Filtering by Tag: quantiles

Control your service levels, don’t let them control you

Published on by Joannes Vermorel.

In retail, many companies don’t have much control over their service levels. In fact, many companies don’t monitor the service level where it matters the most: the physical store. Indeed, measuring in-store service level is a tedious exercise. Some companies - mostly panelists - specialize in doing this sort of measurements, but the cost is steep as there is no workaround for the extensive manpower involved in the process.

Taking a step back, why do we even need to measure the service level?

Wouldn’t it be more convenient if the service level was something obtained by design and defined through explicit settings within the inventory optimization software? This would certainly be a lot more practical. Service levels certainly don't need to be an afterthought of the inventory optimization process.

It turns out that, historically, the need to measure the service levels came from early inventory optimization methods such as the safety stock analysis that offer about no control on actual service levels. Indeed, the underlying models rely on the assumption that the demand is normally distributed and this assumption is so wrong in practice that most retailers gave up on this assumption in favor of ad-hoc safety stock coefficients.

Those ad-hoc safety stock coefficients are not bad per se: they are certainly better than relying on abusive assumptions about the future demand. However, the quantitative relationship between the safety stock and the service level is lost. Hence, retailers end-up measuring their service levels and tweaking coefficients until inventory stabilizes somehow. At the end, the situation is not satisfying because the inventory strategy is inflexible: safety stock coefficients can’t be changed without exposing the company to a myriad of problems, repeating the tedious empirical adjustments done originally.

However, with the advent of quantile forecasting, it’s now possible to produce forecasts that very accurately drive the service levels, even if the quantile forecasts themselves are not accurate. All it takes is unbiased forecasts, and not perfectly accurate forecasts.

Indeed, quantile forecasts directly and very natively address the problem of producing the reorder quantities it takes to cover target service levels. If a new and better quantile forecasting technology is found, then this technology might be capable of achieving the same service levels with less inventory, but both technologies deliver the service levels they promise by design.

This behavior is very unlike the case of classic forecasting allied to safety stock analysis where an improvement of the accuracy, while being desirable, leads to erratic results in practice. For example, for many low volume products, as observed in stores, shifting to a dumb forecasting model that always returns zero usually improves the accuracy defined as the absolute difference between the actual sales and the forecasted sales. Obviously, shifting toward zero forecasts for half of the products can only end with dismal business results. This example might appears as anecdotal but it is not. Zero forecasts are the most accurate classic forecasts in numerous situations.

Thus, in order to take control of your service levels, it takes an inventory optimization methodology where such a control is built-in.

Categories: Tags: quantiles inventory insights inventory optimization No Comments

New video: introduction to quantile forecasting

Published on by Joannes Vermorel.

Not all forecasting methods are born equal. As far as inventory optimization is concerned, classic forecasting methods tend to make no sense whatsoever. The problem does not lie in the models used to produce the forecasts, or the way those models are tuned; it lies instead in the underlying methodology which misfits the actual business needs of commerce.

Quantile forecasts, in contrast, deeply embrace the commerce viewpoint. In this introductive video, we develop two key insights related to lead time and service level. The video illustrates why those two variables need to be at the core of the forecasting methodology in order to properly address the business needs.

Categories: Tags: quantiles video salescast insights 1 Comment

Prevent dead inventory through “double” quantile forecasts

Published on by Joannes Vermorel.

The stock associated to each SKU is an anticipation of the future. From a more technical viewpoint, the reorder point of the SKU can be seen as a quantile forecast. The quantile indicates the smallest amount of inventory that should be kept to avoid stock-outs with a probability equal to the service level.

While this viewpoint is very powerful, it does not actual says anything about the risk of overstocking, i.e. the risk of creating dead inventory, as only the stock-out side of the problem is directly statistically addressed. Yet, the overstocking risk is important if goods are perishable or if demand for the product can brutally disappear – as it happens in consumer electronics when the next-generation replacement enters the market.

Ex: Let’s consider the case of a western retailer selling, among others, snow chains. The lead time to import the chains is 3 months. The region were the retailer is located is not very cold, and only one winter out of five justify the use of snow chains. For every cold winter, the local demand for snow chains is of 1,000 kits. Now, in this context any quantile forecasts with a service level above 80% suggest to have more than 1,000 kits in stock in order to keep the stock-out probability under 20%. However, if the winter isn’t cold, then the retail will be stuck its entire unsold stock of snow chains, 1,000 kits or more, possibly for years. The reorder point calculated the usual way through quantiles focuses on upward situations with peaks of demand, but does not tell anything about downward situations where demand evaporates.

Yet, the risk of overstock can be managed through quantiles as well, however it requires a second quantile calculation to be performed leveraging a distinct set of values for tau (τ not the service level) and lambda (λ not the lead time).

In the usual situation, we have:

R = Q(τ, λ)


  • R is the reorder point (a number of units)
  • Q is the quantile forecasting model
  • τ is the service level (a percentage)
  • λ is the lead time (a number of days)

As illustrated by the example here above, such a reorder point calculation can lead to large values that do not take into account the financial risk associated with a drop of demand where the company ends up stuck with dead inventory.

In order to handle the risk of overstocking, the formula can be revised with :

R = MIN(Q(τ, λ), Q(τx, λx))


  • τx is maximal acceptable risk of overstocking
  • λx is the applicable timespan to get rid of the inventory

In this case, the usual reorder point gets capped by an alternative quantile calculation.

The parameter τx is used to reflect the acceptable risk of overstock; hence, instead of looking at values at 90% as it done for usual service levels, it’s typically a low percentage, say 10% and below that should be considered.

The parameter λx is used to represent the duration that would put the inventory value at risk because the goods are perishable or obsolescent.

Ex: Let’s consider the case of a grocery store selling tomatoes with a lead time of 2 days. The retailer estimates that within 5 days on the shelf, the tomatoes will have lost 20% of their market value. Thus, the retail decides that the stock of tomatoes should remain sufficiently low so that the probability of not selling the entire stock of tomatoes within 5 days remains less than 10%. Thus, the retailer adopts the second formula the reorder point R with τ=90% and λ=2 days in order to maintain a high availability combined with τx=10% and λx=5 days in order to keep the risk of dead inventory in control.

At present time, Salescast does not natively support a double quantile calculation, however, it’s possible to achieve the same effect by performing two runs with distinct lead time and service level parameters.

Categories: supply chain, technical, tips, insights Tags: quantiles overstock dead inventory inventory No Comments

Spare Parts Inventory Management with Quantile Technology

Published on by Joannes Vermorel.

The management of spare and service parts is as strategically important as it is difficult. In a world where most equipment manufacturers and retailers are operating in fiercely competitive markets, a high service level to the existing customer base is a strategic priority for many players.

Not only does a high spare part availability help build a loyal base of customers, product/equipment companies have also discovered services as an often very profitable and recurring revenue stream that is typically more resilient to economic cycles than equipment sales.

However, managing a spare parts inventory efficiently still poses a huge challenge. Despite a forecasting and inventory planning technology industry that is several decades old, spare parts management has remained a difficult for a number of reasons:

  • Large number of parts: Even smaller equipment manufacturers can easily be confronted with managing more than a hundred thousand spare parts.
  • High service level requirement: Stock outs are often very costly, high to very high service levels are therefore paramount in many industries.
  • Infrequent demand: The demand for spare parts is typically sparse and intermittent, meaning that only very low volumes are required occasionally.

Why standard forecasting technology performs poorly

Unfortunately, the combination of these factors makes standard inventory and forecasting technology ill-suited for spare parts planning. In classic forecasting and inventory planning theory, a forecast is produced by applying models such as moving average, linear regression and Holt Winters and a great deal of attention is given to the forecasting error, which is optimized by measuring MAPE or similar indicators. The transformation into a suggested stock level is done in a second step via classic safety stock analysis.

In the case of sparse time series (also called slow movers: low unit and infrequent sales), this methodology fails. The main issue with forecasting slow movers is that what we are essentially forecasting are zeros. This is intuitively obvious when looking at the demand history of a typical spare parts portfolio on a daily, weekly, or even monthly basis: By far the most frequent data point is zero, which can in some cases make up more than 50% of all recorded data points.

The challenge of forecasting slow movers: Good statistical performance and good inventory practice are not the same.

When applying classic forecasting theory to this type of data set, the best forecast for a slow moving product is by definition a zero. A 'good' forecast from a statistical point of view will return mostly zeros, which is optimal in terms of math, but not useful in terms of inventory optimization.

The classic method completely separates the forecast from replenishment. The problem is, the situation can hardly be improved with a “better” forecast. What actually matters in practice is the accuracy of the resulting inventory level (reorder point ), which is not measured nor optimized.

Changing the vision from Forecast Accuracy to Risk Management

When dealing with slow movers, we believe the right approach is not to approach the problem as a forecasting issue and to try to forecast demand (which is mostly zero). Much rather, the analysis should provide an answer to the question how much inventory is needed in order to insure the desired service level.The whole point of the analysis is not a more accurate demand forecasts, but a better risk analysis. We fundamentally change the vision here.

Determining and optimizing directly the Reorder Point

Quantile forecasts allow the forecasting of the optimal inventory that provides the desired inventory level directly: A bias is introduced on purpose from the start in order to alter the odds of over and under forecasting.

Benchmarks against classic forecasting technology in food, non-food, hardware, luxury and spare parts consistently show that quantile forecasts bring a performance improvement of over 25%, that is either more than 25% less inventory or 25% less stock outs.

In our opinion, by solving the problem of forecasting intermittent and sparse demand in spare parts management, quantile technology not only provides a strong performance increase, but also makes classic forecasts plain obsolete.

Whitepaper spare parts management available for download

Download the whitepaper Spare Parts Inventory Management with Quantile Technology for an in-depth discussion of the topic. Further whitepapers and resources on quantile forecasting and inventory management are available on our resources page

Do you have comments, questions or experiences regarding spare parts management to share? Please participate in the comments below, your contribution is highly valuable to our team.


Categories: Tags: bigdata forecasting quantiles slow movers spare parts whitepaper 1 Comment

Video: Quantile Forecasts - Part 2

Published on by Joannes Vermorel.

Last week, we published the Quantile Forecasts - Part 1 video; here comes the Part 2. In the previous video, we discussed what quantiles were about. In short, it's a new way to look at the inventory optimization mechanism itself.

In Part 2, we provide some non-technical insights why quantile forecasts outperforms classic ones in three usual situations.

Video summary (7min46):

  • High service levels
  • Intermittent demand
  • Spiky demand

Don't hesitate to post questions in comments.

Categories: docs, insights, video Tags: insights quantiles video No Comments

Quantiles = Inventory Optimization 2.0

Published on by Joannes Vermorel.

Quantile Logo Getting more accurate forecasts, that turn into profits, is the No1 priority for Lokad. However, demand forecasting has been extensively researched for more than a half a century, and each 0.1% of extra accuracy is typically nothing less than a uphill battle.

Sometimes though, we make a breakthrough. Today, we are announcing the most significant technology upgrade of Lokad since its launch 6 years ago: the immediate availability of quantile forecasts.

Quantiles are disruptive in the sense that in many situations they make classic forecasts plain obsolete as far inventory optimization is concerned - for retail, wholesale and manufacturing businesses.

We have identified 3 situations where quantiles really shine:

  • High service levels at 90% and above.
  • Intermittent demand (slow mover's).
  • Bulk orders (spiky demand).

In those situations, benchmarks against our own classic forecasting technology indicate that quantile forecasts typically bring either 20% less inventory or 20% less stockouts.

Extraordinary claims require extraordinary evidence. Carl Sagan

However, the many benchmarks that we have made so far with our prospects and clients indicate that our classic forecasting technology is already ahead of the competition; but with quantile forecasts, it's whole new level of inventory optimization that can be achieved.

Don't hesitate to put quantiles to the test.

The story behind the quantile upgrade

Quantile forecasting (also called quantile regression) has been around for decades among academic circles. Then, in finance, analysts have been extensively using quantiles for Value at Risk (VaR) analysis since the late 1980s.

At Lokad, quantiles have been around for a long time as well. For example, back in 2009, Sequential Quantile Prediction of Time Series. IEEE Transactions on Information Theory, March 2011, vol. 57, n°3 has been published by one of us. However, until very recently, quantiles were very mistakenly considered a mathematical distraction (business-wise) rather than a mission critical concept.

What did hold us back was not lacking insights in statistics, but lacking insights in the profound relationship between quantiles and inventory optimization. This insight was triggered, mostly out of dumb luck, when a client did ask us to figure out a formula to compute optimal service levels for her inventory.

A breakthrough yes, but a late one

This quantile breakthrough is only very relative in the sense that quantiles have been already applied successfully for decades in other trades. However, there is one aspect that partially explains this late arrival: quantile models typically require about 10x more processing power compared to classic forecasting models. Without cloud computing, we would not have been able to put quantiles in production, while preserving an aggressive pricing.

Categories: accuracy, release, subscriptions, web services Tags: forecasting quantiles No Comments