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ARTICLE IN PRESS8M. Schmidt / Environmental Impact Assessment Review xx (2005) xxx–xxxrevenue is obviously the sum of the bad entering and the good leaving the system, and theexpenditure is the sum of the good entering and the bad leaving the system. Rememberthat the distinction between good and bad is made by the market at any time.However, the purpose of a system is very often to create one specific revenue, e.g. toproduce one good (the system is then called a production system) or to reduce one bad (thesystem is then called a recycling or disposal system). Given this intended revenue, theoverall expenditure will be allocated to it. We call this purpose-based focus on a specificinput or output of the system a perspective. Perspectives are useful for the analysis andcommunication of system properties, as will be shown in Section 4. Given a perspective,the indirect environmental impacts already mentioned simply represent a question ofsystem boundaries. If the system has been selected suitably, the indirect environmentalimpacts of individual processes will be captured elsewhere in the system as directenvironmental impacts.3. System modelling with the aid of netsOne way of describing closed-loop systems as a model is to display them as nets orgraphs. Möller (1994) introduced the bmaterial flow netsQ in which the nodes areinterpreted as transformation processes and the arrows as material flows. By introducing asecond type of node – by analogy with the Petri net from theoretical informatics – it is alsopossible to map storage processes. This allows a distinction to be made between activitiesand states, thus also permitting time-based analysis for instance.Fig. 3a) shows a simple net as an input/output graph. Each process is described throughits input flows and its output flows that can stand in a functional connection with eachother (Schmidt and Keil, 2002). By linking the processes it is possible to build up systemsa)G1G2G6systemboundaryG7P1 G3 P2 G4 P3G5B1 B2 B3R G5b)ExpendituresRevenuese 1_G1e 2_G3e 3_G4e 1_G2r 1_G3 e 2_G6r 2_G4 e 3_G7e 2_G3e 3_G4e 1_B1e 2_B2e 3_B3r 3_G5Fig. 3. a) An I/O graph of a chain of three processes; b) the corresponding expenditure–revenue graph.
ARTICLE IN PRESSM. Schmidt / Environmental Impact Assessment Review xx (2005) xxx–xxx 9of optional complexity. In this case a linear chain of three processes is shown that areconnected to each other by the flow of goods (G3–G4). Thus for example process P1requires goods G1 and G2 as raw materials bfrom the exteriorQ and produces product G3with these. In addition a bad B1 results. It soon becomes clear that the system revenue isthe production of G5. The system expenditure for this is made up of the goods G1, G2, G6and G7 on the input side, and the bads B1, B2 and B3 on the output side.This input–output graph can be converted into an expenditure and revenue graph inaccordance with Fig. 3b) with the aid of good/bad classification (Möller, 2000). Eachprocess is now broken down by the expenditures and the revenues. The quantities e and rstand for the associated coefficients of production of expenditures and revenues, wherebya linear functional connection is assumed and the data are stated in physical quantity units(e.g. kg). The expenditure connected with the system revenue R G5 throughout the entiresystem can thus be calculated easily by determining the production level x i of processes 1to 3 and the expenditures of the individual processes derived from these.This approach makes it possible to map material cycles such as occur in recycling processeswithout any problem too. Fig. 4 shows such a case. The good 4 that is produced in process 2 isused as a raw material in process 1. To calculate the system expenditure for the system revenueR G5 , the production levels x i of processes 1–3 are solved with a linear equation system:x 3 ¼ R G5e 1 G4 =r 1 G3 d x 1 þ x 2 e 3 G4 =r 3 G5 d x 3 ¼ 0x 1 e 2 G3 =r 2 G4 d x 2 ¼ 0This results in the system expenditure E B1 =e _ 1 B1/r _ 1 B1d x 1 etc., for example. It shouldbe noted that this expenditure is determined on the physical quantity level. The advantagea)G1G2G6systemboundaryG7P1 G3 P2 G4 P3G5B1 G4B2 B3R G5b)e 1_G1e 1_G2e 1_G4 e 2_B2 e 3_B3e 1_B1r 1_G3 e 2_G6r 2_G4 e 3_G7e 2_G3e 3_G4r 3_G5Fig. 4. a) An I/O graph of a chain of 3 processes with recycling of good 4; b) the corresponding expenditure–revenue graph.
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Page 13 and 14: energy6000.0 kg9000.0 kg11000.0 kg3
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Page 17 and 18: 3 IT HP PCs (eee)NET PARAMETERS:3 I

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