Continued
Task-list sorted by priorities
In the context of this procedure, tasks that cannot be performed during time period R
because of lack of Resources are postponed to a later period. In most cases this postponement will mean that the same task will require more time to be performed
or might even need a different technique. A typical example: the task at period R is to spray with an herbicide weeds that are about 10 cm high throughout most of a garden
section. The task is postoned to the next period T but by then the same weeds are so high than only mechanical weeding is the technique of choice. The same task then,
will require a much larger time at period T. It may be said that the decision to postpone
entails a penalty which is assumed to be the original cost times a positive factor. This is the meaning of the last column in Tables M-1 and M-2; where the factor has been taken
to be 3 for all cases. This is, of course, an oversimplification, the penalty factor will
not be the same for all the tasks listed. Moreover an exponential factor instead of a
proportionality one can do the trick of higher penalties for higher cost- tasks, which
may be closer to a real situation. If as said in the previous page, we have to leave
low-priority tasks for the next time period (say, all tasks with priority 5 in Table M-2,
with a penalty of 1180 ) because of lack of resources, we will enter the next period T
with an overhead that is going to be added to the normal cost of the task list for period T. If the deficit for period T was the same percentage of the total as in R, the addition of this overhead will increse the deficit to higher levels. If we run this model for a fair number of time periods we will arrive pretty soon to an untenable situation where the costs far outweigh the Resources.
One possible way out of the situation described above is to change the priorities assigned to the various tasks at the begining of each period so that tasks whose postponement involves a higher penalty will receive a higher priority and vice-
versa. In more precise words: the model of the system will be run in such a way as
to minimize costs. A computer program that can fullfill such conditions will be proposed later on.
The concepts from the preceding paragraph lead us to the second point
to be discussed that is: what objective criteria can be used to assign priority values?
At least partly, a consideration for assigning priorities is the penalty to be paid by not
performing the task in the given time period, that is to say, priority 1 will include the tasks with the highest penalties in the list; priority 2 the second highest and so forth.
(please note that in Table M-2 the priorities were set at random ). We can run now iterations of the data at Table M-2 so that if we have to postpone tasks amounting to
10% of the total man-hrs the penalties incurred (and hence the partial costs) will be minimized. But we said " at least partly" because bare penalties cannot provide the only criterion and some factor regarding location has to be considered as well. A pertinent example might be a group of bushes in the outskirts of the gardens; if it is neglected
the costs of restoring it to its initial SNR value may be prohibitive; on the basis of that
that bushery is rarely seen we may decide to ignore it altogether. On the other hand
a similar group of bushes in the center of the garden where it is observed by a large proportion of the public, cannot be neglected for even a short period and hence the tasks
of its maintenance should receive a high priority.
In order to assign priorities according to a location criteria, we need to redefine the tasks listed in Tables M-1 and M-2 so that they will be linked to specific
Garden Units or specific Blocks (sets of adjoining GUs). Next we would have to attach to each location an estimated number of " visits " , that is the number of people that gets to that location per day or per week (similar to what a counter measures at a Website).
If we give to visits and penalties comparable magnitudes say, numbers in a scale from
1 to 1000, then both factors can be added so as to arrive to a composite magnitude
according to which the task list can be re-sorted and new priorities assigned.
A numerical example of that procedure is presented in Table M-3 below.
In the column of task code capitals have been replaced by normal letters to indicate that the tasks of the preceding Tables have been redefined; the values of the penalties have been kept from before but divided by p to facilitate computation; values for the number of visits have been assigned randomly and added to the penalties to give the composite
values. Finally the tasks have been ordered according to descending values of the composite values and new priorities assigned on the basis of these values.
Table M-3
The procedures and numerical examples presented above represent only coarse
first approximations. Closer to actual situations, priorities should be calculated as sums of functions(not necessarily linear)of several variables besides penalties and locations.
Nevertheless the point I intended to put forward with these simple examples
is that priorites may be computed using objective criteria and hence the decision making processes in the management of a gardening system may be performed by a computer
program run on the basics discussed above.
Futher insight into the process of decision making may be attained with help of
ideas from Game Theory, particularly Decision Theory and the use of Consequences and Utilities (instead of the penalties proposed above). The discussion of these concepts
in the context of gardening systems will constitute the next chapter of the management Section. The interested reader is referred to the corresponding pages in Principia Cybernetica Web (links to ) for definitions of these concepts:.
Game Theory
Decision Theory
Consequence and Utility
