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June 13. 2002

Weighing the Choices

Dimensional weights can help decision makers allocate resources appropriately

By Erik Thomsen

Allocations are an important business function (in both an algorithmic and a human process sense) and can apply forward or backward in time. Looking forward, they typically apply to forecasted measures, such as sales, or budgeted measures, such as marketing dollars. Looking backward, they frequently apply to overhead. They're essential whenever you know more about the high-level facts (such as estimated sales for a store as a whole or planned marketing budget for the company as a whole) than about the details (such as estimated sales for particular SKUs or marketing dollars to spend on particular products).

Allocations require some detail facts from the past, such as sales or output, in combination with some high-level constraint, such as total marketing budget or total overhead, in order to allocate the given total to a detail level as a function of the relative weight played by the corresponding detailed facts in the past.

For most, if not all, organizations, and especially for forward-looking functions such as marketing budgets, the allocation process uses allocation algorithms more as a starting point for discussions between key decision makers rather than as a definitive basis for making the allocations.

One of the most frequently used methods for defining allocation functions is cell-based. Given that most organizations are using dimensional models and that the knowledge that's relevant to an allocation process is most effectively expressed in a dimensional language, it makes sense to leverage that dimensional thinking to create more explicitly dimensional methods for defining allocation rules. You can use these methods for both defining allocation algorithms and debating the weighting functions.

In this column, I'll introduce and compare dimensional-based allocation methods to cell-based methods.

Cell-Based Allocations

Consider the simple example in Table 1 composed of a sales model with three major dimensions: geography, product, and zone. Each dimension has only two members.

Now imagine that the total budget for marketing for 2003 is $100, and the question is how best to allocate the $100 across the eight multidimensional cells (or at least what's a useful starting point for the inevitable negotiations to follow). Assuming, to keep things simple, that you want to allocate next year's total marketing budget as a function of past sales performance, you could define an allocation function such as the following:


ALLOCATED BUDGET , TIME.2003 =
((SALES , TIME.2002) / (SALES , TIME.2002 , GEOGRAPHY.ALL ,
PRODUCT.ALL , ZONE.ALL))
* TOTAL BUDGET , TIME.2003

Applied to 2003, this would result, for example, in a marketing budget for U.S. luxury goods in urban zones of ($100 / $1500) * ($100) = $7.50.

This method is cell-based because the weighting factor for each cell to be calculated is based on the relative weight of a past cell of equivalent dimensionality. For example, the allocation weight for luxury goods in urban zones in the United States in 2003 is calculated from the relative sales for luxury goods in urban zones in the United States in 2002.

Now, let's say that you're responsible for marketing luxury goods in urban zones in the United States and you're convinced that the allocated budget for your area should be much higher. How could you most convincingly argue your case to your very empirically minded boss - given only the data shown in Table 1? What's another kind of method that you could use to calculate allocation weights that would more effectively serve as a basis for empirically arguing for or against particular weighting schemes? Think about it.

Dimension-Specific Weights

Instead of using past cell values as the basis for defining allocation weights, you could use past dimensional ratios, or dimension-specific weights. Statisticians call these marginal frequencies, or probabilities, and have been systematically using them for at least the past 30 years to infer (allocate) cell values based on past cell values and estimated relative margin frequencies.