Delft University of Technology
Faculty Mechanical, Maritime and Materials Engineering Transport Technology
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)
