Inventory management, customer trends, and averaging.

The application of averages ( weighted experience ) as the means of forecasting assumes that there are no known causal/predictor/support/ auxiliary/helping/input series/factors.

ARIMA models apply averaging methods. Robust ARIMA models detect and incorporate factors assignable to special cause e.g Pulses , Seasonal Pulses , Level Shifts and/or Local Time Trends.

ARIMA models then are weighted averages where

. The optimal number of periods is determined ( i.e. the length of the smooth )

AND

. the weights to use for each point in the smoothing process.

For example

y(t) = .7*y(t-1)+ .1 *y(t-1) + .2*y(t-12) has a length of 12 and weights of

.7 , .1 , 0. , 0. , 0. , 0. , 0. , .0 , .0 , 0. , 0. and .2

Statistical pattern recognition as incorporated by AUTOBOX et al form these equations BASED on the statistical characteristics of each series .

These tools are being used world-wide to optimize inventory management.

Often there is a sparse demand or intermittent time series that requires different approaches. We have implemented a procedure to deal with cases where there are two random variables ..

1. the time between orders and
2. the actual order count

Hope this helps ..

Dave Reilly Automatic Forecasting Systems

A question about modeling, and what is being modeled here -

I'm sure that I don't understand the reasoning that says, about the titles whose checkout is nearest to the average, "This is an important two percent." The "average" here is far greater than the median -- the distribution must have a long tail, whose extreme (and then, the mean) could depend on how many copies you have available of the

I can see why you would be interested in the two percent that account for 80% (say) of the rentals, or about the 30% that are checked out less than once a month (or whatever).

Is this number, the mean, taken as an arbitrary cutoff for action?

One thing to be careful of. Make sure you distinguish averaging over title and averaging over item. The reason I say this is if you have

Leon Tribe

Hello Mr. Ulrich,

I'll attempt to clarify, the purpose is to determine what genres of Videos, and DVDs i.e., topics of inventory need to be reassessed; inventory which has too often been overlooked, by getting lost in the shuffle, of day-to-day business. Simple averaging (not the mean of values) may help in reassessing inventory.

The two percent is important, as two percent is key; the percentage of titles (the terms “titles” and “items” are used interchangeably) meet the .40 to .50 average times per week criteria. And with over thirty different categories, six different categories (SEE: The findings of categories needing extra attention in original post) showed up predominantly in the survey.

Again, the averaging techniques are only intended as one (a rough measure at that) of many methods in assessing inventory (the sum of the whole is greater than its parts).

Hello Mr. Tribe,

The terms "titles and items" are the same. It is not necessary to account for multiple copies in the survey; as we have found these titles have the roughly the same popularity. The purpose here is to assess inventory that we have often found to be overlooked.