Section VI
The Components of the System
A system performs his main function through the carrying out of a number of specific or partial actions. These actions are carried out by the components of the
system. (the term component may be a bit misleading in gardening systems, we are keping it because it is widely used; the term sub-system may be more appropiate here and it will be used interchangeably)
For the sake of analysis, each specific action should be ascribed to a separate
component even if, as is often the case, the same resources are used in a number of
components. These specific components may later be grouped if desired to form
more inclusive components or sub-systems.
To illustrate the idea of components or sub-systems let's consider the example of
a Hospital.- In a Hospital some components may be defined in terms of specific medical
actions, like say, Department of Cardiology, Urology, Neurology, etc. Other comps.
may be defined in terms of more general medical actions but for specific age groups like
Depts. of Geriatrics or Pediatrics. The specific functions of all these may be stated
unambigously in terms of the patient's health. Alongside them it is necessary to define
other components which are not directly related to the patients health but are nevertheless important to the functioning of the Hospital, examples are Depts. of
Accountancy, Laundry, Building Maintenance and even a Gardening Dept. The specific
functions and performance measures of this type of comps. will have to be stated by
the hospital mangement in terms of their assistance to specific medical functions. (see
however, "Yes, Prime Minister", BBC, part IX for a particularly juicy flaw).
In the case of Gardening Systems the components may be designed along specific or partial missions like Lawn Maintenance, Weed Control, Tree Maintenance, etc. This sort of component design, which may be called "task oriented", should be weighed against a design based on garden sections or blocks, where each component includes all the tasks being performed in a given Section. The advantages and disadvantages of the former criteria against the latter, which may be called "geographically oriented" cannot be weighed easily. Fortunately, a good computer
program can output reports and analysis according to both types of criteriae. From the point of view of "hard" systems analysis the controversy could thus be solved but,
within the context of "soft" systems analysis the allocation of human resources acc. to one or other criteria becomes more tricky. The human factors which may be grouped
under motivation of the worker become highlited ( actually in the soft approach motivation is one of the Resources of the system). In my opinion a person takes more
pride of his work and is willing to assume more responsibility by taking care of a particular garden in all its aspects rather than by doing the same task in a number of
gardens; in the former case the results of his work are more easily assesed and a particular link bet. the garden and the worker is developped. The matter will be discussed more fully when we turn to Soft Systems.(link to)
An important aim of component thinking is to asses to which degree the performance measure of a component is related to the performance measure of the whole system.
A component is relevant to the main function if, as its performance measure increases, so does that of the whole system; otherwise it is irrelevant. The importance of a given component in the performance of the whole system can be ascertained according to the quantitative effect of its measure of performance on that of the entire system.
This question is particularly significant in gardening systems that operate with very tight
budgets. In this case, the allocation of Resources between the various components is
critical because it just there is not enough for all of them and some comps. will have to
be left understaffed or underfunded or even eliminated. I mentioned in the Introduction
that those lucky Gardeners which have enough resources to perform all the tasks that
their Garden requires, do not have to concern themselves with all the concepts and models discussed here; a list of monthly tasks, a diary and an efficient secretary are the
only management tools needed. For the rest of us, common mortals, the tricky decission of staffing some components and stuffing others deemed less important. The Decision
Making (DM) process according to System Analysis will proceed more or less like this:
a) construct a model where the dependence of the performance measure of the main
function on the perf. measure of selected components can be calculated, or at least estimated.
b) run the model for increasing and decreasing perf. measures of given components,
all other things being equal (a.o.t.b.e.)
c) according to the results of b) ascribe score points to the various components and build a scale of descending scores.
d) partition the Resources available bet. the upper component of the list and ignore
the others. How many comps. are ignored will be of course dependent on how
much you've got to distribute.
An example where the factors are very clear cut may be one as follows :
at a particular season we have just enough human resources for the components
Weed Control or Tree Maintenance (a.o.t.b.e.). An ad hoc model tells us that decreasing the perf. measure of Weed Control by 50% will decrease the S.N.R. (the performane measure of the main function) by 30%. On the other hand a similar decrease of 50% in
Tree Maintenance will decrease the SNR values by 5%. So Weed Control gets the allocation and the trees are left unattended.
In general terms, if we denote by pi the perfomance measure of a component
and by Ps that of the whole system then the rate of change is given by
d Ps = f (Ps,pi ) = P's (1)
d pi
(to avoid partial derivatives,we assume a.o.t.b.e.)
The mathematical treatment is usually as first order differential equations of the
general form:
F(x,y,y') = 0 (2)
where y' is dy .
dx
The simplest case of (1)will be of course P's = k that is the
rate of change is constant and the relationship is of form:
Ps = ki * Pi + c (3)
although (3) may rarely hold in practice, it is sometimes legitimate to "force"
the data into a linear equation at least for a given range of values. This because it is easier to compare the k values for various components than to compare a set of parameters. The case of P's = 0 will occur will occur when the function reaches a
minimum or a maximum and, of course when Ps is not a function of pi. The later case
occurs often in practice for the highest (threshold levels) of pi and for low values
when Ps is so low that small changes are inmaterial.
The following example may help to illustrate the concepts so far discussed:
Case 1.- Weed control by mowing:-
A certain section of the garden of area 3000sq.m.
is planted with young trees about 0.5 meter tall with spacing of 6 by 8 meters. Since the trees are hardly noticeable, the outlook is given almost entirely by bare soil in the dry season or as a green grass patch from mixed weeds in the rainy period. If the weeds are
left to grow unattended during this season the overall effect may be quite disastrous,that is SNR very low and even smaller than 1.- The method of choice for weed control for such a situation is to mow the weeds at given intervals; the outlook shortly after mowing
is that of a green carpet which due to the large area may give a high value of SNR (say
bet. 60 and 80). However if the temperatures are moderate the place will revert pretty
soon to low SNR hence,, the more often we mow, the closer we get to a uniform high
value of SNR. In the context of this situation, "Weed control of Section X by mowing"
will be one of the Components of the sytem, the function of the component is to maintain the maximum value of SNR within the constraints imposed by the Environment and by other parts of the system. To this component we have to allocate
human and material Resources, which might be needed by other comps. at the same time.
The first step in the thinking of the situation [step a) in the list above] is to construct a mathematical model for the dependence of the performance measures. Faithful to our previously stated inclinations of going from simple models to more complicated ones and not vice versa, we choose a particularly simple one as the
by Lendrem for a time-sleep situation in animals.
( Lendrem D.: Modelling in Behavioural Ecology, Crom Helm,London 1986 ) .
Denoting by n the number of mowings for a 90 days season, and by B the benefit attained by mowing it is pausible to assume a linear relationship bet. the two variables, that is :
B = b* n (4) where b is an adjustable prop.
parameter
But, the operation has a cost, because of the resources used and an additional one
because the same operator and equipment cannot perform other tasks somewherelse
in the system at the same time. This competition for resources increases the cost of the component mowing, because of the cost of doing unperformed work too late. For this,
instead of a linear relationship we will have a quadratic or a higher exponent function.
Denoting the cost by C and an adjustable parameter by c, we have:
C = c* n^r (5)
and the net benefit N given by the difference bet. B and C. For our case we choose a value of 2 for the exponent r, ( the case of r = 1 is when there is no competition for Resources) , so that N is :
N = B - C = b*n - c* n^2 ( 6)
Differentiating N with dn, we get for the derivative N':
N' = b - 2c*n (7)
Using the maximum condition N' = 0, we get:
n0 = b/2c (8)
where n0 stands for the optimized (maximum) number of mowings consistent with the
constraints imposed by the system. Let us recall that the main constraint arises from the assumption of a competiton between the performance of this component and the performance of other ones; if the competion were more acute, because of a greater
scarcity of resources, we would choose a higher exponent for n, so that the function will peak at a lower value of n.
Some numerical and graphical implications of the above relationships are
presented in the next page.
