Last week we considered how techniques first used in NASA helped retailers plan their inventory. This week we are going to get behind the man and his thinking in a bit more detail.
Rudolf E. Kalman, a graduate research professor emeritus at the University of Florida and ad personam chair at the Swiss Federal Institute of Technology in Zurich is considered the most influential researcher in the field of control and systems theory.
During the 1960s, he was the leader in the development of a rigorous theory of control systems. Among his many outstanding contributions were the formulation and study of most fundamental state-space notions (including controllability, observability, minimality, realisability from input/output data, matrix Riccati equations, linear-quadratic control, and the separation principle) that are today ubiquitous in control.
He is best known for the linear filtering technique that he developed in the years 1959-1961 to strip unwanted noise out of a stream of data. The Kalman filter is widely used in navigational and guidance systems, radar tracking, sonar ranging, and satellite orbit determination (as we saw last week at NASA for the Apollo and other missions, for instance), as well as in fields as diverse as seismic data processing, nuclear power plant instrumentation, and econometrics.
The Kalman filter, which is based on the use of state-space techniques and recursive algorithms, revolutionized the field of estimation and forecasting and while some of these concepts were also encountered in other contexts, such as optimal control theory, it was Kalman who recognized the central role that they play in systems analysis.
During the 1970s Kalman also played a major role in the introduction of algebraic and geometric techniques in the study of linear and nonlinear control systems. His work since the 1980s has focused on a system-theoretic approach to the foundations of statistics, econometric modeling, and identification as a natural complement to his earlier studies of minimality and realisability."
In simple terms Kalman filtering addresses an age-old question: How do you get accurate information out of inaccurate data? More pressingly, How do you update a "best" estimate for the state of a system as new, but still inaccurate, data pour in? The Kalman filter applies a sophisticated algorithm designed to strip unwanted noise out of a stream of data. Strangely this “noise” could be as diverse as unusual inventory movements.
As we saw it should come as no surprise that recently the Kalman filter has proven to have a major contribution to planning some lines of inventory allowing retailers to optimize their stocking levels and subsequently significantly reduce inventory.
Not only is the filter able to remove the noise caused for example by a mother buying 12 pink shorts for her daughter’s netball team but is able to manage in an environment of large amounts of data.
The pink short purchase is an aberration or noise and tends to disturb the normal pattern of sales. This purchase would lead to stock model inaccuracies from the typically unsophisticated planning methods currently deployed such as Moving Average.
Kalman filtering also has a way to link the sales over time such that it effectively uses each new observation to update a probability distribution with no need ever to refer back to any earlier observations.
This has the interesting implication to planning in retail where there are typically large data sets. Once the Kalman filter has been tuned with some initial data it does no more work for the millionth estimate than it does for the first. The net result is an algorithm tailored to applications, where data keeps coming in and decisions have to be made quickly.
It is easy to see why Retail Planning with Kalman filtering is at forefront of modern inventory management but there are even more techniques emerging that augment this filter to more precisely allow for patterns such as seasonality. The latest filters apply routines that some clever Chinese guys applied to robotic vision, but more of this next week.
I say, till next week, bring on the Summer and bring on the shorts!
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