on the identification of sales forecasting model in the...
TRANSCRIPT
On the identification of sales forecasting model in
the presence of promotions
Juan R. Trapero, Nikolaos Kourentzes, Robert Fildes Journal of Operational Research Society, (2014), Forthcoming
This work was supported by the SAS/IIF research grant
Promotional Support Systems
In “Analysis of judgemental adjustments in the presence of promotions” (Trapero et al., 2013)
we showed that:
• Simple statistical promotional models outperform on average human adjustments
• Not all information of human judgment is captured by simple promotional models
• There is room for improvement with more advanced promotional modelling
These limitations explain the observed reliance on expert adjustments
(Lawrence et al., 2000; Fildes and Goodwin, 2007)
Furthermore:
• There is an apparent gap in the published work (and software) for promotional
support systems for SKU level predictions
• Existing brand level promotional models have limitations:
1. Require extensive model inputs → feasibility and cost considera:ons
2. Complex input variable selection is required → which are the relevant
promotions?
3. Promotions are often multicollinear → difficult to es:mate their impact and get
reliable forecasts
4. These models require past promo:on history → promo:onal forecasts for new
products?
5. These models do not capture the demand dynamics adequately
Case Study
A manufacturing company specialized in household detergent products → data available:
• Shipments
• One-step-ahead system forecasts (SF)
• One-step-ahead adjusted or final forecasts (FF)
• Promotional information:
1. Price cuts
2. Feature advertising
3. Shelf display
4. Product category (22 categories)
5. Customer (2 main customers)
6. Days promoted in each week
The data contains 60 SKUs (all contain promotions)
Data withheld for out-of-sample forecast evaluation
Some products do not contain promotions in the parameterisation (historical) sample
Case Study Example time series
Periods highlighted in grey have some type of promotion
Models Statistical Promotional Model
The proposed promotional model contains the following elements:
• Principal component analysis of promotional inputs: The 26 promotional inputs are
combined a new composite inputs that are no longer multicollinear* → Only a few
new inputs are needed now, simplifying the model.
• Pooled regression: When an SKU does not have promotions in each history, we pool
together information from other SKUs (the product category information is available
to the model) to identify an average promotional effect. When enough promotional
history for an SKU is available we do not pool information from other products
• Dynamics of promotions: Carry-over effects of promotions, after they are finished,
are captured
• Dynamics of the time series: Demand dynamics are modelled for both promotional
and non-promotional periods.
*Two inputs are called multicollinear when it is impossible to distinguish what is the effect of each
individual input on the forecasted demand.
For instance, assuming that we run two promotions running in parallel, resulting in a sales uplift of
+300%, it is impossible to identify the individual impact of each promotion. This is very problematic is it is
possible that the promotions can also run separately.
*Two inputs are called multicollinear when it is impossible to distinguish what is the effect of each
individual input on the forecasted demand.
For instance, assuming that we run two promotions running in parallel, resulting in a sales uplift of
+300%, it is impossible to identify the individual impact of each promotion. This is very problematic is it is
possible that the promotions can also run separately.
Models Benchmarks
A series of benchmark models are used to assess the performance of the proposed
promotional model
• System Forecast (SF): The baseline forecast of the case study company
• Final Forecast (FF): This is the SF adjusted by human experts in the company
• Naïve: A simple benchmark that assumes no structure in the demand data
• Exponential Smoothing (SES): An established benchmark that has been shown to
perform well in supply chain forecasting problems. It cannot capture promotions
• Last Like promotion (LL): This is a SES forecast adjusted by the last observed
promotion. When a promotion occurs the forecast is adjusted by the impact of the
last observed promotion
Note that only FF and LL can capture promotions from our benchmarks
Forecast accuracy under promotions
Case Study Results
Positive adjustments Negative adjustments
High error
Low error
Number of
forecasts
Number of
forecasts
Size of adjustment Size of adjustment
DR: Proposed
Promotional Model
DR: Proposed
Promotional Model
Forecast accuracy under promotions
Case Study Results
High error
Low error
DR is always better
under promotions
DR is always better
under promotions
Human judgment
performs
inconsistently
Human judgment
performs
inconsistently
LL has overall
poor accuracy
LL has overall
poor accuracy
DR is more accurate than human experts and statistical benchmarks in promotional periods DR is more accurate than human experts and statistical benchmarks in promotional periods
Forecast accuracy in non-promotional periods
Case Study Results
High error
Low error
DR is models
accurately carry-
over promotional
effects
DR is models
accurately carry-
over promotional
effects
Human judgment
performs poorly
� No reason for
positive
adjustments?
Human judgment
performs poorly
� No reason for
positive
adjustments?
LL has overall
poor accuracy
LL has overall
poor accuracy
DR accurately captures carry-over promotional effects. SF is marginally better because the
forecasts are based on adjusted historical demand. DR is modelled in raw data.
DR accurately captures carry-over promotional effects. SF is marginally better because the
forecasts are based on adjusted historical demand. DR is modelled in raw data.
DR marginally
worse that SF
DR marginally
worse that SF
Overall forecast accuracy
Case Study Results
High error
Low error
The proposed advanced statistical promotional model captures most of the human expert
information, in a systematic way, producing superior forecasts.
The proposed advanced statistical promotional model captures most of the human expert
information, in a systematic way, producing superior forecasts.
DR provides the
most accurate
forecasts overall
DR provides the
most accurate
forecasts overall
Case Study Results
0.607 0.652 0.762 0.629 0.612 0.601 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
SF FF Naïve SES LL DR
1.069 1.327 1.092 0.904 1.122 0.868 0
0.2
0.4
0.6
0.8
1
1.2
1.4
SF FF Naïve SES LL DR
0.671 0.745 0.808 0.667 0.682 0.638 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
SF FF Naïve SES LL DR
High error
Low error
Overall Promotions No promotions
Be
st
Be
st
Be
st
• Proposed promotional model is consistently
the most accurate
• Substantially outperforms current case study
company practice (FF)
• Major improvements during promotional
periods
• Proposed promotional model is consistently
the most accurate
• Substantially outperforms current case study
company practice (FF)
• Major improvements during promotional
periods
+7.8%
+34.6%
+14.4%
0.0% 10.0% 20.0% 30.0% 40.0%
No promotions
Promotions
Overall
Improvement of DR over FF
Conclusions
1. Proposed statistical promotional model significantly outperform human experts and
statistical benchmarks
2. Company can benefit from increased automation of the forecasting process and reduced
effort of experts to maintain forecasts, while accuracy is increased
3. Can produce promotional forecasts when there is no or limited promotional history for an
SKU
4. Overcomes limitations of previous promotional models
5. Final model is relatively simple
Detailed analysis, findings and references in the paper:
http://kourentzes.com/forecasting/2014/04/19/on-the-identification-of-sales-forecasting-
models-in-the-presence-of-promotions/
Detailed analysis, findings and references in the paper:
http://kourentzes.com/forecasting/2014/04/19/on-the-identification-of-sales-forecasting-
models-in-the-presence-of-promotions/