Spar InfoTech, Inc.

Mathematical Model Comparison

Selecting the model to calculate a baseline, forecast or, analysis of Trade Promotions is the most critical decision. Once a model is selected data will be collected, databases built, reports designed, and people assigned to the project. There are endless models but they fall into three types. Even a unique model will have the traits of one of these three. Here is an explanation of the three, how they should be used, and their strengths and weaknesses.

__Exponential Smoothing__

Exponential Smoothing is the easiest to build, use ,and implement. It uses an average of historical data but weights recent data more heavily. For example if the last 5 periods have values of 1,2,3,4 and 5, a straight average would be 3. But if the first four periods were weighted as zero and the last one 100% the weighted average would be 5. There are variations of smoothing such as double and triple exponential smoothing that allow for a more robust analysis to help consider such factors as trends.

Advantages of Exponential Smoothing:

- The math is easy to understand, the calculations simple, and the model easy to build.
- The computer power and data storage requirements are minimal. No matter how much history exists only the average is stored. When the next data point occurs, a new average is calculated by taking the old average, giving is a weight (e.g. 80%), giving the new data point a weight (e.g. 20%), and calculating a new weighted average.
- There is no limit to the number of items that can be processed using exponential smoothing due to the simplicity of the calculations and the minimal storage.
- Having a lot of historical data or causal factors is not necessary and a new forecast can be generated with as little as one data point.

Disadvantages of Exponential Smoothing:

- All historical data is lost.
- No ability to quantify the impact of various conditions (e.g. Trade Promotions) on sales.
- For products impacted by outside events (e.g. Trade Promotions) the projections can be inaccurate.

__Univariate Analysis__

A Univariate analysis considers the variables one by one in an order selected by the user. It is easy to explain and the math is straightforward. It quantifies some measures such as seasonality and trend. A common approach is to calculate seasonality by adding together all the same periods for a number of years (e.g. all the January’s, all the February’s) and de-seasonalize the data. The de-seasoned data is then analyzed to determine the impact of marketing factors such as trade promotion with the difference between the de-seasonalized sales in promoted periods compared against the sales in non-promoted periods.

Advantages of Univariate Analysis:

- Relatively easy to explain.
- The model is easy to build.
- Rarely has processing or logic errors since the model follows set rules.

Disadvantages of Univariate Analysis:

- The order of the variables impacts the results for each variable. In some cases, this is not a problem but in other cases, it can lead to incorrect results. If the only factors impacting sales are seasonality and trade promotions, the de-seasonalized data prior to calculating the impact of a promotion on sales, will give a different answer then if the results of the trade promotion are first calculated and then the seasonality is calculated after backing out the impact of the Trade Promotions.
- Historical data must be maintained and new items cannot easily be quantified.
- There needs to be a minimum amount of history to operate effectively. Usually 2 years of data is required to get a meaningful measure of seasonality.

**Multi-variate analysis**

A multi-variate analysis calculates all the variables simultaneously. This is the most accurate method to do an analysis of Trade Promotions since the order of the variables does not impact the answer. A well-known multi-variate analysis is multiple regression where all the variables are calculated simultaneously. Since all variables are calculated simultaneously new variables can be added or old variables dropped if they are not having an impact. This type of model will allow for the calculation of the impact of different conditions such as Trade Promotions, Price Increases, Seasonality, and Trend. Because of the work involved to have a multi-variate analysis, the payoff for a more accurate analysis must justify the extra cost.

Advantages of Multi-variate models:

- Quantifies the impact of known variables.
- Is the most accurate.
- Allows the user to run simulations changing the impact of different marketing factors and use them to forecast sales.

Disadvantage of Multi-variate analysis:

- Hard to understand how it works and explain to users. Since the underlining math of multi-variate models is a matrix inversion, the user has to accept the mathematics or spend the necessary time to learn how a matrix inversion works.
- Information on all the factors to be quantified by the analysis needs to be maintained in a historical database.
- Skilled model builders and users are needed to build, run, maintain and interpret the results. This is something many Companies don’t have or don’t wish to invest in.

Conclusion: There are many factors that impact the type of model to be used. Choosing the wrong model will result in failure since it will be unworkable or the results too inaccurate. A manufacturer of thousands of SKU’s where demand doesn’t vary can use an exponential smoothing model since it is easily developed and the inaccuracy can be offset by added safety stock. A good example is forecasting 1000’s of SKU’s for a manufacturer of nuts, bolts and screws. Forecasting is quick and items can be easily added even with one period of sales. Errors can be dealt with by increasing the safety stock and the cost of a mistake is minor. Univariate models are best when seasonality is a factor and tens of thousands of items are processed routinely so that the model must run under set logic without creating any need for user input. Companies processing tens of thousands of scanner-level SKU’s such as A.C. Nielsen and IRI will run a Univariate Model. The multivariate analysis is most useful when the value of accurate information is high. Since the skill to handle this type of model is high, it is only used by some Government Departments or large companies that spend hundreds of millions on Trade Promotions as the value of accurate answers more than compensates for the cost of the analysis and the maintenance of the database.