Tests of the detailed models in a retail department store

We have tried to develop a model that would yield testable predictions, but there are two major limits on such a goal. First, we have not been completely successful in defining a model that will make precise predictions in every decision area. Second, where we have been successful in developing a model, we are constrained by the availability of data. The value of data for the purpose of testing models has not always been controlling in dataretention decisions by the firm. Despite these limits, we have been able to develop models for the major price and output decisions and to subject all but one of the major components of those models to some empirical test.

Figure 7.5 Flow chart for mark-down routine (cont.).

1.  Output determination

The output determination model consists of three segments — sales estimate, advance orders, and reorders. In each of the tests described below, the data used are new and are not the data with which the model was developed.

Sales estimation. The sales estimation model is composed of the rule  for estimating sales for the six-month period and the rules for the estimation of the sales of individual months. The data available were for a two-year period so that the test is far from conclusive. However, there is no reason to believe that the model would not be valid for a larger sample of data. The first part of the model, the estimation of total sales for a six-month period, predicts the total within 5 per cent in each of the four test instances. With the set of monthly rules, we can predict about 95 per cent of the monthly sales estimates within 5 per cent. There is no question that the predictive power could be increased still further by additional refinement of the rules. However, at this point it does not seem desirable to expend resources in that direction.

Advance orders. This segment of the model and the sales estimation segment are related as we have shown previously. Therefore, discrepancies between predicted and actual data are difficult to allocate precisely between the two segments although we have some clues from the above testing. Unfortunately, the firm  does not keep its records of advance orders any length of time so no extensive test of the model was possible. We were able to accumulate only four instances in which  the predictions of the model could be compared with the actual figures.

Reorders. This segment is one that it is most important to test. The fact is, however, that the data on reorders are not kept in a systematic fashion, and we have not been able to make any kind of test.

2. Price determination

Much more adequate data are available for the pricing models. In each case the model was tested and performed adequately.

Mark-up. In order to test the ability of the model to predict the price decisions that will be made by the buyer on new merchandise, an unre-stricted random sample of 197 invoices was drawn. The cost data and classification of the item were given as inputs to the computer model. The output was in the form of a predicted price. Since the sample consisted of items that had already been priced, it was possible to make a comparison of the predicted price with the actual price.

The definition of a correct prediction was made as stringent as possible. Unless the predicted price matched the actual price to the exact penny, the prediction was classified as incorrect. The results of the test were encouraging; of the 197 predicted prices, 188 were correct and 9 were incorrect. Thus 95 per cent of the predictions were correct. An investigation of the incorrect predictions showed that with minor modifications the model could be made to handle the deviant cases. However, at this point it was felt that the predictive power was good enough so that a further expenditure of resources in this direction was not justified.

Sale pricing. In order to test the model, a random sample of 58 sales items was selected from the available records. For each item the appropriate information as determined by the model was used as an input to the computer. The output was in the form of a price that was a prediction of the price that would be set by the buyer. Again we used the criterion that to be correct the predicted price must match the actual price to the penny. Out of the 58 predictions made by the model, 56 (or 96 per cent) were correct.

Mark-downs. In testing this part of the model the basic data were taken from “mark-down slips,” the primary document of this firm. Naturally such slips do not show the information that would enable us to categorize the items for use in the model. It was necessary, therefore, to use direct methods such as the interrogation of the buyer and sales personnel to get the information necessary to classify the items so that the model could be tested. All of the data used were from the previous six-month period. It would be possible on a current basis to get the information that would enable the model to make the classifications itself as part of the pricing process.

The test for a correct prediction was as before — correspondence to the penny of the predicted and the actual price. A total sample of 159 items was selected and predictions made of the mark-down price for each item. Of the 159 prices predicted, 140 were correct predictions by our criterion and 19 were wrong. This gives a record of 88 per cent correct — the poorest of the three models. Though this model does not do as well as the other two, its record is, in our view, adequate.

Source: Skyttner Lars (2006), General Systems Theory: Problems, Perspectives, Practice, Wspc, 2nd Edition.

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