity, (v) Equal opportunity

– Economy : (i) Wealth, (ii) Produc-tive sectors, (iii) Consumption

– Society : (i) Institutions, (ii) Socialcapital, (iii) States, (iv) Regions

All those aspects or themes and the par-tial look at them help to understand thecomplex concept of sustainability, to ac-knowledge the multiple and conflicting ob-jectives to be sustained and developed, andto grasp the practical consequence of cer-tain behaviours.

1.2 Use of MathematicalModelling

The description of natural phenomena us-ing mathematical models has a long his-tory. The development of modern analysisby Newton and Leibniz in the 17th centuryis an attempt to assess physical effects us-ing a mathematical description. In order tobe able to achieve this goal, they developedthe modern differential and integral calcu-lus. One of the first applications of cal-culus to describe a non-physical but envi-ronmental problem was the predator-prey-cycle model of Volterra [10] and Lotka [11].This model was the birth of mathematicalbiology around the 1930s. It can not onlybe used to model a biological problem, butcan also be applied in economical settings,for example the Goodwin model, to de-scribe economical cycles of growth and de-

pression [12]. A prominent example for theanalysis of economical and environmentalresources is the World3 model developed byMeadows et al. [5]. These models are all nu-merically solved by simulation techniques,where the outcome of the model is deter-mined by the given parameters and theirfunctional relationships. In order to controlsuch models, it is necessary to specify cer-tain variables that allow a gradual changeof the system’s dynamic, and to introducean objective function (or several objectivefunctions, see the next paragraph). Thensimulation techniques can no longer be ap-plied, but methods from the field of optimalcontrol and nonlinear optimisation, see [13],for instance.

Modern algorithmic approaches inmulti-criteria (linear) optimisation are of-ten based on variants of the Simplex Algo-rithm which was first presented by GeorgeDantzig in 1947. During this time Dantzigwas occupied with optimisation problemsarising in military logistics. Linear pro-gramming plays an important role in mod-elling optimisation problems encountered indifferent scientific areas ever since [14].

The concept of efficient solutions com-monly used in mathematics and computerscience is synonym with the concept ofPareto optimal solutions. The latter isnamed in honour of Vilfredo Pareto whowas an Italian economist, sociologist andengineer. The term of Pareto optimal solu-tions is commonly used in economics.

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2 METHODOLOGY

2.1 Selection of Sustainabil-ity Aspects for GlobalManufacturing

With the help of published sets of indicatorsand sustainability aspects, e.g by the Ger-man Strategy on Sustainability or the CSD,it is possible to bridge the manufacturingnetwork with the goal to identify, measureand create a set of indicators and aspectsto represent the sustainable value creationprocess. The approach is twofold and willbe applied in parallel.

First, a table with all the published setsof used indicators in the business surround-ing is constructed. The description of theindicators helps to identify similar indica-tors, although the wording may be differ-ent, and use them on manufacturing pro-cesses. Therefore a matrix needs to be es-tablished with the relevant processes (pro-duction as well as management) in a verti-cal column and the indicators in a horizon-tal line. If the process can be measuredwith the indicator the intersection pointwill be marked. From that matrix a modelcan be derived to serve as a basis for math-ematical optimisation. Within the model,the investigated parameters describe the in-teraction of the real system. Nevertheless,the indicators can usually be grouped or or-ganised into sub-themes, which can be usedfor deriving a model as well, especially atthis early stage of research. The sustain-ability aspect of climate change for examplecan not only be described by the indicatorof greenhouse gas emission, but also by thechange in average temperature, the rise ofthe sea level, the amount of rain, and oth-ers.

Second, a SD model according to sec-

tion 2.2.1 can be developed. The buildingblocks of the model will be equal to sus-tainability aspects which have been chosenat random at this early stage of research inorder to check the way of thinking in themathematical modelling of manufacturingprocesses in terms of achieving sustainabledevelopment. Later, the building blockswill represent real indicators by adoptingthis approach to a real case study, e.g. theproduction of a bamboo bicycle [15].

2.2 Mathematical Mod-elling

2.2.1 System Dynamics and Optimi-sation

We can think of indicators or aspects origi-nating from the economy, the environment,or the society as complex entities, whichform a finely balanced network of mutualdependencies together with their interre-lations. Almost all indicators are influ-encing each other having either support-ing or weakening effects. For the descrip-tion of these relationships the “System Dy-namics” (SD) approach provides the ap-propriate framework. SD was introducedby Jay Forrester in the 1950s to the 1970s[16, 17] as a unified framework to describetime-dependent effects of complex systemshaving stocks, flows, and feedback loops.It received much public attention becauseof Forrester’s research on the “Limits toGrowth”, which he conducted for the “Clubof Rome” [18].

Deriving an SD model is a processthat consists of multiple steps. The firststep, however, is an oral description of themodel’s scope. It is necessary to clearly de-fine the application area of the model and,equally important, what the model should

5

not represent. Usually, models are not de-veloped by a single person, but by a groupinstead. Hence a mutual agreement rightfrom the beginning on the intended purposeand the goal needs to be achieved. Duringthis process the basic entities (or aspects inour application) will be defined as buildingblocks of the SD model.

As a next step, the relationships ofa system’s indicators are represented in acausal loop diagram. Such a diagram re-veals the dependencies among the indica-tors by showing if a certain indicator re-acts while changes to some other indica-tor occur. This yields a qualitative modelof the system, showing its basic underly-ing structure. Usually the indicators areconnected with arrows. These arrows haveattached either plus or minus symbols, rep-resenting the growth or reduction of the in-dicator at the arrow’s head, depending onthe growth of the indicator at the arrow’stail. By studying the circles that are formedby some arrows one can already distinguishtwo types of loops. Reinforcing feedbackloops have an even number of minus signs.They show that parts of the system are ableto accelerate a dynamical trend. Counter-wise, balancing feedback loops have an oddnumber of minus signs.

In a refined version of the causal loopdiagram also numerical values are attachedto the arrows, showing actually how much acertain indicator reacts depending on otherindicators. This is a first step from a quali-tative model towards a quantitative modelthat allows numerical simulations of its fu-ture behaviour using a linear pulse model:Starting from an initial state x0 at time step0, the next time step 1 can be deduced byevaluating the equation x1 = A · x0. HereA is a square matrix with the aspects asrows and columns and the numerical arrow

values as entries, and x0, x1, . . . are vectorswhere each of their components representone aspect. In general, the state in timet + 1 is obtained from the state in time tby xt+1 = A ·xt. The trajectories x0, x1, . . .describe the future development of the sys-tem, as it is forecasted by the causal loopdiagram in matrix A.

In a final modelling step, the causal loopdiagram is further refined into a stock andflow diagram. Stocks are able to accumu-late or vanish over time, and flows describethe change rate of a stock. The stock andflow diagram is transformed into a set ofequations, which are usually nonlinear dif-ference or differential equations. In order tosimulate such systems on a computer, it isnecessary to discretise the differentials by,for example, an Euler- or a classical Runge-Kutta-method [13].

Because of the nonlinear relationshipsthe simulation of SD systems often showsa surprising, non-intuitive behaviour fromthe modellers point of view. Predicting theoutcome of a simulation beforehand, or esti-mating the long-term behaviour of a systemis also a difficult mathematical problem.

Usually SD models are not only used tosimulate the future development of a sys-tem, but also to influence the system byintroducing certain policies. Such a policycan be an additional indicator with arrowsconnecting it with other existing ones, anda variable weight at these arrows. Whensetting these variables manually to certainfixed values, one can perform a simula-tion run for each setting. In this wayit is possible to evaluate the outcome ofthe simulation and select a trajectory thatseems favourable. The mathematical con-trol problem for an SD model asks for thenumerical computation of these policy vari-ables that lead to a best possible (optimal)

6

trajectory, with respect to a given objectivefunction.

2.2.2 Multi-Criteria Analysis

We consider the environmental, the eco-nomical and the social dimension which aretaken into account in sustainable manufac-turing as equally valued. Instead of prefer-ring one over another, we want each indi-cator to be an independent objective func-tion that needs to be optimised. However,in general, different sustainability indica-tors or aspects may be in conflict with eachother and one cannot expect to find a solu-tion that optimises all considered indicatorssimultaneously. Instead, one has to copewith trade-offs. For example, a manufac-turing process that shows a better environ-mental performance (e.g. low amount ofemissions damaging the environment or thehuman health) may probably not be veryeconomical (higher investment and opera-tion cost for additive technology, like filtersor integrated technology, like closing mate-rial loops) or vice versa. A decision makermay be interested in a process whose per-formance for each indicator cannot be im-proved without a resulting trade-off in an-other indicator. This leads to the concept ofefficiency and non-dominance, respectively.An efficient solution is a solution that can-not be improved in one objective withoutworsening another. In other words, consid-ering an environmental, an economical anda social indicator as three different objec-tive functions of a manufacturing processwould be efficient if we cannot find anothermanufacturing process (producing the samegoods) whose performance for each indica-tor is at least as good including a strict im-provement in one of the indicators. Theobjective values of an efficient solution are

called non-dominated in the space of objec-tives. One of the goals in multi-criteria op-timisation is to compute all non-dominatedpoints and corresponding efficient solutions,respectively. A decision maker could thenchoose the most convenient solution out ofthis set.

X

x1

x2

c1

c2

c1x

c2x

Y := {Cx : x ∈ X}

y1

y2

y3

W1

W2

W3

Figure 2: Solution space with two ob-jective functions and corresponding ob-jective space with three non-dominatedpoints and corresponding weight spacedecomposition.

A well-known equivalence result statesthat optimising the weighted sum of the ob-jectives λ1c1 + λ2c2 + λ3c3, where the λiare positive weights and the ci are the con-sidered objectives, yields an efficient solu-tion. Furthermore, for each efficient solu-tion one can find positive weights for whichthe weighted sum takes its optimum at theconsidered solution. Each non-dominatedpoint corresponds to a set of weights whichlead to this point in the weighted sumproblem (see Figure 2). From an evalua-tion point of view, this weight space de-composition enables one to validate theobjectives. In other words, the knowl-edge which weights and which weightedsum objectives, respectively, yield whichnon-dominated points qualifies the modelbuilder to evaluate whether the used indi-cator values fall into place.

From an algorithmic point of view,the main incentive is the ability of a fast

7

computation of the set of non-dominatedpoints. Due to the huge size of the latterthat is still a challenging problem even fora small number of objectives.

3 DESCRIPTION OFA MODEL EXAM-PLE

As outlined in Section 2.2.1 we start with adescription of the scope of the model.

The model “manufacturing” should beable to derive a qualitative and justifiedstatement of the development of a dynamicmanufacturing process. The dynamic of themanufacturing process depends on the sus-tainability aspects, e.g. depletion of min-eral resources, damage to human health,macroeconomic performance, etc. (see Fig-ure 3). If the long-term behaviour of themodel shows instabilities, the model shouldbe able to point out possibilities for its sta-bilisation. It is not expected that the modelreturns a detailed description of necessaryactions to be taken, but rather identifieshot-spots in order to look closer at the un-derlying indicators.

Figure 3: Causal loop diagram for theSD model “Manufacturing” in conjunc-tion with costs as well as environmentaland societal aspects.

The model shown in Figure 3 con-sists of the following sustainability aspects:depletion of abiotic resources, damage tohuman health, climate change, macroe-conomic performance, technology develop-ment, employment, and air quality (in-door). The direction of the arcs showthe influence direction as described below,whereas “+” stands for an increase and “−”stands for a decrease of the impact. Thevalues at the arcs show the relative strengthof a certain relation between the corre-sponding sustainability aspects. These as-pects have the following qualitative interre-lations:• If depletion of abiotic resources increases,

then manufacturing activity will decreaseas well as the macroeconomic perfor-mance.

• If manufacturing increases, then the po-tential damage to human health will in-crease.

• If damage to human health increases,then employment will decrease.

• If manufacturing increases, then climate

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change will increase, and this may resultinto a decrease of the manufacturing ac-tivity itself.

• If climate change increases, then this maylead to an increase of potential damage tohuman health.

• If manufacturing increases, then themacroeconomic performance will in-crease and as a reaction the manufactur-ing increases further.

• If macroeconomic performance increases,then the climate change will decrease,but the technology development will in-crease.

• If technology development increases, thenmanufacturing activity will benefit andincrease, but there will be a decrease atthe employment.

• If employment increases, then the manu-facturing will increase.

• If manufacturing increases, then the airquality (indoor) will decrease.

• If air quality (indoor) increases, then themanufacturing activity increases as well.

A shift away from traditional manufactur-ing processes and consumption patterns isdesired in order to adopt new – ideally sus-tainable – processes around the world andwithin the total value creation. For exam-ple, the raise of the macroeconomic per-formance by one unit due to an increaseof the manufacturing activity could lead tothe following two outcomes (see Figure 3).On the one hand, money from the GDP, asan indicator of the aspect ‘macroeconomicperformance”, in a magnitude of 0.011 unitsshould be used to compensate the socialcost related to carbon [19]. Using thesenumbers we are able to set up a linear pulsemodel and perform a dynamic simulation,as outlined in Section 2.2.1.

Moreover, it is possible to give an or-dering of the elements according to their

passive, active, critical and buffering capa-bilities within the system (see Vester, 2007[20]). This is done by the analysis of theactive and passive sum (row and columnsums in matrix A, respectively). Then thefollowing information is obtained from themodel’s data:• most active element (affects others, but

not strongly influenced by others): tech-nology development;

• most passive element (strongly influ-enced by others, but little effect on oth-ers): damage to human health;

• most critical element (affects others andinfluenced by others): manufacturing;

• most buffering element (little effect onothers and little influence from others):depletion of abiotic resources;If the system is in a critical unstable

state (in whatever sense), then the influ-ence of an arc such as “technology develop-ment→ Manufacturing”, between the mostactive and the most critical element, is cru-cial. Hence we will later study the dynamicbehaviour depending on this value, whichwe denote by C1 in Figure 3.

Since we want to take control of theclimate change, we additionally identifythe arc “macroeconomic performance→ cli-mate change” as important, and analyse thedynamic behaviour of the model dependingon this arc weight denoted by C2.

4 RESULTS & DIS-CUSSION

The linear pulse model described in Sec-tion 3 is simulated to forecast the influenceof a single-unit increase of manufacturingat time t0 on all the other sustainability as-pects. This increase can be related to a po-litical desired stimulation of the economy,

9

and can therefore help to understand the ef-fect of such short term measure in the longrun.

0 1 2 3 4 5 6 7 8 9 10-0,2

0

0,2

0,4

0,6

0,8

1

1,2

1,4Manufacturingindoor air qualitydepletion of abiotic resourcesdamage to human healthemploymentclimate changetechnology developmentmacroeconomic performance

Figure 4: Results from the SD model“Manufacturing” for all aspects, un-scaled.

The arc values shown in Figure 3 causethe system to reach a steady state withina reasonable period of time, which meansthat the effect of single stimulation of themanufacturing activity (by one unit) fadesoff after only a very few time steps (Fig-ure 4). If all arc values are scaled by a largepositive constant factor, then a single pulsewill be self-energising and the whole systemdiverges. Thus it is possible to identify thetipping point between a complete absorp-tion of the start impulse and a divergingsystem. This threshold level at which thesystem changes from one to the other statelies at approximately 1.95. What does thatmean? If influences of the sustainabilityaspects are as given or at most (roughly)two times higher, then the system will stillbe able to reach a steady state condition.This steady state corresponds to a higherlevel of manufacturing, but also to a higherlevel of climate change, as the simulationresults indicate. If the scaling parameterbecomes greater, the system does not reach

a steady state any more, compare Figure 4and Figure 5. At this point a self-energisingeffect becomes visible and e.g. manufactur-ing keeps growing at an exponential growthrate, but also climate change as well.

0 10 20 30 40-0,5

0

0,5

1

1,5

2

2,5

Figure 5: Results from the SD model“Manufacturing” for all aspects, scaledwith a factor of 2 (legend see Figure 4).

Being at the system’s tipping point, itbecomes interesting to analyse the dynam-ical behaviour of the system depending onthe arc values of those arcs in Figure 3 de-noted by C1 and C2. When varying thevalues at these arcs the simulation will re-spond immediately to even small changes.From the change in the trajectories of thesustainability aspects it is then possible todeduce measures for a strategic control ofthe modelled system.

10

0 10 20 30 40-0,2

0

0,2

0,4

0,6

0,8

1

1,2Manufacturing

climate change

technology development

Figure 6: Results from the SD model“Manufacturing” for the aspects cli-mate change and technology develop-ment, scaled with a factor of 1.8, C1 setto 1.

The values of arcs connecting to the ac-tive and critical elements are then variedin order to simulate their influence on thesystem. By setting the scaling factor to1.8 near the tipping point, a change of thevariable C1 to 1 leads to no significant ef-fect (Figure 6), but with a scaling factorof 2 and a change of C1 = 1, the manu-facturing activity grows much faster (com-pare Figure 5 with Figure 7). The initialidea of increasing technology developmentespecially to enhance manufacturing activ-ity is clearly visible. However, the environ-mental burden, here climate change, is alsoincreasing at the same time, which shouldbe avoided by means of sustainable devel-opment. Therefore, the variable C2 has tobe adopted. By setting C2 = −0.103 theaspect “climate change” reaches a steadystate. This means an increase of the GDPdrawing by the factor of approximately 10to −0.103 units from the macroeconomicperformance is needed to pay for compensa-tion action concerning climate change (Fig-ure 8) and still have an increase of manu-facturing.

0 10 20 30 40-1

0

1

2

3

4

5

6

Manufacturing

climate change

technology development

Figure 7: Results from the SD model“Manufacturing” for the aspects climatechange and technology development,scaled with a factor of 2 and C1 = 1.

0 10 20 30 40-1

0

1

2

3

4

5

6

7

8

Manufacturing

climate change

technology development

Figure 8: Results from the SD model“Manufacturing” for the aspects cli-mate change and technology develop-ment, scaled with a factor of 2, C1 setto 1, C2 set to −0.103.

5 CONCLUSION &OUTLOOK

This paper has shown that the dynamicsimulation of a complex model like the oneused in this study is possible and leads to

11

reasonable results. Nevertheless, this theo-retical approach has to be validated with acase study in the upcoming period. There-fore, the demonstrator (Life Cycle of a bam-boo bike) by Schau et al. [15] will be usedto do so.

An idealistic long-term goal is the com-bination of the system dynamics approachwith multi-criteria optimisation. Each re-sulting trajectory from the system dynam-ics approach can be considered as an objec-tive which needs to be optimised. Consid-ering a certain function that can be eval-uated for each trajectory (e.g. an integralfunction evaluating the surface area underthe plotted graph) yields different objec-tive values for each considered trajectory.Meanwhile, finding the trajectories whichare efficient for a given function leads to amulti-criteria optimisation problem.

ACKNOWLEDGEMENTWe gratefully acknowledge the fund-ing of this work by the German Re-search Association (Deutsche Forschungs-gemeinschaft, DFG), Collaborative Re-search Center CRC1026 (Sonderforschungs-bereich SFB1026).

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