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Debtors' Payments: Fuzzy Approach to Planning

The financial aspect is essential to any containing info on invoices, their birth
kind of business. How a company receives dates, adjournment periods for each of
funding and incomes determines its the debtors, actual dates of debtors'
overall welfare. For any B2B company, one payments that have occurred in the past,
of the major concerns is the control over we can view the statistics "Past payment
the payments of the non-bank debtors, delays". The density function of this
i.e. the payments resulting from sales of statistics can be viewed as a subnormal
goods and/or services. Indeed, this fuzzy set. This set, labeled "A", will be
inflow enables the company to assess its the first of the three fuzzy sets to be
efficiency, playing the role of the components of the resulting fuzzy set
factor underlying the company's profits. "payment date forecast". The density
Having produced some goods or services, function can give us a general idea about
the company sells the ware, receiving the "payment discipline" of a specific
money for the ware -- which becomes debtor in the past. The density function,
income. The company crucially needs this in a general case, will be containing
income in order to be able to buy some several "waves" because it's usually not
raw materials and equipment needed to a trend-containing characteristic as to
produce new portions of goods. Thus, it how many days a debtor will be evading
is essential that the company receives from paying the debt.Firstly, in most
income regularly. What is regularity, in cases the amount of days of a payment
this case? It's in fact receiving the delay is a random variable. It can be
money on a predetermined schedule. The fluctuating within a couple days' limits.
one that has been formed with a necessity Secondly, statistical forecasts of delays
in mind to meet the company's needs in may be differing significantly for
financing its expenditures. However, we different periods of time. This is
are living in a REAL world, which means because B2B relationships are not static,
that, inevitably, there are delays in they are developing all the time.
debtors' payments. This, in turn, can Sometimes, the selling company comes to
lead to a complete breakdown of the "shaking hands" with the buying company
financial plan. The latter may cause a for the latter to pay a couple days
non-reversible failure of the company. earlier, whereas sometimes the buying
Effective planning of these delays is the company may be facing temporary financial
key to successful financial problems (e.g., resulting from a huge
management.Given the stated facts, we credit to be returned to a bank by the
arrive at the importance of a system that buying company), so that the buying
would be able to forecast potential company warns the selling company that
delays in debtors' payments. Errors there may be slight delays of payments.
(deviations of the actual payment dates This is reflected in another component of
from forecasted dates) should be minimal the resulting fuzzy forecast, -- fuzzy
in order for such a system to be set "C". It is in fact a linguistic
considered effective. Now this is a tough variable "Payment delay most likely"
point. Existing works show that ordinary fuzzy set. The linguistic variable may
statistical models cannot bear really take one of the following values:
effective results that would be stable in "Neutral" (which means that there are no
time. From our viewpoint, the best way to specific anticipations of the payments
solve this issue is to use the so-called delay value for the specific debtor), "A
"fuzzy approach", which is based on the slight delay is possible", "A slight
fuzzy set theory, originally suggested by delay is most likely", "A large delay is
L. Zadeh.The basics of the fuzzy sets are most likely", "An on-time payment is most
explained in a huge amount of articles likely", "Payment in advance is most
and books -- use web search engines to likely". Each of these term-values has
find out what fuzzy logic is and how it its own membership function. A
all works, if there's such a need. Here, corresponding membership function is used
we only suggest a ready-to-use principle each time when building a forecast for a
of forecasting debtors' payments, basing specific debtor. The membership functions
on the fuzzy approach. The principle for the term-values of the linguistic
suggested in this article has been variable "Payment delay most likely" are
realized in the form of a computer given below:"An on-time payment is most
program. The program has been tested on likely": y=SQRT(1-ABS(x)/2), x belongs to
real data of a real company. The [-2;2]"A slight delay is most likely":
mean-square deviation thus calculated y=SQRT(1-ABS(x-4)/3), x belongs to
estimated 3, which suggests the idea that [1;7]"A slight delay is possible":
the principle presented herein is rather y=(1-ABS(x-4)/3)**2, x belongs to [1;7]"A
effective, but can be subject to further large delay is most likely":
improvement.Given a relational database y=SQRT(0.25-(12-x)/24)+0.5, x belongs
(which may be in fact realized in any [6;12]y=(0.71-(6-x)/4.23)**2, x belongs
way, including but not limited to, MS to [3;6)y=0, x12"Neutral": y=0.
Access, MS Excel DB-like data sets etc.)




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