Most statistical forecasting works in one direct flow from past data to forecast. Forecasting with leading indicators works a different way. A leading indicator is a second variable that may influence the one being forecasted. Applying testable human knowledge about the predictive power in the relationship between these different sets of data will sometimes provide superior accuracy.

Most of the time, a forecast is based solely on the past history of the item being forecast. Let’s assume that the forecaster’s problem is to predict future unit sales of an important product. The process begins with gathering data on the product’s past sales. (Gregory Hartunian shares some practical advice on choosing the best available data in a previous post to the Smart Forecaster.) This data flows into forecasting software, which analyzes the sales record to measure the level of random variability and exploit any predictable aspects, such as trend or regular patterns of seasonal variability. The forecast is based entirely on the past behavior of the item being forecasted. Nothing that might have caused the wiggles and jiggles in the product’s sales graph is explicitly accounted for. This approach is fast, simple, self-contained and scalable, because software can zip through a huge number of forecasts automatically.

But sometimes the forecaster can do better, at the cost of more work. If the forecaster can peer through the fog of randomness and identify a second variable that influences the one being forecasted, a leading indicator, more accurate predictions are possible.

For example, suppose the product is window glass for houses. It may well be that increases or decreases in the number of construction permits for new houses will be reflected in corresponding increases or decreases in the number of sheets of glass ordered several months later. If the forecaster can distill this “lagged” or delayed relationship into an equation, that equation can be used to forecast glass sales several months hence using known values of the leading indicator. This equation is called a “regression equation” and has a form something like:

Sales of glass in 3 months = 210.9 + 26.7 × Number of housing starts this month.

Forecasting software can take the housing start and glass sales data and convert them into such a regression equation.

Graph displaying a relationship between example figures for time-shifted building permits and demand for glass
Leading indicators demonstrated
However, unlike automatic statistical forecasting based on a product’s past sales, forecasting with a leading indicator faces the same problem as the proverbial recipe for rabbit stew: “First catch a rabbit”. Here the forecaster’s subject matter expertise is critical to success. The forecaster must be able to nominate one or more candidates for the job of leading indicator. After this crucial step, based on the forecaster’s knowledge, experience and intuition, then software can be used to verify that there really is a predictive, time-delayed relationship between the candidate leading indicator and the variable to be forecasted.

This verification step is done using a “cross-correlation” analysis. The software essentially takes as input a sequence of values of the variable to be forecasted and another sequence of values of the supposed leading indicator. Then it slides the data from the forecast variable ahead by, successively, one, two, three, etc. time periods. At each slip in time (called a “lag”, because the leading indicator is lagging further and further behind the forecast variable), the software checks for a pattern of association between the two variables. If it finds a pattern that is too strong to be explained as a statistical accident, the forecaster’s hunch is confirmed.

Obviously, forecasting with leading indicators is more work than forecasting using only an item’s own past values. The forecaster has to identify a leading indicator, starting with a list suggested by the forecaster’s subject matter expertise. This is a “hand-crafting” process that is not suited to mass production of forecasts. But it can be a successful approach for a smaller number of important items that are worth the extra effort. The role of forecasting software, such as our SmartForecasts system, is to help the forecaster authenticate the leading indicator and then exploit it.

Thomas Willemain, PhD, co-founded Smart Software and currently serves as Senior Vice President for Research. Dr. Willemain also serves as Professor Emeritus of Industrial and Systems Engineering at Rensselaer Polytechnic Institute and as a member of the research staff at the Center for Computing Sciences, Institute for Defense Analyses.

The destructive impact of Hurricane Sandy has been both staggering and instructive. Our thoughts and best wishes for rapid recovery go out to all who have suffered personal or economic loss or damage. Now, in Sandy’s aftermath, we find ourselves thinking about accelerating recovery and planning for the next unforeseen event.

Our work with clients in the heavily hit mass transit sector presented a sobering view of damaged infrastructure, heavy equipment, and losses of essential inventory. Those most affected have seen a crush of work as inventory managers take stock of what they have, what they need and procure a mountain of replacement parts and products. This uniquely massive replenishment cycle presents all sorts of opportunities and considerations. For those who are still in this phase, and to help our collective preparation for the Next Big Event, here are a few thoughts:

Opportunity to immediately “right size” inventory

You may be in a position to receive a large, one-time infusion of funding for replacement inventory. It could be insurance money, federal relief or rainy day funds from your own treasury. Use the funding to establish the best possible inventory mix. Do not order to previously established Min/Max levels. Doing so may simply repeat excesses and shortfalls of the past.

A major event like Sandy presents a rare opportunity to transform your inventory. Start with an accurate demand forecast over the replenishment period, and generate safety stocks and reorder points that would address your critical needs. This can be accomplished in a matter of hours or days. Ordinarily, implementing optimal inventory levels may occur over several years, as excess inventory is gradually depleted. Now, however, you have a one-time opportunity to jump to the right answer. This shift can substantially reduce replenishment spending, freeing hundreds of thousands of dollars for other, more critical recovery uses.

Prioritize classes to be replenished

Be clear on what you need for crucial operations, and prioritize your replenishment. Which parts have long lead-times, and which are readily available? Obviously short lead-time items can be acquired in stages—getting just enough now, making funds available for the longer lead-time items.

Determine how much is “just enough”

This is where an accurate demand forecast, safety stocks and reorder point calculations come into play. Consider the service level you require—the likelihood that products will be on the shelves when you need them—which is really your tolerance for risk. Do this for each item, or class of items. This will tell you how much safety stock, in addition to your expected lead time forecast, you should have on hand. Iterating on service level-driven requirements will enable you to maximize the value of the replenishment budget at hand.

Statistical forecasting for intermittent demand vs. ‘rule of thumb’ methods

Now is the time to shift from ‘the way we’ve done it’ to the most accurate demand forecasting and inventory optimization process available to you. Greater forecast accuracy requires less safety stock—again, making inventory dollars available for other users. The greatest single category for improvement is intermittent demand. Most organizations do not apply solid statistical methods to this, instead resorting to the “heavy hammer rule”—have lots on hand because no one knows. Here is an area where SmartForecasts is especially adept, with a patented solution for forecasting intermittent demand. The resulting safety stock recommendations hit the service level goal nearly 100% of the time. Getting this right will save lots of spending now, and help minimize the potential for excess, obsolete inventory in the future.

Nelson Hartunian, PhD, co-founded Smart Software, formerly served as President, and currently oversees it as Chairman of the Board. He has, at various times, headed software development, sales and customer service.

Fluctuations in an inventory supply chain are inevitable. Randomness, which can be a source of confusion and frustration, guarantees it. A ship carrying goods from China may be delayed by a storm at sea. A sudden upswing in demand one day can wipe out inventory in a single day, leaving you unable to meet the next day’s demand. Randomness creates frictions that make it hard to do your job.

At first blush, it sometimes seems best to respond to randomness with the ostrich approach: head buried in the sand. You can settle on a prediction and proceed on the assumption that the prediction will always be spot on. The flaw in that approach is that it ignores statistical methods that allow us to make use of a wealth of knowledge about our knowledge itself—how confident we can be in our predictions, and what breadth of possibilities confront us. The efficient approach to tackling the problems that stem from randomness is not to ignore uncertainty, but to embrace it with eyes open.

As a fundamental tenet of Smart Software’s approach to forecasting, we will always provide you with an assessment of the level of uncertainty in forecasts. If you are expecting nothing more than an absolute figure—the demand for widgets in February will be 120 units—you may dismiss the added element of uncertainty as a negative, or lose faith in a forecast you had hoped would be definite. But we argue for what we consider the adult approach; you need to know what you are risking when you commit to a forecast and premise your decision-making upon it.

Your forecasts can have big consequences that go beyond inventory stocking levels. They can determine your raw materials needs or staffing levels—forecasts drive many important resource allocation decisions. If you have too much faith in the most likely outcome, without also specifically considering just how likely it is, you aren’t really understanding the risks you face, and you may put yourself in a precarious position.

The need to make fully informed decisions forces us to see, in a forecast, the plus/minus range of results with a certain likelihood of occurring. In the specific case of forecasts that are going into inventory systems, this is an important part of deliberately planning for contingencies. This is how you determine not only the inventory you need to maintain in order to satisfy typical demand, but also the additional inventory you need on hand to deal with most unexpected outcomes.

This importance only increases when you are trying to maintain a reliable store of critical spare parts. Between the cost of stocking additional inventory, and accounting for the degree of reliability in your forecasts, there is a balance that crystallizes when an airplane that you need in the air is grounded—because you don’t have the replacement for a damaged part.

(While stocking extra inventory relies on the high end of the uncertainty range, if cash flow is tight, it’s the low end of the range that becomes important. Treasury-minded users find value in this other side of uncertainty in scenarios where even minimal overstocking can be more of a problem than a missed sales opportunity, for example. Reliable information about the lowest likely outcomes pays off at this time.)

Inventory theory says that you need to think about the outer ends of likely possibilities and prepare to cope with more scenarios than just what is most likely. Randomness is a reality that can’t be ignored. The average is not the answer.

Thomas Willemain, PhD, co-founded Smart Software and currently serves as Senior Vice President for Research. Dr. Willemain also serves as Professor Emeritus of Industrial and Systems Engineering at Rensselaer Polytechnic Institute and as a member of the research staff at the Center for Computing Sciences, Institute for Defense Analyses.