WO2002005149A1 - Method and system for processing and display of variables in a user generated network diagram representing a balanced system - Google Patents
Method and system for processing and display of variables in a user generated network diagram representing a balanced system Download PDFInfo
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- WO2002005149A1 WO2002005149A1 PCT/DK2001/000474 DK0100474W WO0205149A1 WO 2002005149 A1 WO2002005149 A1 WO 2002005149A1 DK 0100474 W DK0100474 W DK 0100474W WO 0205149 A1 WO0205149 A1 WO 0205149A1
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- G—PHYSICS
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- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q10/00—Administration; Management
- G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
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- the invention concerns a method and a system for accounting and management of financial and environmental resources.
- Daniel Bricklin and Bob Frankston introduced the first PC-based electronic spreadsheet (VisiCalc) anticipated by Mattessich's pioneering work on the mainframe. Although its first application concerned accounting and financial simulation, the computerised matrix approach did not catch on. Even today, software systems for accounting and financial management are based on the ancient debit-credit method and do not exploit the considerable advantages of the input-output method.
- the PC-based electronic spreadsheet has advanced accounting, economic and ecological modelling to a great extent, but it remains to abandon the debit-credit method and instead apply the input-output method. It further remains to unify financial and environmental accounting (en- ergy/materials accounting), and to establish an account processing system, which economists, accountants, ecologists, engineers and students can readily understand and apply on a daily basis.
- the present invention is the prototype of such a processing system.
- a computer system for processing and display of variables in a user generated network diagram representing a balanced system, said variables representing stocks and flows of resources and key ratios being ratios of linear combinations of flows and/or stocks of resources, said system comprising:
- a user interface for graphically creating a balanced system depicted by a network diagram having one or more nodes, at least one input flow from a giving system into a node, at least one output flow from a node into a receiving system, and/or one or more flows between nodes, said giving and receiving systems being systems outside the balanced system, each node representing a subsystem with a stock of resources and each flow representing a flow of resources into or from a subsystem,
- each subsystem means for generating and/or user-defining, for each subsystem, a number of key ratio equations, each said key ratio equation consisting of a key ratio being an independent variable set equal to a fraction, a ratio, with a linear combination of flows and/or stocks in the numerator and another linear combination of flows and/or stocks in the denominator, said number of key ratio equations being equal to the number of dependent variables assigned to said subsystem minus one, a user interface for entering numerical values of some or all of the independent variables, and
- system is adapted for displaying entered values of independent variables and calculated values of dependent variables.
- the means for calculating the values of the dependent variables is adapted for generating, for each subsystem, a balance equation, said balance equation stating the balance: flows of resources into the subsystem minus flows of resources out of the subsystem equals the stock of resources contained in the subsystem.
- the means for calculating the dependent variables may be adapted for performing said calculation based on balance equations and key ratio equations.
- the means for calculating the dependent variables may be adapted for performing said calculation based on a set of n + m simultaneous linear equations where n is equal to the number of subsystems in the network, and thereby to the number of balance equations, and m is equal to the sum of the number of key ratio equations attached to each subsystem.
- the means for generating the key ratio equations may be adapted for generating m default key ratio equations, where m is equal to the sum of the number of key ratio equations attached to each subsystem.
- the key ratio equations may be generated as default equations by the computer processing system or may be entered by a user.
- the means for generating and/or defining the key ratios may comprise a user interface for entering user-defined key ratios.
- the means for generating a default key ratio equation is adapted for generating key ratio equations having a numerator given by a single output flow from the corresponding subsystem.
- the means for generating a default key ratio equation may be adapted for generating key ratio equations so that all generated key ratio equations have a numerator given by a single output flow from the corresponding subsystem.
- the means for generating a default key ratio equation may also be adapted for generating key ratio equations as output coefficients having the above mentioned numerator and a denominator given by the total flow output from the corresponding subsystem plus the stock of the corresponding subsystem.
- the means for generating a default key ratio equation may be adapted for generating key ratio equations having a denominator given by the total flow input to the corresponding subsystem. It is preferred that the computer processing system is adapted for displaying the system-generated or the user-defined key ratios.
- the computer processing system may be adapted for attaching a tag, a variable identifier, to each node and each flow, said calculated and/or entered values of flows and stocks being displayed adjacent to the corresponding tag.
- the computer processing system of the invention is adapted for identifying the stock contained in each subsystem by a single-indexed tag.
- the system of the invention may also be adapted to link each node to a dialog box allowing a user to assign the stock to be a dependent or an independent variable. It is also preferred that the system of the invention is adapted for identifying each flow by a double-indexed tag holding information of the system or subsystem of origin of the flow and of the receiving system or subsystem.
- system of the invention may be adapted to link flows to a dialog box allowing a user to assign a flow to be a dependent or independent variable.
- the means for generating the key ratio equations may use said identifiers, thereby representing flows identified by said double-indexed flow identifiers, and stocks identified by said single-indexed stock identifiers.
- the system may indicate for each flow the direction of the flow of resources. Also, the system may display each node in the form of a rectangle.
- the system of the invention may display the values of some of the variables, values of a selected number of the variables, or all entered values of independent variables and all calculated values of dependent variables. If a variable is not known, i.e. the value has not been entered or the system is not capable of calculating the value due to for example missing values of independent variables, the system may display the value of unknown independent and dependent variables as unknown to the user.
- the means for generating key ratio equations may be adapted for generating, for each subsystem being a flow account in which the stock is an independent variable, a default key ratio equation for each outgoing flow from the subsystem minus one.
- the means for generating the key ratio equations may further be adapted for generating, for each subsystem being a stock account in which the stock is a dependent variable, a default key ratio equation for each outgoing flow.
- the means for calculating the values of the dependent variables may be adapted to arrange the (n + m) linear equations in a form corresponding to a matrix equation with the values of the matrix elements being derived from the set of (n + m) linear equations and the entered values of independent variables.
- the means for calculating the values of the dependent variables may be adapted to derive a single row of the matrix elements from a key ratio equation. Also, the means may be adapted to derive a single row of the matrix elements from a balance equation.
- the means for calculating the values of the dependent variables preferably is adapted to calculate said values by solving the matrix equation.
- the present invention also provides a computer processing system operating in a so-called hindcast mode of operation.
- the computer system may be adapted to alternate between hindcast and forecast.
- the first aspect of the invention also relates to a computer implemented method of operation.
- a computer implemented method for processing and display of variables in a user generated network diagram representing a balanced system said variables representing stocks and flows of resources and key ratios being ratios of linear combinations of flows and/or stocks of resources, said method comprising:
- a balanced system depicted by a network diagram having one or more nodes, at least one input flow from a giving system into a node, at least one output flow from a node into a receiving system, and/or one or more flows between nodes, said giving and receiving systems being systems outside the balanced system, each node representing a subsystem with a stock of resources and each flow representing a flow of resources,
- each subsystem assigning all flows of resources from the giving system into a node as an independent variable, for each subsystem generating and/or user-defining a number of key ratio equations, each said key ratio equation consisting of a key ratio being an independent variable set equal to a fraction or a ratio with a linear combination of flows and/or stocks in the numerator and another linear combination of flows and/or stocks in the denominator, said number of key ratio equations being equal to the number of dependent variables assigned to said subsystem minus one,
- the method further comprises displaying entered values of independent variables and calculated values of dependent variables.
- each subsystem has a corresponding balance equation, said balance equation stating the balance: flows of resources into the subsystem minus flows of resources out of the subsystem equals the stock of resources contained in the subsystem.
- the calculation of the values of the dependent variables may be based on the balance equations and the key ratio equations.
- the calculation of the values of the dependent variables may be based on a set of (n + m) simultaneous linear equations, where n is equal to the number of subsystems in the network, and thereby to the number of balance equations, and m is equal to the sum of the number of key ratio equations attached to each subsystem.
- some or all of the key ratio equations are default or system- generated key ratio equations. However, some or all of the key ratio equations may be user- defined key ratio equations.
- a key ratio equation or all of the key ratio equations may have a numerator given by a single output flow from the corresponding subsystem.
- a key ratio equation or all of the key ratio equations may have a denominator given by the total flow output from the corresponding subsystem plus the stock of the corresponding subsystem.
- some or all of key ratio equation may have a denominator given by the total flow input to the corresponding subsystem. It is preferred that the system-generated or user-defined key ratio equations are identified and displayed, and it is also preferred that the entered values of key ratios are displayed.
- a tag or a variable identifier is attached to each node and each flow, said calculated and/or entered values of flows and/or stocks being displayed adjacent to the corresponding tag.
- the stock may be identified by a single-indexed tag.
- each node is linked to a dialog box allowing a user to assign the stock to be a dependent or an independent variable.
- each flow is identified by a double-indexed tag referring to the system or subsystem of origin of the flow and of the receiving system or subsystem.
- Each flow may also linked to a dialog box allowing a user to assign the flow to be a dependent or an independent variable.
- the flows in the key ratio equations may be represented by said double-indexed flow identifiers and the stocks may be represented by said single-indexed stock identifiers.
- each flow graphically indicating the direction of the flow or resources.
- a flow may be represented by an arrow showing the direction of the flow of resources.
- a node may have the form of a rectangle.
- the subsystems may be divided in flow accounts and stock accounts, where for each subsystem being a flow account having the stock assigned as an independent variable, a key ratio equation is set up for each outgoing flow from the subsystem minus one, and where for each subsystem being a stock account having the stock assigned as a dependent variable, a key ratio equation is set up for each outgoing flow.
- the values of the dependent variables in the form of output flows and/or stocks may be calculated as functions of the independent variables in the form of key ratios, input flow(s) from the giving system, and/or stock(s) of subsystems.
- a method is provided in which the (n + m) linear equations are arranged in a form corresponding to a matrix equation with the values of the matrix elements being derived from the set of (n + m) linear equations and the entered values of independent variables.
- each key ratio equation may be represented by a single row in the matrix equation, and each balance equation may be represented by a single row in the matrix equation. It is also within an embodiment of the method of the first aspect of the invention to calculate the values of the dependent variables by solving the matrix equation.
- the present invention also provides a computer processing system which may be characterised as operating in a so-called hindcast mode of operation.
- a computer system for processing and display of variables representing stocks and flows of resources in a network diagram representing a balanced system comprising:
- a user interface for graphically creating a balanced system depicted by a network diagram having one or more nodes, at least one input flow from a giving system into a node, at least one output flow from a node into a receiving system, and/or one or more flows between nodes, said giving and receiving systems being systems outside the balanced system, each node representing a subsystem with a stock of resources and each flow representing a flow of resources,
- a user interface for assigning for each subsystem one variable as a dependent variable, said dependent variable being either a flow of resources to or from said subsystem or the stock of resources contained in said subsystem,
- a user interface for entering data representing values of some or all of the independent variables
- the system of the second aspect of the invention may further comprise means for generating and/or defining, for each subsystem, a number of key ratio equations, each said key ratio equation being a dependent variable defined as a ratio, a fraction, with a linear combination of flows and/or stocks in the numerator and another linear combination of flows and stocks in the denominator, said generating means being adapted for generating, for each subsystem in which the stock is assigned as an independent variable, a default key ratio definition for each outgoing flow from the subsystem minus one, and said generating means being adapted for generating, for each subsystem in which the stock is assigned as a dependent variable, a default key ratio definition for each outgoing flow.
- the means for calculating the values of the dependent variables is adapted for generating, for each subsystem, a balance equation, said balance equation stating the balance: flows of resources into the subsystem minus flows of resources out of the subsystem equals the stock of resources contained in the subsystem.
- the means for calculating the values of the dependent variables may be adapted for calculating the values of the dependent variables based on a set of n simultaneous balance equations where n is the number of subsystems in the network.
- the system may be adapted for attaching a tag or a variable identifier to each node and each flow, said entered values of the independent flows and/or stocks variables and the calculated values of the dependent flows and/or stocks variables being displayed adjacent to the corresponding tag.
- the system may be adapted for identifying the stock contained in each subsystem by a single-indexed tag, and the system may also be adapted to link each node to a dialog box allowing a user to assign the stock to be a dependent or an independent variable.
- the system is adapted for identifying each flow by a double-indexed tag holding information of the system or subsystem of origin of the flow and of the receiving system or subsystem, and the system may also be adapted to link each flow to a dialog box allowing a user to assign the flow to be a dependent or an independent variable.
- the system may indicate for each flow the direction of the flow of resources.
- a flow may be represented by an arrow indicating the direction of the flow of resources.
- the system may be adapted to display each node in the form of a rectangle.
- the means for calculating the values of dependent variables may be adapted to perform a process comprising the steps of:
- the means for calculating the values of the dependent variables should preferably be adapted to: d) repeating steps a-c until all subsystems have been selected.
- the means for calculating the values of dependent variables may further be adapted to: e) when all subsystems have been selected according to steps a-d determining if one or more values of dependent variables have been calculated, if not, stop any further calculation of values of dependent variables, or if yes, f) repeating steps a-d.
- the means for calculating the values of dependent variables may further be adapted to: g) repeating steps a-f until no more values of dependent variables have been calculated.
- the system may keep going through a calculation process until no further values of dependent variables are calculated.
- the system of the second aspect of the present invention may be adapted to include another type of dependent variables described as key ratios.
- the system may comprise means for generating or, by means of a user interface, for user-defining a number of key ratios, each said key ratio being a dependent variable set equal to a fraction, or ratio, with a linear combination of flows and/or stocks in the numerator and another linear combination of flows and/or stocks in the denominator.
- the means for generating key ratio equations which may be generated default key ratio equations, may be adapted to define the numerator by a single output flow from the corresponding subsystem.
- the means for generating key ratio equations may also adapted to define the denominator by the total flow output from the corresponding subsystem plus the stock of the corresponding subsystem.
- the means for generating key ratio equations may be adapted to define the denominator by the total flow input to the corresponding subsystem.
- the flows in the key ratio equations may be represented by said double-indexed flow identifiers, and the stocks may be represented by said single-indexed stock identifiers.
- the generated or defined key ratio equations are preferably displayed by the system.
- the system may use these values together with entered values of the independent values to determine values of key ratios as defined from the key ratio equations.
- the system may be adapted to calculate the numerical values of key ratios based on entered or calculated values of flows and/or stocks.
- the system may also be adapted to display the calculated values of the key ratios.
- the system may be adapted to display only part of the values of the independent and dependent variables, but it is preferred that the system is adapted to display all entered values of independent variables and all calculated values of dependent variables. If the value of a variable is not known or may not be determined, the system may display the value of such a variable as an unknown.
- the system may store each said set of calculated and entered values of variables, whereby each said set can be displayed one set at a time.
- the sets of values of independent variables may be considered as inputs being changed in time, and for each point in time a change occurs on the input side, a new set of values of dependent variables may be determined.
- the second aspect of the present invention also relates to a computer implemented method of operation.
- a computer implemented method for processing and display of variables representing stocks and flows of resources in a network diagram representing a balanced system comprising:
- a balanced system depicted by a network diagram having one or more nodes, at least one input flow from a giving system into a node, at least one output flow from a node into a receiving system, and/or one or more flows between nodes, said giving and receiving systems being systems outside the balanced system, each node representing a subsystem with a stock of resources and each flow representing a flow of resources,
- said dependent variable being either a flow of resources to or from said subsystem or the stock of resources contained in said subsystem, the remaining variables of stocks and flows being independent,
- each subsystem has a corresponding balance equation, said balance equation giving a balance be- tween flows of resources to and from the subsystem and the stock of resources of the subsystem.
- the calculation of the values of the dependent variables is based on a set of n simultaneous balance equations where n is the number of subsystems in the network.
- a tag or a variable identifier is attached to each node and each flow, and the calculated values of the dependent variables and the entered values of the independent variables may be displayed adjacent to the corresponding tag.
- the stock contained in the subsystem is identified by a single-indexed tag, and that each node may be linked to a dialog box allowing a user to assign the stock to be a dependent or an independent variable.
- the flow is identified by a double- indexed tag referring to the system or subsystem of origin of the flow and to the receiving system or subsystem.
- the flow may be linked to a dialog box allowing a user to assign the flow to be a dependent or an independent variable.
- each flow indicates the direction of the flow of resources.
- the flow may be represented by an arrow indicating the direction of the flow of resources.
- a node may be displayed in the form of a rectangle.
- the method provides a process of calculating the values of the dependent variables, said process comprising: a) selecting a subsystem, b) for said selected subsystem counting the number of variables having an unknown value, and if said number is greater than one selecting a new subsystem, or, if said number equals one, c) calculate the value of the unknown dependent variable by means of the balance equation for the selected subsystem.
- the process may further comprise: d) repeating steps a-c until all subsystems have been selected.
- the process of calculating the values of the dependent variables may further comprise: e) when all subsystems have been selected according to steps a-d determining if one or more values of dependent variables have been calculated, if not, stop any further calculation of values of dependent variables, or if yes, f) repeating steps a-d.
- the process may further comprise: g) repeating steps a-f until no more values of dependent variables have been calculated.
- the system of the second aspect of the present invention may be adapted to include another type of dependent variables described as key ratios.
- the generated key ratio equations may be system generated default key ratios, while the defined key ratio equations may be defined by a user via a user interface.
- a subsystem has one or more corresponding key ratio equations, which may be default key ratio equations, and a key ratio may have a numerator defined by a single output flow from the corresponding subsystem.
- a key ratio may have a denominator given by the total flow output from the corresponding subsystem plus the stock of the corresponding subsystem.
- a key ratio may have a denominator given by the total flow input to the corresponding subsystem plus.
- the flows in the key ratio equations may be represented by said double-indexed flow identifiers, while the stocks may be represented by said single-indexed stock identifiers.
- the values of some or all of the key ratios are calculated when the values of flows and/or stocks corresponding to the definition given by the key ratio equations have been entered or calculated.
- the calculated values of the key ratios are displayed, and it is also preferred that all entered values of independent variables and all calculated values of dependent variables are displayed.
- the values of the flows and stocks may be displayed in the network diagram.
- the value of a variable is unknown, the value of said variable may be displayed as unknown, for example by a question mark.
- the stock of a subsystem may be assigned as an independent or a dependent variable. If the stock is an independent variable, the subsystem may be named a flow account having one flow assigned as a dependent variable, the remaining flows and the stock of said subsystem being independent variables. If the stock is a dependent variable, the subsystem may be named a stock account having the stock assigned as a dependent variable and all flows of said subsystem being independent variables. It should be understood that according to the different aspects of the present invention, the resource flowing in the balanced system may be selected from a group of resources comprising: money, energy, and materials.
- the present invention also provides a processing system which may be used both in the hindcast and the forecast mode of operations.
- a computer system for processing and display of variables in a user generated network diagram representing a balanced system said variables representing stocks and flows of resources and key ratios being ratios of linear combinations of flows and/or stocks of resources, said system comprising:
- a user interface for graphically creating a balanced system depicted by a network diagram having one or more nodes, at least one input flow from a giving system into a node, at least one output flow from a node into a receiving system, and/or one or more flows between nodes, said giving and receiving systems being systems outside the balanced system, each node representing a subsystem with a stock of resources and each flow representing a flow of resources to or from a subsystem,
- each said key ratio equation consisting of a key ratio being a variable set equal to a fraction or a ratio with a linear combination of flows and/or stocks in the numerator and another linear combination of flows and/or stocks in the denominator, said number of key ratio equations being equal to the number of dependent variables assigned to said subsystem minus one,
- a user interface for entering data representing values of some or all of the independent variables
- the means for calculating the values of the dependent variables is preferably adapted for generating or user-defining, for each subsystem, a balance equation, said balance equation stating the balance: flows of resources into the subsystem minus flows of resources out of the system equals the stock of resources contained in the subsystem.
- the system may further comprise a user interface for selecting either a hindcast or a forecast mode of operation.
- the system may comprise:
- a user interface for assigning, for each subsystem, the stock of resources as either a dependent or an independent variable
- the system When the system is set to the forecast mode of operation, the system may by default assign all stocks as independent variables.
- system may further comprise any of the embodiments of systems according to the first aspect of the invention.
- the system of the third aspect of the invention When the system of the third aspect of the invention is selected to be in the hindcast mode of operation, the system may comprise:
- a user interface for assigning, for each subsystem, one variable as a dependent variable, said variable being either a flow of resources or the stock of resources of said subsystem, and
- the system may further comprise any of the embodiments of systems according to the second aspect of the invention.
- a computer program may be provided for programming or adapting a computer accordingly.
- a first computer program comprising computer program code means for adapting a computer to a system selected from the embodiments of systems according to the first aspect of the invention when said program is installed on the computer.
- the first computer program may preferably be embodied on a computer-readable medium.
- the second computer program may preferably be embodied on a computer-readable medium.
- a third computer program comprising computer program code means for adapting a computer to a system selected from the embodiments of systems according to the third aspect of the invention when said program is installed on the computer.
- the third computer program may preferably be embodied on a computer-readable medium.
- the present invention may include the energy/materials dimension (the environmental dimension), and applies to any conserved quantity.
- the invention is a simple solution to an apparently insoluble problem: the provision of a simple, and yet universal, method and software system for financial accounting, budgeting and management as well as environmental accounting and management.
- Fig. 1 shows a screen view of a network diagram of a balanced system comprising a single subsystem visualised by a processing system according to an embodiment of the present invention
- Fig. 2 shows that the subsystem in Fig. 1 is located between a giving and a receiving reservoir or system
- Fig. 3 shows a print-out of a balanced system comprising two interacting subsystems
- Fig. 4 shows the input-output and the key ratio matrices of the network diagram (graph) in Fig. 3,
- Fig. 5 shows a network diagram of a balanced financial system comprising eight subsystems (accounts),
- Fig. 6 shows a screen view of the network diagram in Fig. 5 visualised by a processing system according to an embodiment of the present invention
- Fig. 7 illustrates flows in network diagram representing the nitrogen cycle of agriculture
- Fig. 8 shows a balanced system representing the nitrogen account of Danish agriculture in million kg N in the middle of the 1980ies
- Fig. 9 shows a balanced system representing an account plan for a company selling counseling and software
- Fig. 10 shows a balanced system representing an energy account in 1000 kWh per annum for a company producing plastic devices
- Fig. 11a-11c are flow chart showing an algorithm for calculating dependent variables in the hindcast mode of operation according to an embodiment of the present invention
- Fig. 12 is a flow chart showing an algorithm for calculating dependent variables in the forecast mode of operation according to an embodiment of the present invention
- Fig. 13a, 13b are flow chart showing an algorithm for processing key ratio equations according to an embodiment of the present invention, said algorithm being part of the algorithm of Fig. 12,
- Fig. 14a-14d are flow chart showing an algorithm for processing an Operational String according to an embodiment of the present invention, said algorithm being part of the algorithm of Fig. 13, Fig. 15 is a flow chart showing an algorithm for deriving Column Number and Operational Term according to an embodiment of the present invention, said algorithm being part of the algorithm of Fig. 14,
- Fig. 16a-16g are flow chart showing an algorithm for processing balance equations according to an embodiment of the present invention, said algorithm being part of the algorithm of Fig. 12,
- Fig. 17 shows an example of a balanced system in hindcast mode according to an embodiment of the present invention.
- Fig. 18 shows an example of a balanced system in a forecast mode according to an embodiment of the present invention.
- the method and system of the present invention may be based on three axioms:
- Double entry bookkeeping concerns accounting for conserved quantities. The same amount is entered in two places. None disappears and nothing is created in the transfer of money from one account to another. In other words: In double entry bookkeeping, flows and stocks of money behave exactly as flows and stocks of energy and materials. Mathematically it makes no difference whether the currency is $ or kg nitrogen for example. Double entry bookkeeping is "made" to account for all conceivable conserved quantities in natural and man-made systems.
- a mathematical model is formed in three steps: 1 ) counting the unknowns, the dependent variables, 2) setting up simultaneous equations in the same number, and 3) solving them.
- the generalised model of double entry bookkeeping consists of two combinations of linear equations called modes of operation.
- One mode ('hindcast') is applied when setting up and predicting financial or energy/materials accounts.
- the equations are the balance equations, one for each subsystem in the network.
- the other ('forecast') is applied for financial and environmental management by means of key ratios and inputs from the giving system.
- the equations are the aforementioned balance equations in addition to equations defining key ratios in a number necessary and sufficient to close the system of equations governing each subsystem.
- the special thing about the processing system of the present invention is that it may set up the equations in addition to solving them. Hence, in order to create an input-output model, the user practically needs only to draw his system as a network diagram and "count" the unknowns.
- the input-output matrix is visualised as a graph or network diagram with flows of resources between the network's nodes and stocks contained in these nodes. Two modes of presentation may be obtained: the accounting matrix and the network visualisation, which are equivalent in terms of information, the difference being that the network is much easier to grasp.
- D1 X0,1 - X1.
- W Stock input - output
- the processing system may generate the balance equation from the user's drawing of a network diagram and make sure that the correct balance, the actual stock, is calculated after each and every pulse of water entering or leaving the tub, or pulse of money entering or leaving the bank account.
- Flow accounts in which stocks per definition are independent variables
- stock accounts in which stocks per definition are dependent variables
- Flow accounts in which stocks per definition are dependent variables
- Fig. 5 If a stock is assigned to be a dependent variable, then the account in which the stock is found is a stock account. If a stock is assigned to be an independent variable, then the account in which the stock is found is a flow account.
- the processing system may work with n balance equations, where n is the number of subsystems in the system. So, instead of generating and solving only one equation with one unknown, the processing system of the present invention may generate and solve n equations with n unknowns.
- n is the number of subsystems in the system.
- the processing system of the present invention may generate and solve n equations with n unknowns.
- the mathematics is the same. We can also think of the network as a hydrological or an ecological model, or a model of the economy of a business.
- the network is an account plan. We can then record the independent variables, enter them into a long list of transactions and calculate a new value, a new step on a curve, after each transaction for all elements of the account, including the elements of the income statement and the balance sheet. This makes it a powerful early warning and management tool since one can predict transactions fairly accurately and hence predict the financial balance with the same accuracy, see also 'Further examples of networks' below.
- Embodiments of a processing system of the present invention may run 'forwards' and 'backwards', in forecast and in hindcast mode.
- the processing system may be an input- output model-maker, we may say that when we run the model backwards, i.e. when we are in hindcast mode, we calibrate it, while when we run it forwards, i.e. when we are in forecast mode, we apply it.
- the processing system may then automatically assign all outputs from subsystems to be dependent variables (in addition to stocks in stock accounts).
- the processing system may convert the key ratio from a model output to a model input, i.e. from a variable that merely reflects the performance of the system to a variable that governs it.
- a model output i.e. from a variable that merely reflects the performance of the system to a variable that governs it.
- D1 and X1 ,W two dependent variables
- the first equation is the balance equation.
- the second is the above stated equation defining the key ratio a1 ,W.
- a user can then by a click change the entered value of the (material) input X0,1 and/or the key ratio a1 ,W and calculate D1 and X1 ,W at each click.
- a processing system may take that step and establish an input-output model of a complex network of subsystems without the user knowing it, based on the information that the user transfers to the software system, merely by drawing the network diagram.
- a processing system of the present invention may generate the list of key ratios so that the number of ratios is necessary and sufficient to close the system of equations, i.e. to make the model work.
- the number of key ratios is determined in forecast mode based on axiom No. 2.
- a system consisting of a network of n subsystems, all of which are flow accounts. Stocks in flow accounts and inputs from the exterior are by definition independent variables, and all outputs from subsystems are by definition dependent variables in forecast. The number of necessary and sufficient key ratio equations is therefore equal to the total number of outputs from subsystems in the system or network (n 0 ).
- the equations are of two kinds: Balance and key ratio equations. Since the number of balance equations is equal to the number of subsystems, the number of key ratio equations (and key ratios) is equal to the number of outputs from subsystems (n 0 ) minus the number of subsystems. This applies if all accounts are flow accounts, i.e. when the number of stock accounts is zero.
- n k n 0 -n+n s
- an embodiment of a processing system of the present invention may apply a certain class of key ratios called output coefficients, see below.
- a user can overwrite the numerator and the denominator to obtain physically or financially meaningful key ratios. For instance, if we are dealing with a physical system, the user can define the efficiency of a subsystem and enter this definition.
- the processing system may then accept the definition as a governing equation and include it in the set of equations on which it operates. From now on the manager may be in control of flows and stocks in the entire network by controlling inputs and key ratios.
- a user creates a network diagram in which a subsystem embedded in a larger system is a node (containing a stock) and a connection between subsystems (and between subsystems and unbalanced systems outside the system) is represented by an arrow representing a flow
- a user assigns variables to be either dependent (data out) or independent (data in)
- the processing system may generate and display a list of key ratios and their definition in the necessary and sufficient number, d.
- a user is invited to define non-default (custom) key ratios, e. a user enters independent variables
- the processing system may generate and solve a set of simultaneous linear equations ensuring that the number of equations is equal to the number of dependent variables, g. the processing system may display the values of the variables in the network diagram and in the list generated in step c whenever a new value of any of the independent variables is entered.
- a user creates a network diagram in which a subsystem embedded in a system is a node (containing a stock) and a connection between subsystems (and between subsystems and unbalanced systems outside the system) is represented by an arrow carrying a flow, b. assigning one flow among the flows connected to each subsystem to be a dependent variable, and stocks to be independent variables, c. the processing system may generate and display a list of key ratios in the necessary and sufficient number, d. a user may define non-default key ratios, e. a user enters independent variables, f. generating a set of simultaneous linear equations consisting of the subsystems' balance equations only, g. the processing system may display the values of the variables in the network diagram and in the list generated in step c whenever a new value of one of the independent variables is entered.
- a user creates a network diagram in which a subsystem embedded in a system is a node (containing a stock) and a connection between subsystems (and between subsystems and unbalanced systems outside the system) is represented by an arrow carrying a flow, b. assigning one flow among the flows connected to each subsystem to be a dependent variable, and stocks to be independent variables, c. the processing system may generate and display a list of key ratios in the necessary and sufficient number, d. a user may define non-default key ratios, e. a user enters independent variables, f. generating a set of simultaneous linear equations consisting of the subsystems' balance equations only, g.
- the processing system may display the values of the variables in the network diagram and in the list generated in step c whenever a new value of any of the independent variables is entered, h. assigning stocks in stock accounts to be dependent variables, leaving flows connected to stock accounts to be independent variables, i. creating and storing a list of business transactions, i.e. a database of time series of increments of independent variables, j. displaying and storing income statement and balance sheet at any time selected between the beginning and the end of the list of business transactions, k. storing graphical images of the variables from the beginning to the end of the list of business transactions.
- a user creates a network diagram in which a subsystem embedded in a system is a node (containing a stock) and a connection between subsystems (and between subsystems and unbalanced systems outside the system) is represented by an arrow carrying a flow, b. assigning outputs from each subsystem to be dependent variables, c.
- the processing system may generate and display a list of key ratios in the necessary and sufficient number, d.
- a user may define non-default key ratios, e. a user enters independent variables, f. generating a set of simultaneous equations consisting of the subsystems' balance equations in addition to key ratio equations, g. the processing system may display the values of the variables in the network diagram and in the list generated in step c whenever a new value of any of the independent variables is entered.
- a user creates a network diagram in which a subsystem embedded in a system is a node (containing a stock) and a connection between subsystems (and between subsystems and unbalanced systems outside the system) is represented by an arrow carrying a flow, b. assigning outputs from each subsystem to be dependent variables, c.
- the processing system may generate and display a list of key ratios in the necessary and sufficient number, d.
- a user may define non-default key ratios, e. a user enters independent variables, f. generating a set of simultaneous equations consisting of the subsystems' balance equations in addition to equations defining key ratios, g.
- the processing system may display the values of the variables in the network diagram and in the list generated in step c whenever a new value of any of the independent variables is entered, h. assigning stocks in stock accounts to be dependent variables, leaving flows connected to stock accounts to be independent variables,
- Combination A+C covers green accounting.
- To include financial accounting dimension (combinations B+D) is merely a matter of distinguishing between flow and stock accounts and add a few further steps.
- Financial and green accounting are not only analogous, they are mathematically identical. The financial dimension thus emerges by adding steps specific to financial accounting and management, for instance the list of business transactions, the set up of the income statement, the balance sheet, and graphical features relevant to financial management.
- Account No. 1 in Fig. 3 is a flow account in which the stock per definition is an independent variable.
- Account No. 2 is a stock account in which the stock per definition is a dependent variable.
- D1 22 is a known, part of the model input.
- Fig. 4a shows the input-output matrix behind the graph in Fig. 3. It is Leonianas input-output table supplemented with the two previously mentioned reservoirs System 0 and System W.
- Fig 4b is the key ratio matrix derived from the input-output matrix.
- Fig. 4a we have three variables in forecast mode: X1 ,2, X1 ,W and D1 of which D1 is known.
- the two unknowns (X1 ,2 and X1 ,W) require two equations.
- i is the number of the current subsystem
- j is the number (plus the letter W for the receiving system) of the subsystem or system to which the output goes.
- Xi,j is a flow from subsystem i into subsystem j
- Di is the stock in subsystem i.
- the denominator is the sum of all outputs from the subsystem plus the stock contained in the subsystem.
- a user can choose default key ratios or form his own custom key ratio definitions or equations. He can delete the numerator and/or the denominator and instead enter linear combinations of a mixture of dependent and independent variables.
- a user can later change this value as he wishes since it is an independent variable in that mode of operation.
- the default and the custom key ratio equations happens to be identical by virtue of the balance equation.
- a processing system may include the key ratio equation along with the balance equation to complete the set of equations governing subsystem 1.
- the processing system may include the two key ratio equations along with the balance equation to complete the set of equations governing subsystem 2.
- the two first equations are the balance equations, the remaining three are the custom key ratio equations in rearranged form.
- linear equations may be solved in several ways, an example of which will be described below.
- a processing system may be provided which sets up a valid set of equations (i.e. 'makes' an input-output model) leaving it to the user only to make up his mind what he wishes to measure (assign variables to be independent), and what to calculate (assign variables to be dependent).
- Fig. 5 is a further detailing of Fig. 3 like Fig. 3 was a detailing of Fig. 1.
- Subsystem 1 in Fig. 3 is perceived as four interacting subsystems in Fig. 5 in the income and expenses group of accounts called flow accounts.
- subsystem No. 2 in Fig. 3 is in Fig. 5 perceived as another four interacting subsystems in the asset and liabilities group of accounts called stock accounts.
- the 10 transactions are:
- the stocks in the four flow accounts are:
- the balance sheet is updated immediately after the last business transaction is entered.
- the balance sheet is a function of the transactions, which in turn is a function of time. Not only can we produce continuously updated balance sheets, we can also predict all their components, for instance the liquidity.
- the income statement and the balance sheet in a traditional format printed from a processing system according to the present invention after entering the 14 independent variables mentioned above are as follows:
- Fig. 6 shows the graph or network diagram in Fig. 5 drawn and calculated by a processing system according to the present invention. It is the same system or network as in Fig. 5. On the screen, knowns are green and unknowns are red. As opposed to paper in black and white print, it is easy to tell whether the model is in hindcast or forecast mode, and to see the variable setting (dependent or independent).
- the hindcast mode is the calibration and budget simulation mode. Switching to the forecast mode, all flows in Fig. 6 turn dependent, except X0,1. They are functions of X0,1 in addition to the key ratios listed in the white background area to the left of the graph in Fig. 6.
- a user may choose a step size by which he can down- or up-step the independent variables and immediately see the result in terms of dependent variables that change in such a way that the balance equations are never violated.
- the key ratios in analysis of financial accounts have so far been passive players. Now they are 'active', i.e. input to the model, making them options in financial and environmental management.
- Fig. 7 Nitrogen losses from agriculture is the subject of some concern because of rising levels of nitrate in ground water and eutrophication of lakes and open seas.
- Fig. 8 shows the nitrogen account of Danish agriculture in Mkg N per annum in the middle of the 1980ies. This account is based on statistical data on flows of agricultural goods multiplied by their nitrogen content and added over all goods in the flow.
- the nitrogen account in Fig. 8 is primarily a function of three efficiencies: 1) the plants' nitrogen uptake efficiency, 2) the fodder efficiency and 3) the fertiliser efficiency of nitrogen in manure.
- the nitrogen management model can readily be applied to investigate what it takes in terms of a) reducing the input of new nitrogen and b) increasing the subsystems' efficiencies to obtain a certain balance. If, for instance, the goal were to reduce the output of nitrogen to the environment by 50 percent over a period of 10 years, and at the same time increase the agricultural production output by 2 percent per annum, the software system can be applied to calculate the combination of input of new nitrogen and the key ratios that meet these simultaneous goals.
- the nitrogen model is essentially capable of answering questions of the type: What happens if... ?
- Fig. 9 shows the account plan for a company selling counseling and software. Note that the account numbers are ordered so that the first digit is 1 , 2, 3, or 4, the number of the four categories (rows) of accounts listed to the right of the graph in Fig. 5.
- a R&D account an intangible asset, is included.
- a knowledge asset is not a conserved quantity and can for that reason not be dealt with by double entry bookkeeping. But nothing prevents us from recording the asset as the amount actually spent on R&D.
- Fig. 10 shows the energy account in 1000 kWh per annum for a company producing plastic devises.
- the input-output model is calibrated by applying a mixture of empirical key ratios and recorded flows of electric energy.
- a processing system may continually maintain a set of default key ratio equations, examples of which are shown to the left of the graph in Figs. 1 , 6, 17 and 18.
- the number of default key ratio equation for a subsystem is the number of dependent variables attached to that subsystem less one.
- subsystem 1 in Fig. 18 has three dependent variables (X1 ,1 ; X1 ,2; X1 ,W) and two key ratio equations (a1 ,1 ; a1 ,2).
- Subsystem 2 in Fig. 18 has three dependent variables (X2,0; X2,1 ; D2) and two key ratio equations (a2,0; a2,1).
- subsystem 1 has a key ratio for each output less one since the stock is an independent variable in that subsystem.
- subsystem 2 has a key ratio equation for each output, since the stock is a dependent variable in this subsystem.
- a default key ratio definition or equation is an output coefficient:
- i is the number of the current subsystem
- j is the number of the subsystem to which the output goes.
- Xi,j is a flow from subsystem i into subsystem j
- Di is the stock in the subsystem.
- the denominator is the sum of all outputs from the subsystem plus the stock contained in it.
- the processing system of the present invention may correct the equations attached to that subsystem. For instance, if the user adds a flow from subsystem 1 into System 0 (to the right in Fig. 18), the processing system may add X1 ,0 to the denominator of the equation as follows:
- the processing system may add X1 ,0 to the denominator of equation a1 ,1 in Fig. 18. And since we now have one more dependent variable for the subsystem, the processing system may set up an additional default key ratio equation:
- the processing system may remove X1 ,2 from the denominator of all default key ratio equations for subsystem 1 , and remove the default key ratio equation a1 ,2.
- the processing system may have a fixed order in which default key ratio equations are set up:
- the processing system may set up a default key ratio equation for X1 ,0 if the flow exists, else it will try the flow X1 ,1 and so forth, until it has the number of key ratio equations required.
- a custom key ratio equation is a user-defined key ratio.
- the user can modify the numerator and denominator of key ratio definitions or equations.
- the numerator and the denominator must be conform to the following format:
- T can be a flow, for instance X1 ,0, or a stock, for instance D2.
- T can be an independent or a dependent variable. In forecast at least one variable must be dependent.
- a processing system may stop maintaining it. So, after editing the network diagram, the user must update the modified (custom) key ratio equations affected by the changes.
- a key ratio equation is linked to an (existing) output from a subsystem. For example a1 ,2 is linked to the flow X1 ,2. This link is remained even when the user modifies a default key ratio equation. That is, if a user has modified a2,0 in Fig. 18, and later deletes X2,0, the processing system of the present invention may delete the a2,0 key ratio equation. So, for a2,0 to exist there must be a flow X2,0, but X2,0 need not at all be present in the numerator of the user modified key ratio. In order to produce a solution, the system of linear equations must meet certain conditions:
- the matrix of coefficients must be quadratic, which is another way of saying that the number of dependent variables must equal the number of equations.
- the number of equations is equal to the number of subsystems (equal to the number of balance equations) plus the number of key ratio equations.
- an embodiment of a processing system may operate a set of algorithms which calculate the dependent variables and make sure that the values displayed on the screen are valid, i.e. that the balance equations are never violated.
- Fig. 11 Calculation algorithm, hindcast This algorithm calculates the unknowns: flows, stocks and key ratios as functions of the knowns, i.e. other flows and stocks.
- the governing equations are the balance equation, one for each subsystem.
- the key ratios are subsequently calculated according to their definition simply by inserting the values (a mixture of knowns and unknowns) in the formula defining the key ratio.
- the algorithm can calculate the unknowns that are possible to calculate from the known variables given by the user. If, for example, the user has not quantified the known variables D1 and X1 ,5 then the unknown X0,1 cannot be calculated since the balance equations reads
- the unknowns that can be calculated may be marked as knowns (independent) internally in the processing system according to the present invention, the rest may be marked as unknowns (dependent).
- knowns On the screen, knowns may be indicated by a figure and unknowns by a "?”.
- Each variable in the processing system may have two properties: A value and a status. If the processing system marks a variable as a dependent variable, it may actually set its status to dependent (unknown).
- the algorithm runs through the subsystems as many times as required to solve for the dependent variables (only flows and stocks, not key ratios in hindcast).
- the algorithm processes the subsystems one at a time.
- OSU Operational Subsystem is the subsystem the algorithm is working on at the moment. The algorithm starts with subsystem number 1 , and continues with subsystem number 2 and so forth. In box 2 the algorithm sets the operational subsystem (OSU) to subsystem number 1. In box 3 the algorithm counts the number of dependent variables for the operational subsystem. The algorithm counts the number of dependent variables, because it can only solve the subsystem if there is only one dependent variable left to solve.
- Box 7 controls the loop that runs through the subsystems one at a time.
- Box 8 controls the loop that runs until the loop controlled by box 7 hasn't solved any dependent variables.
- This part of the algorithm runs through the key ratio equations one at a time, and checks if it is possible to calculate the key ratio. If it is possible to calculate a key ratio it does so, for instance, the first key ratio equation on Fig. 17 is
- a1 ,1 X1 ,1 / X1 ,1 +X1 ,2+X1 ,W+D1
- Box 9 The algorithm sets the operational key ratio equation to key ratio equation number 1 (the topmost key ratio equation to the left of the graph in Fig. 17).
- Box 12 The algorithm sets the operational key ratio equation to the next key ratio equation.
- Box 13 controls the loop that runs through the key ratio equations one at a time.
- Box 10 The algorithm checks if a key ratio can be solved which is done by testing all the variables in the numerator and denominator of the operational key ratio equation; if all variables are known, the key ratio can be calculated.
- the screen is updated with the calculated dependent variables, and with '?' where the calculation was unsuccessful.
- Fig. 12 Calculation algorithm, forecast: This algorithm calculates the unknowns: output flows and stocks as functions of key ratios and knowns i.e. other stocks and inputs from the exterior. The calculation is either successful in terms of finding a solution or not. If it is successful then the solution is shown in terms of quantified flows and stocks on the graph. The algorithm sets up the quadratic coefficient matrix A and the column vector (y) composed of knowns on the right hand side of the equation:
- the flowchart shows how dependent variables are calculated in forecast mode according to a preferred embodiment of the present invention.
- the graph shown in Fig. 18 will be used as reference in the following description.
- a1 ,1 X1 ,1 / (1 ,1+X1 ,2+X1 ,W+D1)
- the algorithm runs through the key ratio equations and updates the matrixes MA, MB as required to calculate the dependent variables in box 4, Fig. 12.
- the algorithm runs through the subsystems and sets up a balance equation for each subsystem, see Fig. 16 and the corresponding description.
- the balance equation is used to update the matrixes MA, MB as required to calculate the dependent variables in box 4, Fig. 12.
- the solution matrix is calculated as MB/MA, see description elsewhere.
- Fig. 13 Process equations: This algorithm is part of 'Calculation algorithm, forecast' (see Fig. 12). The graph shown in Fig. 18 will be used as reference in the following description.
- This algorithm runs through the key ratio equations (for instance 4 equations in Fig. 18), and calls an algorithm, 'Process OS' (see Fig. 14) for each numerator and denominator. For instance: When this algorithm processes the key ratio equations in Fig. 18, it will first call 'Process OS' with the string 'X1 ,1', and then 'X1 ,1 +X1 ,2+X1 ,W+D1', and then 'X1 ,2', and then-
- Fig. 14 Process OS: 'Process OS' updates the matrixes MA, MB as required to calculate the dependent variables in box 4, Fig. 12.
- OS stands for Operational String, which is the string on which the embodiment of the processing system of the present invention operates at the moment, for instance "X1 ,0+X1 ,1 +X1 ,W”.
- OE stands for Operational Equation, which is the equation on which the embodiment of the processing system operates at the moment.
- This algorithm is part of 'Calculation algorithm, forecast' (see Fig. 12).
- the graph shown in Fig. 18 will be used as reference in the following description.
- This algorithm runs through an input string, term by term and updates the matrixes MA, MB as required to calculate the dependent variables in box 4, Fig. 12.
- the input string could for instance be the denominator from key ratio equation 2 in Fig. 18
- This string has 4 terms, which are processed individually. See description of MA & MB matrixes, and the explanation of how the matrixes are calculated.
- numerator the rule is that the subsequent mathematical operation is applied when the algorithm operates on a numerator of a key ratio equation.
- denominator the rule is correspondingly that the subsequent mathematical operation is applied when the algorithm operates on a denominator of a key ratio equation.
- 'Process OS' processes the term 'X1 ,1' (Numerator, first key ratio equation Fig. 18).
- X1 ,1 is a dependent variable, and the algorithm processes it in boxes 4-5 in Fig. 14. First it finds the column number for X1 ,1 in the MA matrix, then it subtracts 1 from the value in the MA matrix in row nr 1 (since this is the first key ratio equation).
- 'Process OS' processes the term 'D1' (Denominator, first key ratio equation Fig. 18).
- the matrixes MA, MB will have the following values:
- the matrixes MA, MB will have the following values:
- the matrixes MA, MB will have the following values:
- the matrixes MA, MB will have the following values:
- 'D' (see box 10-17 in Fig. 14), which is the symbol for the sum of all the stocks in the graph. For instance, 'D' equals 'D1+D2' in Fig. 18.
- Fig. 15 Find CNR for OT: This algorithm is part of 'Calculation algorithm, forecast' (see Fig. 12). See description elsewhere.
- CNR stands for Column NumbeR and OT for Operational Term, which is the term on which the algorithm in Fig. 15 is operating at the moment, for instance "X1 ,0".
- CNR is a column number for OT. It is conducive to imagine the matrix MA as indicated below
- the algorithm When the algorithm is applied to find a column number for an unknown, e.g. X1 ,2 it begins by checking whether the first column in MA contains X1 ,2. If it is not found, it proceeds to the next column and checks again. When it finds the column in which the unknown is present it uses this column. If not found, it continues checking columns until a "?" is reached. When that happens the algorithm "knows” that no column has been allocated for this unknown and therefore uses the "?” column and replaces the "?” by X1 ,2.
- Fig. 16 Process balance equations: Again OT stands for Operational Term which is the term on which the embodiment of the processing system is operating at the moment. The balance equations are not actually set up by the embodiment of the processing system, instead the embodiment of the processing system runs through the subsystems and updates the matrixes as necessary.
- the algorithm finds an available row in the matrices MA and MB. This is the first row with all zero values, for instance the last row in the matrix shown above.
- This algorithm is part of 'Calculation algorithm, forecast' (see Fig. 12).
- the graph shown in Fig. 18 will be used as reference in the following description.
- This algorithm runs through the subsystems utilizing balance equations to update the matrixes MA, MB as required to calculate the dependent variables in box 4, Fig. 12.
- it first checks if the subsystem has any dependent variables (box 3, Fig. 16). If not it moves to the next subsystem (box 16, Fig. 16).
- the algorithm adds a row to the MA, MB matrix. Then the algorithm checks whether the stock for the current subsystem is a dependent variable (Box 4, Fig. 16). If the stock is unknown the algorithm finds the column number for this unknown in the MA matrix, and subtracts 1 from the value in the new row (box 19-21 , Fig. 16). It the stock is known, the algorithm adds the stock value to the MB matrix in the new row (box 5, Fig. 16).
- the algorithm runs through all outputs from the current subsystem. For each flow it finds the column number for it in the MA matrix, and subtracts 1 from the value in the new row (box 22-27, Fig. 16).
- the algorithm runs through all inputs to the current subsystem. If the current flow is from System 0 (for instance X0,1 or X0,2), then the algorithm subtracts the flow value from the MB matrix in the new row (box 18, Fig. 16). Flows from System 0 are always known variables. If the current flow is not from System 0, the algorithm finds the column number for the flow in the MA matrix, and adds 1 to the value in the new row (box 12, Fig. 16).
- the matrixes MA, MB will have the following values: MA MB 1X1,1 X1,2X1,WX2,0X2,1 D2 ]
- the matrixes MA, MB will have the following values:
- Fig.17 shows an example of a balanced system in a hindcast mode according to an embodiment of the present invention
- Fig.18 shows an example of a balanced system in a forecast mode according to an embodiment of the present invention.
- the systems of Figs.17 and 18 have default key ratio equations, that is key ratio equations set up according to an embodiment of a processing system of the present invention.
- the system Fig.17 is discussed in connection with the flow chart of Fig.11
- the system of Fig.18 is discussed in connection with the flow charts of Figs.12-16.
Abstract
Description
Claims
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AU2001272361A AU2001272361A1 (en) | 2000-07-07 | 2001-07-06 | Method and system for processing and display of variables in a user generated network diagram representing a balanced system |
US10/332,445 US20040059654A1 (en) | 2000-07-07 | 2001-07-06 | Method and system for processing and display of variables in a user generated network diagram representing a balanced system |
EP01951442A EP1301884A1 (en) | 2000-07-07 | 2001-07-06 | Method and system for processing and display of variables in a user generated network diagram representing a balanced system |
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- 2001-07-06 EP EP01951442A patent/EP1301884A1/en not_active Withdrawn
- 2001-07-06 WO PCT/DK2001/000474 patent/WO2002005149A1/en active Application Filing
- 2001-07-06 AU AU2001272361A patent/AU2001272361A1/en not_active Abandoned
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