smoothing level. There is, thus, no contradiction with respect to the dimensions,
either. Similar to the steady state, the output rate of a delay equals the input rate, the
smoothed level adopts the value of the variable being smoothed in the steady state.
Furthermore, the transient response characteristics of smoothing are accurately
comparable to the transient response characteristics of the delays. Using this line
of argument, some researchers have introduced the concept of ‘delay in information’, and of ‘cascaded smoothing’, thus bringing in the concept of ‘higher-order
smoothing’.
6.5.7 Table Functions
Sometimes a rate (or an auxiliary variable) is associated to another variable (a level
or an auxiliary) through a complicated nonlinear relationship. Defining this relationship and estimation of the parameters linked to this function may present some
difficulties. Past data is often inexistent or is inadequate to completely define the
relationship. As the system identification and estimation techniques available can be
extremely complex, system dynamics enables model builders to avoid this problem
by defining table functions for such cases.
Another justification for table functions is that even when the function relating
two variables is linear, the conversion coefficient (the proportionality constant) may
not be easily recognisable in the real system.
Consider, for example, the case of customer order rate (OR) as a function of
delivery delay (DD). Assuming a linear relationship such as:
OR t
ð Þ ¼ a þ b  DD t
ð Þ
OR has a dimension (units/week), and the dimension of DD is (week). So the
dimension of b is (units/week). Such a dimension is meaningless in a real sense.
Using statistical procedures, such as least square estimation, the parameters a and
b can be estimated. However, system dynamics offers a substitute in the form of
table functions.
A table function gives a static relationship between two variables. In this case, the
values of the affected variable y are estimated for discrete values of the causal
(independent) variable x covering the whole feasible range over which the causal
variable x can vary. The pairs of values of the two variables (x, y) can then be
tabulated. Thus, y can be expressed as a function of x through the use of a table,
hence the name ‘table function’.
Coming back to the case of order rate (OR) as a function of delivery delay (DD),
assume that under normal conditions, OR is 10,000 units/month and DD is 4 months.
The feasible range of values over which DD can vary is first established. It is
assumed that this range lies from 0 to 8 months. Next, certain equally spaced point
values of DD are chosen, say 0, 2, 4, 6, and 8 months. The most likely values of OR
6.5 Elements of System Dynamics Modelling
181
either. Similar to the steady state, the output rate of a delay equals the input rate, the
smoothed level adopts the value of the variable being smoothed in the steady state.
Furthermore, the transient response characteristics of smoothing are accurately
comparable to the transient response characteristics of the delays. Using this line
of argument, some researchers have introduced the concept of ‘delay in information’, and of ‘cascaded smoothing’, thus bringing in the concept of ‘higher-order
smoothing’.
6.5.7 Table Functions
Sometimes a rate (or an auxiliary variable) is associated to another variable (a level
or an auxiliary) through a complicated nonlinear relationship. Defining this relationship and estimation of the parameters linked to this function may present some
difficulties. Past data is often inexistent or is inadequate to completely define the
relationship. As the system identification and estimation techniques available can be
extremely complex, system dynamics enables model builders to avoid this problem
by defining table functions for such cases.
Another justification for table functions is that even when the function relating
two variables is linear, the conversion coefficient (the proportionality constant) may
not be easily recognisable in the real system.
Consider, for example, the case of customer order rate (OR) as a function of
delivery delay (DD). Assuming a linear relationship such as:
OR t
ð Þ ¼ a þ b  DD t
ð Þ
OR has a dimension (units/week), and the dimension of DD is (week). So the
dimension of b is (units/week). Such a dimension is meaningless in a real sense.
Using statistical procedures, such as least square estimation, the parameters a and
b can be estimated. However, system dynamics offers a substitute in the form of
table functions.
A table function gives a static relationship between two variables. In this case, the
values of the affected variable y are estimated for discrete values of the causal
(independent) variable x covering the whole feasible range over which the causal
variable x can vary. The pairs of values of the two variables (x, y) can then be
tabulated. Thus, y can be expressed as a function of x through the use of a table,
hence the name ‘table function’.
Coming back to the case of order rate (OR) as a function of delivery delay (DD),
assume that under normal conditions, OR is 10,000 units/month and DD is 4 months.
The feasible range of values over which DD can vary is first established. It is
assumed that this range lies from 0 to 8 months. Next, certain equally spaced point
values of DD are chosen, say 0, 2, 4, 6, and 8 months. The most likely values of OR
6.5 Elements of System Dynamics Modelling
181