How an Agile Data-Centric Demand Forecasting and Planning Process is So Beneficial in a Disruptive Supply Chain Environment

This is a foundational article about a demand modeling and forecasting approach that supports an agile data-centric demand forecasting and supply planning process Conventional modeling assumptions may no longer work effectively in today’s disruptive supply chain environment, where unusual events and outliers tend to distort demand patterns. Demand forecasting has become a new challenge for demand and supply planning organizations, who need to maintain decision support systems designed with conventional (Gaussian) modeling assumptions.

For example regular and intermittent demand forecasting procedures are used for demand and inventory planning processes in practice, when?

• modeling product mix based on future patterns of demand at the item and store level
• selecting the most appropriate inventory control policy based on type of stocked item
• setting safety stock levels for SKUs at multiple locations

Data Exploration is an Essential Quality Check in the Forecasting Process

Consumer demand-driven historical data, in the retail industry can be characterized to a large extent by trends (e.g., consumer demographics, business cycles) and seasonal patterns (consumer habits: economics). Before making any specific modeling assumptions, demand forecasters and planners should first examine data quality in the context of the new environment along with an exploratory data analysis (EDA) examination of the changing data characteristics and quality in demand history. If you need to achieve greater agility in forecasting for the entire supply chain, this preparatory step can be time consuming initially but is an essential undertaking in the long run,?

Looking for insight into data quality in this spreadsheet, you see that an expected seasonal peak for December 2016 seems to appear in the following month (Jan 2017). Interchanging the December with the January value appears to have a significant impact on the underlying seasonal variation, including uncertainty and other factors (compare ‘before’ in column 2 with ‘after’ in column 3 in the table below).

Also, May 2017 appears unusually weak, but we would call on domain experts to advise the forecaster on that unusual event. In any case, from a preliminary examination into the quality of the data, we see that consumer habit (an economic factor) may constitute about two-thirds of the total variation in the demand history?(befor and after result obtained with a Two-way ANOVA w/o replication algorithm):

First Takeaway:?“Bad data will beat a good forecaster every time” (Paraphrasing W. Edwards Deming)

Embrace Change & Chance by improving data quality through exploratory data analysis (EDA) as a preliminary step essential in creating agility in the demand?forecasting and planning process.

For intermittent demand forecasting, it is important to examine the dependence of the inter-demand intervals on the distribution of non-zero demand sizes. Intermittent demand (also known as sporadic demand) comes about when a product experiences several periods of zero demand. Often in these situations, when demand occurs it is small, and sometimes highly variable in size. In inventory control applications, the level of safety stock depends on the service level you select, on the replenishment lead time as well as the reliability of the forecast.

The widely used Croston methods will under closer scrutiny point to flawed assumptions about the independence of zero intervals and demand volumes. Assumptions about Interval sizes and nonzero demand volumes should be reconciled in practice with real data, not just with simulated data or assumed probability models.

Characterizing intermittent data with a SIB model differs fundamentally from Croston-based methods in that a dependence of interval sizes on demand can be made explicit and can be validated with the new LZI method and can be validated with real data.

The LZI Method For Forecasting with Intermittent Demand

The evidence of the dependence on interval durations for demand size can be explored by examining the frequency distribution of ‘lag time’ durations.?I?define a ”Lag-time” Zero Interval LZI as the zero-interval duration preceding a nonzero demand size. In my previous LinkedIn article on SIB models for intermittent and regular demand forecasting, I focused on measurement error models for forecasting and evaluating intermittent demand volumes based on a dependence of an interval duration distribution.?

A Structured Inference Base (SIB) Model for Lead Time Demand

Step 2. Leadtime Demand Forecasting Needs a Specified Lead-time (Time Horizon) For lead-time demand forecasting with a fixed horizon, a location scale measurement error model can be created for assessing the effectiveness and accuracy of the demand forecasting process. The Profile Forecast Error (FPE) data used in modeling the accuracy and performance of lead-time demand forecast errors can be represented in a SIB model as the output of a measurement model:?FPE = β + σ ?, in which β and σ are unknown parameters, ?and the input ? is a measurement error with a known or assumed non-Gaussian distribution.

Keeping in mind the pervasive presence of outliers and unusual values in today’s real-world forecasting environment, I will henceforth shy away from the conventional normal distribution assumptions. ?Rather, for error distribution assumptions, I will be referring to a flexible family of distributions, known as the Exponential family. This is a rich family of distributions particularly suited for SIB modeling; it contains many familiar distributions including the normal (Gaussian) distribution, as well as distributions with thicker tails and skewness, so much more appropriate in today’s disruptive forecasting environment. These are some of the reasons I regard this article as foundational. However, by following a step-by-step development using a real-world data example and nothing more than arithmetic, some algebra and the logarithm, I hope that you can follow the process.

The SIB modeling approach is algorithmic and data-driven, in contrast to conventional data-generating models with normality assumptions.?The measurement model for Forecast Profile Error = β + σ ? is known as a location scale measurement model because of its structure. The Forecast Profile Error (FPE) model shows that the FPE data result from a translation and scaling of an input measurement error ?. For the three forecasting approaches (judgment, method and model), used as examples, I display the FPE data below.

The forecast profile errors in the spreadsheet are calculated with the formula where a(i)?are the components in the actual alphabet profile (AAP) and f(i) are the components in the forecast alphabet profile (FAP). These have been explained before in several previous articles available on my LinkedIn Profile and the my Delphus website blog.

The sums of the rows can be interpreted as a measure of ignorance about the forecast profile error. The closer to zero the better and the sign indicates over- or under-"forecasting" the profile of actuals. The units are known as ‘nats’ (for natural logarithms).

What Can Be Learned About the Measurement Process given the Forecast Profile Errors and the Observed Data?

Step 3. Setting Up the Model with Real Data

In practice, we have multiple measurements of observed forecast profile errors (over a time horizon m = 12 in the spreadsheet example):

and where ??= {?1, ?2, ?3, . . . ?12} are now 12 realizations of measurement errors from an assumed distribution in the Exponential family.

Step 4. A Critical Data Reduction Step

What information can we uncover about the forecasting?process? Like a detective, we can explore a SIB model and find that, based on the observed data, there is a clue revealed now about the unknown, but realized measurement errors ?. This is evidence that will guide us to the next important SIB modeling step: It points to a decomposition of the measurement error distribution into two components: (1) a marginal distribution for the observed components and (2) a conditional distribution (based on the observed components) for the remaining unknown measurement error distribution, which depends on the parameters β and σ. So, what are these observed components of the error distribution that we uncover?

The insight or essential information is gleaned from the structure of the model and the recorded forecast profile error data. If we now select a suitable location measure m(.), and a scale measure s(.), we can make a calculation that yields important observables about the measurement process for each forecasting technique used. The SIB model shows, with some elementary algebraic manipulations, that the observables can be expressed in equations?like this (using a 12-month lead-time):

That is, the d-vector d = (d1, d2, … , d12) represents the left hand-side and right-hand side equations. Thereby, we can reduce the SIB model to only two equations with two unknown variables m(?) and s(?) that represent the remaining unknown information in the measurement error model

Step 5. Conditioning on What You Know to be True

We do not need to go any further with details at this point.?The conditional distribution (given the known d-vector d = (d1, d2, … , d12) for the variables?m(?) and?s(?) can be derived from the second equation using an assumed distribution for??.

Using the selected location measure m(.), and a scale measure s(.), we can make a calculation that yields important observables about the measurement process for each method or model. If I select m(.) = relative skill measure as the location measure, the calculated?Profile Relative Skills for the three approaches are obtained by summing the values on each row.

The relative skill measures can range over the whole real line, the smaller the score in absolute value the better. The relative skills will always be zero for constant level profiles, like MAVG-12.

The s(.) = Profile Accuracy D(a|f) divergences for the scale measure are found to be

We note that the 12 left-hand?side equations named d(FPE) are equal to the right-hand side equations ?d(?). In the spreadsheet example for the 12 Lead-time demand values for Part #0174, d = d(FPE) = d(?) is shown in the table.?Then d = (d1, d2, … , d12), where we can now calculate

Step 6. Embracing Change and Chance. Deriving Posterior Distributions for the Unknown Parameters β and σ Along with Posterior Prediction Limits and Likelihood Analyses

The derivations and formulae can be found in U of Toronto Professor D.A.S. Fraser’s 1979 book Inference and Linear Models, Chapter 2, and in his peer-reviewed journal articles dealing with statistical inference and likelihood methods. These are not mainstream results in modern statistical literature, but that does not diminish their value in practice.

Statistical inference refers to the theory, methods, and practice of forming judgments about the parameters of a population and the reliability of statistical relationships

These algorithms can be implemented with existing computing algorithms used in a machine learning applications. like MCMC. This was not the case more than four decades ago when I was first exposed to them. With normal (Gaussian) error distribution assumptions, there are closed form solutions (i.e. solvable in a mathematical analysis) that have a semblance to more mainstream Bayesian inference theory.

Step 7. Application to Inventory Planning

The SIB inferential analysis will yield a posterior distribution (conditional on the observed d) for the unknown parameters β and σ from which we can derive unique confidence bounds for β and σ (Forecast Profile Accuracy). These confidence bounds will give us the service levels we require to set desired level of safety stock. In turn, given the actuals and the inherent SIB model structure, the posterior distribution can lead to a probability forecast of the Forecast Profile.

1.??????For the ETS(A,A,M) model and data example, the reduced error distribution for location measure m(?) and scale measure s(?) is conditional on observed d = (d1, d2, … , d12):

·???????Location component:????????????m(?) = [m(FPE) – β]/ σ = [0.001 – β]/ σ

·???????Scale component:??????????????????s(?) = s(FPE)/ σ = 0.044/ σ

2.??????Define “Safety Factor” SF = √12 m(?) /s(?) = √12 {0.001 – β 0}/ 0.044, where β 0 = max β under a selected contour boundary

Then,???β 0 = 0.001 + SF * 0.044 / √12 Is the desired level of safety stock for the service level you select.

Final Takeaway:

A data-driven non-Gaussian SIB modeling approach for lead-time demand forecasting?is based on

• No independence assumptions made on demand size and demand interval distributions
• Non-normal (non-Gaussian) distributions assumed throughout the inference process.
• Using bootstrap resampling (MCMC) from a SIB model if the underlying empirical distributions are to be used
• Deriving posterior lead-time demand distributions with bootstrap sampling techniques
• Determining upper tail percentiles of a lead-time demand distribution from family of exponential distributions for lead-time demands or from empirical distributions

Final Note: Improving Data Quality Through Data Exploration and Visualization Makes for Smarter and More Agile Forecasting.??

I write to help practitioners make their forecasting more agile with effective tools easy to implement. Keep tuned in! If you'd like me to cover a specific topic, get in touch. For instance, I find that in demand forecasting with a predictive data-generating model under normality assumptions, the prediction limits look different in the case of ‘with’ and ‘without’ unusual values or isolated outlier situations and end up with different interpretations of probability limits. This is not generally recognized or taken into consideration by practitioners who believe that there is always, somewhere, a ‘best’ model that should automatically mitigate or compensates for this increase in uncertainty. Many demand planners tend to manipulate model fitting parameters to seek ‘better’ models without first gaining insight into the quality of the data. Forecast modeling without first performing and documenting data cleaning steps first may find out that bad data will beat a good forecaster every time!?

Hans Levenbach, PhD is Owner/CEO of Delphus, Inc and Executive Director,?CPDF Professional Development Training and Certification Programs.

Dr. Hans is the author of a new book (Change&Chance Embraced) on Demand Forecasting in the Supply Chain.

With the endorsement of the International Institute of Forecasters, Hans created the first certification curriculum in demand forecasting and has conducted numerous hands-on Professional Development Workshops for Demand Planners, Managers and SC professionals for multi-national supply chain companies worldwide. Hans is a Past President, Treasurer and former member of the Board of Directors of the?International Institute of Forecasters.

He is Owner/Manager of these LinkedIn groups:

(1)?Demand Forecaster Training and Certification, Blended Learning, Predictive Visualization, and

(2)?New Product Forecasting and Innovation Planning, Cognitive Modeling, Predictive Visualization.

I invite you to join these groups and share your thoughts and practical experiences with intermittent data and demand forecasting performance in the supply chain. Feel free to send me the details of your findings, including the underlying data without identifying proprietary descriptions.