####
A.M. Beeksma
*
Vraagvoorspelling met substitutie-effekten.
*

Computer program,
Report 93.3.LT.4208, Transport Engineering and Logistics.

In companies incoming orders are often received by telephone. This can cause
a problem concerning the registration of the orders. If a client wants to
order an article that is out of stock, no orders will be registered because
no articles can be sold at this time. Sometimes there is a possibility to
offer a substitute-article, which is not out of stock, to the client. In
that case only the demand for the substitutie will be registered. This way a
false registration of orders is being made. As a consequence the forecasts
for the next periods, that are based on the last registration, will have a
certain deviation as well.

In order to reconstruct the original demand for all the articles we have
developed a so called demand-filter. Special requirements for this filter
were simplicity of the filter and the fact that very few data (actually only
the stock-level and the registered demand for articles) would be needed for
the implementation of the filter.

We have used the following filter-model:
- If the registered demand is less than the stock-level at the beginning
of a period, then the demand consists of an original demand for the article
and a substitute-demand by other articles, that are out of stock. We can
now make an estimation of the percentage of substituties and estimate the
original demand by subtracting the substitutes from the registered demand.
We have done so by multiplying the registered demand by a so called
substitutie factor α. (where 0 < α < 1).
- If the registered demand for an article equals the stock-level at the
beginning of a certain period, then we can assume that the article is out
of stock. In this case the registered demand can be less than the original
demand. An estimation of the original demand can be made by using a
forecast, based on the average demand in the previous periods.

In order to test this model we have carried out simulations in an
object-oriented Pascal program. In this program a demand for certain
articles is generated, substitute- and out-of-stock effects are added, and
the resulting registered demand is being filtered by different versions of
the filter-model stated above. After this the filtered demand is compared
with the original demand.

lf we consider the situation with only the out-of-stock effects, and no
substituting effects, then the filter model that is stated above (with
α = 1) gives a fair estimation of the original demand.
However, if substitute effects are to be considered as well, things get more
complicated. Especially the role of α becomes very important. The
α-factor gives an estimation of the expected substitute-percentages. We
have calculated these percentages by calculating the expected average demand
for the article during the periods in which there is no substituting at all.
After having calculated this average demand we can simply give an approximation
of the substitute-percentage in a period by calculating the difference of the
registered demand and the average demand. In our simulation this resulted in
quite good estimations of the average demand for a certain time-span. There is
however a weakness in this method: if there are few periods in which there is
no substituting, the results tend to get worse very fast. So in this case we
probably need more information, for example about the substituting percentages
of the article to others, for good estimation results.

Reports on Transport Engineering and Logistics (in Dutch)

Modified: 2008.01.19;
logistics@3mE.tudelft.nl
, TU Delft
/ 3mE
/ TT
/ LT.