Debtors' Payments: Fuzzy Approach to Planning

The financial aspect is essential to any kind ofExcel DB-like data sets etc.) containing info on invoices,
business. How a company receives funding andtheir birth dates, adjournment periods for each of the
incomes determines its overall welfare. For any B2Bdebtors, actual dates of debtors' payments that have
company, one of the major concerns is the controloccurred in the past, we can view the statistics "Past
over the payments of the non-bank debtors, i.e. thepayment delays". The density function of this statistics
payments resulting from sales of goods and/orcan be viewed as a subnormal fuzzy set. This set,
services. Indeed, this inflow enables the company tolabeled "A", will be the first of the three fuzzy sets to
assess its efficiency, playing the role of the factorbe components of the resulting fuzzy set "payment
underlying the company's profits. Having produceddate forecast". The density function can give us a
some goods or services, the company sells the ware,general idea about the "payment discipline" of a
receiving money for the ware -- which becomesspecific debtor in the past. The density function, in a
income. The company crucially needs this income ingeneral case, will be containing several "waves"
order to be able to buy some raw materials andbecause it's usually not a trend-containing characteristic
equipment needed to produce new portions of goods.as to how many days a debtor will be evading from
Thus, it is essential that the company receives incomepaying the debt.Firstly, in most cases the amount of
regularly. What is regularity, in this case? It's in factdays of a payment delay is a random variable. It can
receiving the money on a predetermined schedule. Thebe fluctuating within a couple days' limits. Secondly,
one that has been formed with a necessity in mind tostatistical forecasts of delays may be differing
meet the company's needs in financing itssignificantly for different periods of time. This is
expenditures. However, we are living in a REAL world,because B2B relationships are not static, they are
which means that, inevitably, there are delays indeveloping all the time. Sometimes, the selling company
debtors' payments. This, in turn, can lead to a completecomes to "shaking hands" with the buying company
breakdown of the financial plan. The latter may causefor the latter to pay a couple days earlier, whereas
a non-reversible failure of the company. Effectivesometimes the buying company may be facing
planning of these delays is the key to successfultemporary financial problems (e.g., resulting from a
financial management.Given the stated facts, wehuge credit to be returned to a bank by the buying
arrive at the importance of a system that would becompany), so that the buying company warns the
able to forecast potential delays in debtors' payments.selling company that there may be slight delays of
Errors (deviations of the actual payment dates frompayments. This is reflected in another component of
forecasted dates) should be minimal in order for suchthe resulting fuzzy forecast, -- fuzzy set "C". It is in
a system to be considered effective. Now this is afact a linguistic variable "Payment delay most likely"
tough point. Existing works show that ordinaryfuzzy set. The linguistic variable may take one of the
statistical models cannot bear really effective resultsfollowing values: "Neutral" (which means that there are
that would be stable in time. From our viewpoint, theno specific anticipations of the payments delay value
best way to solve this issue is to use the so-calledfor the specific debtor), "A slight delay is possible", "A
"fuzzy approach", which is based on the fuzzy setslight delay is most likely", "A large delay is most likely",
theory, originally suggested by L. Zadeh.The basics of"An on-time payment is most likely", "Payment in
the fuzzy sets are explained in a huge amount ofadvance is most likely". Each of these term-values has
articles and books -- use web search engines to findits own membership function. A corresponding
out what fuzzy logic is and how it all works, if there'smembership function is used each time when building a
such a need. Here, we only suggest a ready-to-useforecast for a specific debtor. The membership
principle of forecasting debtors' payments, basing onfunctions for the term-values of the linguistic variable
the fuzzy approach. The principle suggested in this"Payment delay most likely" are given below:"An
article has been realized in the form of a computeron-time payment is most likely": y=SQRT(1-ABS(x)/2),
program. The program has been tested on real datax belongs to [-2;2]"A slight delay is most likely":
of a real company. The mean-square deviation thusy=SQRT(1-ABS(x-4)/3), x belongs to [1;7]"A slight delay
calculated estimated 3, which suggests the idea thatis possible": y=(1-ABS(x-4)/3)**2, x belongs to [1;7]"A
the principle presented herein is rather effective, butlarge delay is most likely": y=SQRT(0.25-(12-x)/24)+0.5,
can be subject to further improvement.Given ax belongs [6;12]y=(0.71-(6-x)/4.23)**2, x belongs to
relational database (which may be in fact realized in[3;6)y=0, x12"Neutral": y=0.
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