INTRODUCTION
In this report, the final state of the systems design project, performed in Procter &
Gamble, is explained. Starting from October 2008, the project group BigM has analyzed the
current problematic situation in the sponsoring firm for the first three months. By the end of
January 2009; the group started to generate alternative ways to solve the problem.
The problematic situation can be explained as the inaccurate weekly forecasting
occurred during the pricing periods due to the unexpected purchasing behaviour of the
customers, briefly.
This report consists of the following parts:
First the sponsoring firm and the current forecasting system is explained. By the
guidance of the current system analysis, the problem formulation is given in order to clarify
the problematic situation. After giving the formulated problem; alternative solution
approaches and models are given. The results obtained by using these models are given right
after the explanation of models. These results are compared in order to find the best solution.
This report shows the last frame of the work done. It is a good reference to compare
the previous situation and the new offered situation for the forecasting process in Procter &
Gamble. The detailed explanation of each step in the project process is explained in detail on
the following pages.
FIRM INTRODUCTION
Procter & Gamble Turkey is one of the biggest companies in Turkey, which is
operating in the fast moving consumer goods industry. P&G Turkey has six main categories
of products and under these categories 24 brands and 973 SKU (stock keeping units). These
main categories are; laundry care, P&G beauty, baby care, men care, small appliances and
batteries.
P&G Turkey has six main categories of products and under these categories 24 brands
and 973 SKU (stock keeping units)*. The project given to METU Project Team is about the
case whenever there is a price change in the market; monthly forecasts cannot be splitted
accurately into the weeks and SKU level. This issue is explained below in detail. In the
context of the project, the project team specifically focused on Hair Care Category due to
being affected by pricing activities dramatically and being in a very competitive market. The
main competitors and their respective shares in the market are shown in Appendix (Graph A).
Under the Hair Care Category, 2 main brands: Pantene and Blendax are taken under
consideration. There are several reasons for this selection. First; hair care category is one of
categories which is most sensitive to change in P&G’s shelf prices or competitors prices.
Secondly; these two brands are the brands which have the highest volume in total hair care
category sales. Thus, if the analyses are done on these brands, they can be easily expanded to
the other categories or other brands. Under these two brands there were 75 stock keeping units
to be analyzed.
CURRENT SITUATION
Current Forecasting Process
Main relevant process of demand planning is forecasting by considering different
dynamics as market size, past shipment data, reflecting marketing activities and pricing
effect.
Forecasting process starts with the initial statistical forecasting. Main input of this
statistical forecasting is past shipment data. Actualized past three years shipment values are
taken as input of statistical forecast. For making statistical forecast, GDF (Global Demand
planning Foundation) is used. GDF (Global Demand planning Foundation) is a tool of SAP
that uses different kind of profiles like seasonality, trend, stationary, etc. By fitting
appropriate profile for past three years shipment values, GDF produces monthly and SKU
(stock keeping unit) based forecast for 18-month horizon. As a result of the GDF (Global
Demand planning Foundation) output, 18-month statistical pure forecast is obtained for each
SKU.
Statistical forecasting is the first step of the forecasting process. After making
statistical forecasting, adjustments are made on the statistical forecast. Adjustments on the
forecasts are made by the category team. Category team includes demand planner of the
category, MS&P (Market & Strategic Planner), CMK (Consumer Marketing Knowledge) and
the financier from the Finance Department. Before making adjustments on statistical
forecasts, monthly and SKU based forecasts are aggregated to brand based in order to reflect
marketing activities, pricing activities and other activities on brand level. Then, adjustment
activity is made by considering the market information as stock amount, pricing activities,
promotion activities etc. At this point, P&G makes a significant assumption that all the
market activities have the same impact on every SKU. For example, increase in the price
level of Blendax brand is assumed to affect all the SKUs of Blendax. After making
adjustments, forecasts are firmed and sent to the General Manager. If the General Manager
approves the adjusted forecast, this adjusted forecast is taken as final forecast and sent to
European P&G General Office. This final forecast includes 18-month brand based forecast
and updated every month by rolling the horizon. In the figure below, summary of the current
monthly forecast process can be seen.
Figure-1: Current monthly forecast process.
The next step of forecasting process is splitting the monthly brand based forecasts into
weeks and SKU (stock keeping unit) level. Category Demand Planner is responsible for this
step of forecasting process. Firstly, weekly split will be explained. After statistical forecasts
are adjusted, monthly brand based forecast is distributed into weeks of the month. If P&G
does not consider any activity, weekly splitting for Hair Care Category is assumed to be
approximately equally distributed. However, if any activity, especially pricing activity, is
considered, then weekly split of the brand based monthly forecast is changed. Weekly split is
not anymore approximately equally distributed. If an activity like pricing occurs, splitting of
brand based monthly forecast is done by looking the past weekly splits when similar pricing
activity occurred. There are mainly three types of pricing activities: Price ups, price cuts and
temporary price reductions (TPR). These types of pricing activities are applied generally on
brand base. For instance, if P&G decides to make pricing activity, it includes all Pantene
products or Blendax products. Price cuts and temporary price reductions are applied abruptly
- without informing the customers i.e. distributors and National Accounts. In contrast to price
cut and temporary price reduction, buyers are informed before P&G makes price up activity.
Exactly one month before, all buyers i.e. distributors, National Accounts (Migros, Kipa, Real,
etc...) and retailers located under the distributor in the supply chain know that price up
activity is going to be done one month later. At this point during pricing periods, the demand
planner tries to estimate the consumers tendencies based on the pricing type. Basically,
demand planner checks the past weekly splits of the time when the similar pricing activity
was applied, then sets the weekly split values of the month. As a result, weekly brand based
forecast is obtained. The process of splitting the monthly forecast to weekly forecast can be
seen in figure-2.
Figure-2: Splitting monthly forecast to weekly forecast
Secondly, SKU split is explained. After, monthly brand base forecast is distributed
into weeks of that month; weekly brand based forecast has to be split into SKU (stock
keeping unit) of that brand. This SKU splitting is done by using statistical forecasting tool,
GDF (Global Demand Foundation). GDF gives SKU (stock keeping unit) based monthly
forecast. Demand Planner uses the ratio of each SKU over brand from the monthly forecast of
GDF. Then, she finds the weekly SKU splits by multiplying weekly split value and the ratios
found from GDF. The process of splitting weekly forecast to stock keeping unit is
summarized in Figure-3, below.
Figure-3: Splitting weekly forecast to stock keeping unit
This process can be easily seen from the example provided below.
Example: For January 2008,
1) Demand Planner enters the each SKU’s shipment values of 3 years period (2005-
2008) to GDF.
2) Obtain 18 month SKU (A1, A2 and A3 SKUs) based monthly forecast from GDF.
 Total of 50 kg
A1 = 15 kg A2 = 25 kg
A3 = 10 kg
SKU split from GDF:
s1 = 15/50 = %30
s2 = 25/50 = %50
3) Demand Planner aggregates SKU to brand.
A1, A2 and A3 SKUs  Brand A
A = 50 kg
s3 = 10/50 = %20
4) Adjustments  Demand Planner (MS&P and CMK)
Adjustment factor of %20  %20 increase in the quantity demanded
Brand A
After adjustments A = 50*1,2 = 60 kg
5) Weekly splits  Demand Planner
1st week : %10
 W1 = 60*0,1 = 6 kg
2nd week : %20  W2 = 60* 0,2 = 12 kg
3rd week : %30
 W3 = 60 * 0,3 = 18 kg
4th week : %40
 W4 = 60 * 0,4 = 24 kg
6) Finally, weekly splits of brand are disaggregated into weekly SKU splits by using
SKU split from GDF (found in part 2) and Demand Planner obtains the final forecast
value.
1st week : W1 = 60*0,1 = 6 kg
For SKU of A1, 1st week’s forecast 
s1 * W1 = 0,3 * 6 = 1,8 kg
For SKU of A2, 1st week’s forecast 
s2 * W1 = 0,5 * 6 = 3 kg
For SKU of A3, 1st week’s forecast 
s3 * W1 = 0,2 * 6 = 1,2 kg
2nd week : W2 = 60* 0,2 = 12 kg
For SKU of A1, 2nd week’s forecast 
s1 * W2 = 0,3 * 12 = 3,6 kg
For SKU of A2, 2nd week’s forecast 
s2 * W2 = 0,5 * 12 = 6 kg
For SKU of A3, 2nd week’s forecast 
s3 * W2 = 0,2 * 12 = 2,4 kg
3rd week : W3 = 60 * 0,3 = 18 kg
For SKU of A1, 3rd week’s forecast 
s1 * W3 = 0,3 * 18 = 5,4 kg
For SKU of A2, 3rd week’s forecast 
s2 * W3 = 0,5 * 18 = 9 kg
For SKU of A3, 3rd week’s forecast 
s3 * W3 = 0,2 * 18 = 3,6 kg
4th week : W4 = 60 * 0,4 = 24 kg
For SKU of A1, 4th week’s forecast 
s1 * W4 = 0,3 * 24 = 7,2 kg
For SKU of A2, 4th week’s forecast 
s2 * W4 = 0,5 * 24 = 12 kg
For SKU of A3, 4th week’s forecast 
s3 * W4 = 0,2 * 24 = 4,8 kg
By the way, it is noted that the reason why demand planner aggregate the SKU based
statistical forecast to brand level before making adjustment is that pricing and promotion
activities are done on brand based. As a result, demand planner aggregates the SKU forecast to
brand level to be able to adjust forecasts and then again split forecasts into SKU level.
At this point, BigM team try to imply systematic model to split aggregate adjusted
monthly forecast into SKU (stock keeping unit) and weekly.
Problem Situation and Formulation:
Throughout spring and fall semester, it is observed that P&G Turkey Demand
Manager complain is that P&G Turkey has very high weekly SKU (stock keeping unit) based
APE (Absolute Percentage Error) values and high weekly brand based WAPE (Weighted
Absolute Percentage Error) values during pricing periods. This value shows the error between
the weekly SKU based forecast value and the actual shipment of this SKU for this week. High
WAPE values cause P&G Turkey to mislead the supply chain and production plans are
dramatically affected. In addition to this, stock-out situations and high inventories can occur.
High weekly SKU APE (Absolute Percentage Error) values and high weekly brand WAPE
(Weighted Absolute percentage Error) are first symptoms we faced.
The relevant processes and their steps are explained above. The main interest of
system is splitting step of forecasting process. After statistical forecasts are obtained and
adjustments are made on these statistical forecasts, monthly brand level forecast is occurred.
This forecast is accepted as given and fixed; the splitting of this monthly brand level forecast
into weeks of that month and then splitting into stock keeping unit is defined as target. The
main problem is non-accurate forecast during pricing periods sourced from customers’
unpredictable fluctuating demand. As a result, the problem is stated that there is not decision
mechanism can be evaluated to make weekly split and then SKU split. The figure below
shows the situation clearly:
Weekly SKU based WAPE
values are out-of- target.
Symptom
WHY ?
Weekly split is not done
accurately.
WHY ?
Pricing effect can not be
reflected to weekly splitting
WHY ?
There are not decision criteria
that can be used in the weekly
splitting.
Problem
Figure-4: Problem formulation
MODELLING APPROACH
The forecasting system involves two stages as it is stated in the current system part.
Firstly, monthly brand based forecasts is splitted into weeks. After splitting it into weeks,
weekly based brand forecast is gained. At the second stage, weekly based brand forecast is
splitted into stock keeping units (SKU) of that brand.
In the modeling approach, three different approaches are used to make weekly forecast,
Regression models, mathematical model with the objection of forecast error minimization and
time-series methods. Firstly, models used for the weekly split stage are explained and then
models used for the SKU split stage is explained.
Models Used for the Weekly Split Stage
Regression Model:
The major aim to use regression models is to find the major factors that affect the
weekly and SKU splits. By using the regression model, these factors are determined,
quantified and used to make better and accurate forecasts.
At the first stage, four regression models are used for splitting monthly brand based
forecasts into weeks. Each of regression models represents each week of the month.
Dependent variable of the regression model is shipment value of week that is desired to
forecast.
Additionally, independent variables such as prices, shipment values of prior weeks
and the cost of living index are used in model. Also price indexes are used in order to
evaluate both price of P&G product and the price of its competitor’s product at the same time.
Price indexes represent the price of related product versus the price of competitor’s product.
Price index is expressed in terms of percentage values for months. It is calculated by the
division of price of the related product to price of the competitor’s product.
Cost of living index is expressed monthly based in terms of percentage values. Cost of living
is the cost of maintaining a certain standard of living. Cost of living index is also expressed
monthly.
Product prices are directly taken from the P&G. Product prices are the selling price of the
product from National accounts and retailers to consumers, namely these are shelf prices.
Shipment values represent the actual amount that is shipped from P&G to the distributor.
However, there is a significant issue that based on P&G time schedule, some months has 5
weeks and some have 4 weeks that is, some weeks are divided between two months. For
instance, week-5 is divided between January and February, 2008, four days of week-5 belong
to January and the remaining three days belong to February. Also shipment values are also
divided between these two months by considering the fact that week-5 is divided between two
months. For those months, shipment values are normalized.
Normalization of Shipment Values
Since some months have four weeks and other months have five weeks, months with five
weeks are adjusted to get each month with four weeks to be able to use regression model. The
example presented below will give information about how the problem handled with this
situation.
Jan 2008
Shipment values
# days in week
week1
week2
week3
week4
week5
19.08
34.65
158.97
54.49
37.69
6
7
7
7
4
Table-1: Weekly Shipment of Blendax in Jan 2008
Feb 2008
Shipment values
# days in week
week5
week6
week7
week8
week9
13.59
35.68
82.48
31.72
66.07
3
7
7
7
5
Table-2: Weekly Shipment of Blendax in Feb 2008
In these tables above, the shipment values and number of days in each week are given.
As seen, week-5 is included in both months. Firstly, four days of week-5 in Jan 2008 is put
into the fourth week on that month. As a result, it is computed for week-4 in Jan 2008 as 11
days with shipment value of 37.68779 + 54.65522 = 92.17685. (This shipment value is for 11
days.) By multiplying it with (7/11), last week shipment value of January is got for 7 days.
The same procedure is followed for the first week of the February that shipment value of
week-5 with three days into week-6 is taken and then multiplying it by (7/10), in order to get
shipment value of first week of February with 7 days. The resulting table is as follows:
Jan 2008
Shipment values
# days in week
week1
week2
week3
week4
19.08
34.65
158.97
58.66
6
7
7
7
Table-3: Weekly Shipment of Blendax in Jan 2008(adjusted)
Feb 2008
week6
Shipment values
week7
week8
week9
34.49
82.48
31.73
66.08
7
7
7
5
# days in week
Table-4: Weekly Shipment of Blendax in Feb 2008 (adjusted)
Regression Equations
Month 1
Month 2
WEEKS
-2
-1
0
1
2
3
4
Blendax Regression Equations for Determining the Weekly Splits
For the Blendax brand, significant factors that affect the weekly split are determined.
After that, appropriate functional from that will give the highest R^2 values is found.
According to this procedure, the regression models are set for weekly split of Blendax is as
follows:
For the first week of the month;
Shipment value of week(1) = β0 + β1 * shipment value of week(0) + β2 * shipment value of
week(-2) + β3 * price index + β4 * cost of living index
For the second week of the month;
LOG(Shipment value of week(2)) = β1 * LOG(shipment value of week(1)) + β2 * LOG(price
index) + β3 * LOG(cost of living index)
For the third week of the month;
LOG(Shipment value of week(3))
=
β0 * LOG(shipment value of week(2)) + β1 *
LOG(shipment value of week(1)) + β2 * LOG(price index)
For the fourth week of the month;
LOG(Shipment value of week(4)) = β0 + β1 * LOG(shipment value of week(3)) + β2 *
LOG(cost of living index) + β3 * LOG(ELIDOR)
As seen in the formulations, weekly previous shipment data for Blendax brand,
monthly cost of living index, competitor price, Blendax own price and monthly price index are
used. In the firm, Blendax and Elidor are seen as substitutes. Blendax is P&G product and
Elidor is Unilever product. These two brands are competitors of each other. Therefore, while
using regression model, the price index value of Blendax versus Elidor are used. Weekly
shipment Blendax data is taken from Shipment file and put together all SKUs’ of Blendax and
their weekly shipment values that Blendax from 2007 January to 2008 December is available
for the model. Cost of living index are taken from the website of Turkish Central Bank. Price
index values are taken from pricing file supported by P&G that presents weighted shelf prices,
weighted net prices of P&G and competitors’ brand monthly. By dividing the price of Blendax
to price of Elidor, price index is found.
Pantene Regression Equations for Determining the Weekly Splits
According to the procedure followed for Blendax, the regression models are set for
weekly split of Pantene is as follows:
For the first week of the month;
Shipment value of week(1) = β0 + β1 * shipment value of week(0) + β3 * price index + β4 *
cost of living index
For the second week of the month;
Shipment value of week(2) = β0 + β1 * shipment value of week(1) + β2 * shipment value of
week(0) + β3 * shipment value of week(-1) + β4 * PANTENE + β5 * cost of living index
For the third week of the month;
LOG(Shipment value of week(3)) = β0 + β1 * LOG(shipment value of week(2)) + β3 *
LOG(price index)
For the fourth week of the month;
LOG(Shipment value of week(4)) = β0 + β1 * LOG(shipment value of week(3)) + β2 *
LOG(cost of living index)
In the above calculations, weekly previous shipment data for Pantene brand, monthly
cost of living index, Pantene own price, competitor price and monthly price index are used.
After evaluating the different functional forms, the equations stated above are obtained. Model
approach for weekly split stage can be summarized in Figure-5, below.
Inputs
Shipment values of weeks
Price change
Cost of living index
Four Regression Models
(Each of them is for each
week of specified month)
Coefficient of independent variables
(i.e. coefficient of shipment values of prior weeks, coefficient of
price change, coefficient of cost of living index)
By using regression model
Weekly shipment value of dependent variable
(
(i.e. shipment value of specified week)
Figure-5: Model Approach for Weekly Split Stage
This picture is generated for every four regression model, for every week of specified
month. There is one more step, normalization step that is used. In normalization step by
considering monthly brand forecast, normalization is made on the weekly brand shipment,
output of regression model, and final weekly brand shipment forecasts is got. At this point, it is
assumed that monthly forecasts are close to realized shipments values. Actually, it is examined
this relation by using graphs and see that these two values are close to each other. The graphs
can be seen in Appendix B.
These all models and explanations are for weekly splitting stage. There is also one
more stage to handle with. The second stage, splitting weekly brand based forecast into SKUs
of that brand is made. Firstly, the SKUs are splitted into groups based on ABC analysis. An
ABC classification is performed for the products of brands Blendax and Pantene. The aim in
this is to observe the critical SKU’s (stock keeping units). The main criteria used in ABC
analysis is the shipment volume of the products. According to the shares of each SKU’s
shipment volume in the total shipment volume of the related brand; the SKUs which has the
highest share are classified as Category A, second group is classified as Category B and the
rest is called Category C.
For Blendax, there appears to be 9 SKU’s in Category A, 9 SKU’s in Category B and
15 SKU’s in Category C. Category A consists of the 78% of the whole volume, Category B
consists 16% of the whole volume and Category C consists 6% of the whole volume.
For Pantene, there appears to be 14 SKU’s in Category A, 10 SKU’s in Category B and
18 SKU’s in Category C. Category A consists of the 81% of the whole volume, Category B
consists 12% of the whole volume and Category C consists 7% of the whole volume.
For every brand, Category A includes only 750 ml products. This is as expected since
these products –products with 750 ml volume- are the most consumed products in the market.
Mathematical Model:
The main reason to use mathematical model - link network model - is to reflect
different dynamics as semantic factors on forecast. The model includes weekly shipment data,
price index of competitors for related products and living index to minimize total weekly
forecast error. By using the model, the target is to quantify coefficients for each week and
make better, accurate forecasts.
In this model, four different mathematical models should be run for each brand in order
to support the lag among weeks. For the current week’s (week 1) forecast of any brand; the
inputs should be the shipment data of week 0, week -1, week -2, price of related product & its
competitor, price index and living index. These inputs’ logarithmic and sin(pi) functions are
used in the model to estimate the coefficient of these factors. The reason of this is to reduce the
variance in the data used in the models.
For every brand, first the 10-base logarithmic function is used for each data set. After
calculating the 10-base logarithmic values; a forecast result is obtained by multiplying these
values with the constants which are obtained by running the model; i.e. the decision variables
are the constants of the inputs. By using these obtained forecasts; the errors between the
relevant weeks’ shipment values are calculated. The sum of square errors is calculated as the
objective function. The common constraint in the model is the distinction between the prices
and the price indices. If the price of a SKU and its main competitor is used, then the
coefficient of the price index is set as zero; or vice versa. For different iterations; the
coefficient of past weeks’ shipment values are set to zero respectively; i.e. for the first iteration
only the closest weeks’ coefficient takes a value, for the second iteration the closest two
weeks’ coefficients take values and for the third iteration, all of the past three weeks’
coefficient take values. The aim on this is to observe the effect of previous weeks. Generally
the best results are obtained by using all of the past three weeks’ shipment data.
The same procedure expressed above is applied with only the change in the function.
This time, in addition to the logarithmic function, the obtained 10-base logarithmic values are
used in the formula Sin(pi*x), where x’s are the parameters. The rest of the procedure is the
same with the previous one; and this procedure again iterated by giving zero coefficients for
different weeks. Mathematical model forecasting procedure is displayed in Figure-6.
Figure-6: Mathematical Model Forecasting
Models Used for the SKU Split Stage
After conducting brand based weekly split analysis, several SKU split models are
implemented. Firstly, time series forecasting model is executed. Since the problem is to forecast
shipment with respect to changing price, inserting price into single variable time series models
causes some trouble. In order to give place to price in time series models, shipment/price ratios
are taken for each SKU. By this way two variables (shipment and price) are reduced into one
variable (ratio). Time series forecasts are designed for this ratio, in other words ratio forecasts
are carried out rather than shipment forecasts. After getting ratio forecasts for this time series
analysis, these ratio forecasts are multiplied by the SKU’s price which becomes clear for the
beginning month. Then weekly SKU shipment forecasts are found by this way.
Example is provided as follows:
Suppose one of the SKUs of Blendax has the following shipment and price data for
hypothetical month:
Blendax SKU
Week 1
Week 2
Week 3
Week 4
Actual Shipment 5
6
8
10
Price
2
2
2
2
Shipment/Price ratios are found as follows for this SKU:
Blendax SKU
Week 1
Week 2
Week 3
Week 4
Shipment/Price
2,5
3
4
5
Suppose above calculation is done for 2 years and Shipment/Price ratios are found for 2
years. Then time series forecasting is implemented by using these ratios with trying several
fitted models such as moving average, exponential smoothing or double exponential
smoothing. According to models’ MAPE (Mean Absolute Percentage Error) values, best fitted
model is chosen and this model’s forecast values are taken into account.
Suppose following ratio forecasts are generated after choosing appropriate model for
next month:
Blendax SKU
Week 1
Week 2
Week 3
Week 4
Shipment/Price
3
3,5
4
2
And the beginning month’s SKU price is 3. By multiplying this price with above ratio
values, following forecast shipment scheme is generated for this SKU:
Blendax SKU
Week 1
Week 2
Week 3
Week 4
Shipment
9
10,5
12
6
Forecast
By comparing these forecast values with actual shipments, MAPEs of forecasts are
found. This result is shown in the results and findings part. Secondly, regression model is used
for weekly SKU splits. At this point there are two alternatives, namely, implementing
regression analysis in SKU level or using brand based forecasts and GDF splits for each SKU.
In former analysis, two A classified SKU is taken and conducted regression analysis. For this
analysis each week’s shipment values are taken. Months which have 5 weeks are reduced into
4 weeks by normalization similar with brand based regression analysis but this time SKU
shipments are taken into account. Also price, costs of living, competitors’ price are taken into
account. As brand based regression analysis, in order to find each week’s forecasts week’s
actual shipment value is taken as dependent variable and preceded 3 week’s shipment values,
cost of living and competitor’s price are taken as independent variables.
For example for Blendax Antidant 750 ml, the following regression models are applied:
Log(w1)= log (w0)+ log (price)+ log (costofliving)
w2 = constant + w1 +w(-1)+ price + log(costof living)
w3 = price + w 2 + w1 + w0
w4 = constant + w3+w1 + costofliving
Pantene Basic Norm 750 ml, the following regression models are applied:
w1 = w(-1) + elidor price1 + costofliving
w2 = w1 + w0 + price + costofliving
w3 = constant + w2 + price + costof living
w4 = w3 + w2 + w1
The regression model for SKU level seems to be obsolete for the following reasons:
 lack of data for SKU shipment
 variance is so high in shipment data2
 the significance levels in the model do not meet specifications
 R square is low
 zero values in dependent variable restrict regression implementation
Although these reasons hinder regression model implementation, regression models are
constructed for above SKUs and MAPE values are calculated. For these reasons second
alternative which is multiplying GDF SKU weekly splits with brand based regression weekly
splits is conducted. For this alternative brand based weekly split forecasts are taken and
multiplied with GDF’s SKU splits. After getting weekly SKU based split forecasts, they are
compared with actual SKU shipments and MAPEs are calculated3 and it is found that this
method is better than SKU based regression model when MAPEs are compared.
For example hypothetical brand based weekly split depend on regression is as follows:
Brand
Week 1
Week 2
Week 3
Week 4
Weekly Split
20%
20%
30%
30%
1
For Pantene, Elidor is considered as competitor.
2 Graphs for two SKUs’ shipment variance are provided in Appendix C.
3 Detailed analysis is conducted in results part.
And suppose this brand consists of 5 SKUs. Hypothetical GDF output for SKU splits is as follows:
SKU
Week 1
Week 2
Week 3
Week 4
SKU-1
10%
12%
15%
8%
SKU-2
10%
12%
20%
17%
SKU-3
20%
36%
15%
26%
SKU-4
25%
24%
25%
19%
SKU-5
35%
16%
25%
30%
So the brand based weekly SKU splits are as follows4:
SKU
Week 1
Week 2
Week 3
Week 4
SKU-1
2% (20%*10%)
2,4%
4,5%
2,4%
SKU-2
2% (20%*10%)
2,4%
6%
5,1%
SKU-3
4% (20%*20%)
7,2%
4,5%
7,8%
SKU-4
5% (25%*20%)
4,8%
7,5%
5,7%
SKU-5
7% (35%*20%)
3,2%
7,5%
9%
4
Detailed SKU forecast analysis is given in results part.
The flow chart in Figure-7 shows the general solution approach.
Mathematical
Model Split for
each week (%)
Regression
Model Split
for each week
(%)
Time Series
(Q/P) Method
Split for each
week (%)
Multiplying with
Monthly Adjusted
Brand based
Forecast
Week1
forecast at
brand level
Week2
forecast at
brand level
Week3
forecast at
brand level
Weekly forecast at brand level
Multiplying with
weekly adjusted
brand based
forecast
GDF split for
each sku
(%)
Weekly
forecast at sku
level
Weekly
forecast at sku
level
Week4
forecast at
brand level
Weekly
forecast at sku
level
Figure-7: Solution Approach
VALIDATION/VERIFICATION OF THE MODEL
Verification of the Model
In model verification, it is tried to understand that the model is structured and specified
properly and does not contain an error internally. For the verification phase, different cases and
conditions are specified and entered to the model.
Firstly, factors that affect the actual shipment of the first week of the month for Blendax
brand are directly analyzed and their coefficients are obtained. For each factor,
Dependent Variable: W1
Variable
Coefficient
C
43.25385
0.083763
PINDEX
Dependent Variable: W1
Variable
Coefficient
C
86.73699
0.007162
LIVING
By looking the sign of the coefficients, price index and cost of living have negative relation
with the weekly shipment. This is a very meaningful result because increase in price or cost of living
directly decreases the consumer’s purchasing power. Therefore, weekly shipment value is
decreasing.
After that, regression model is constructed for determining how much to ship in the first
week of the month for Blendax brand. Using different functional forms, following models are found.
Shipment value of week(1) = β0 + β1 * shipment value of week(0) + β2 * shipment value of week(2) + β3 * price index + β4 * cost of living index
(Eq1)
Dependent Variable: W1
Variable
Coefficient
C
W0
W_2
LIVING
PINDEX
155.8097
0.153890
0.179655
-0.011595
-0.475914
LOG(Shipment value of week(1)) = β0 + β1*LOG(shipment value of week(0)) + β2*
LOG(shipment value of week(-2)) + β3 * LOG(price index) + β4 * LOG(cost of living index)
(Eq2)
Dependent Variable: LOG(W1)
Variable
C
LOG(W0)
LOG(W_2)
LOG(LIVING)
LOG(PINDEX)
Coefficie
nt
28.16742
0.160295
0.090479
2.337356
1.031377
Eq1 and Eq2 are the models with the same factors but different functional forms. However,
sign of the coefficients are same with each other in the equations. Also, sign of the coefficients are
similar with the individual regression models. Since model exactly reflects the real life situation and
internally appropriate, regression model is verified.
Validation of the Model
The project given to METU Project Team is that whenever there is a price change in the
market, monthly forecast cannot be accurately splitted into weeks and SKU level.
In the context of the project, Hair Care Category is selected as target due to being affected by
pricing activities dramatically and being in very competitive market. Under the Hair Care Category,
2 main brands are selected: Pantene and Blendax with 75 stock keeping units. Regression Model,
Mathematical Model and time series method is run for Pantene and Blendax brand for its stock
keeping units. The constraints in model; past shipment data, competitor and related brand prices,
price index and living cost are found relevant and sufficient dynamics for the model by the firm.
When the outputs of the models compared with Procter & Gamble forecasts by subtracting from
actual shipments regression model gives better error than current forecasting system. The numeric
comparisons and graphs could be found in the results and comparisons part. Besides the better
forecast results, the model provides easy and systematical way to reach forecasts. Additionally, the
firm could add new data and reach next term forecasts by running the model.
MODEL RESULTS, FINDINGS, COMPARISONS AND SUGGESTIONS
As explained above, three different types of model are suggested for weekly split and SKU
split stages. These models are regression model, mathematical model with the objection of error
minimization and time series forecasting method. At this part, results of each model, our findings
and comparisons of each model with the current system are served. Firstly, these three models we
stated above is used for splitting monthly brand basis forecast into weeks. This is done for two
brands: Blendax and Pantene. The results of models are as follows:
For Blendax:
Model
Time Series (Q/P)
Regression Log-Model Sin(Pi(Log))-Model EXPO (η=0,4)
MAPE
42.14
43.09
55.64
51.65
P&G Forecast
MA(5)
52.87
51.84
The comparison of models is done on the basis of MAPE (Mean Absolute Percentage Error).
MAPE is calculated by averaging the absolute error of each week. As seen on the table, the
regression model gives the best result in terms of MAPE. Current system mean absolute percentage
error is 51,84. The improvement we get by using regression model is ((51,84-42,14)/51,84)*100 = %
18,7. As a result, it is concluded that regression model should be used in splitting monthly brand
basis forecast into weeks. Below, absolute percentage values are shown for Regression model and
P&G forecast for weeks of 2008 in Graph-1. (January 2008 to November 2008).
300
Absolute Percentage Error (%)
250
200
150
REGRESSION
P&G Forecast
100
50
Weeks 2008
%0
1
3
5
7
9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43
Graph-1: Absolute percentage values for Regression model and P&G forecast for weeks of 2008 for
Blendax brand.
The graph-2 below shows the actual shipment values, forecasted shipment values generated
from regression model and currently used P&G forecasts values.
160
140
120
100
ACTUAL
80
REGRESSION
P&G Forecast
60
40
20
MSU
0
Weeks 2008
1
3
5
7
9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45
Graph-2: Comparison of actual shipment, regression and P&G forecasts for Blendax brand.
For Pantene:
Model
Regression Log-Model
MAPE
33.52
36.04
Times Series (Q/P)
sin ∏ log
MA(1)
Expo(0.9)
82.87
60.24
54.17
P&G
Forecast
68.81
The comparison of models is done on the basis of MAPE (Mean Absolute Percentage Error).
MAPE is calculated by averaging the absolute error of each week. As seen on the table, the
regression model gives the best result in terms of MAPE. Current system mean absolute percentage
error is 68,81. The improvement we get by using regression model is ((68,81-33,5)/68,81)*100 =
% 51,3. As a result, it is concluded that regression model should be used in splitting monthly brand
basis forecast into weeks. Below in graph-3, absolute percentage values are shown for Regression
model and P&G forecast for weeks of 2008. (January 2008 to November 2008).
400
Absolute Percentage Error (%)
350
300
250
Regression
200
P&G P&G
150
100
50
%
0
1
3
5
7
9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43
Weeks 2008
Graph-3: Absolute percentage values for Regression model and P&G for Pantene.
The graph-4 below shows the actual shipment values, forecasted shipment values generated
from regression model and currently used P&G forecasts values.
300
250
200
Actual
150
Regression
P&G
100
50
MSU
0
Weeks 2008
1
3
5
7
9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43
Graph-4: Comparison of actual shipment, regression and P&G forecasts for Pantene.
Secondly, we get forecast error results for SKUs of each brand. We follow three main
approaches for this stage. The first approach is getting SKU forecasts by multiplying weekly brand
basis forecast, obtained from models we used in weekly split stage, with the GDF SKU split values.
The second approach is to use regression model for each SKU. The third one is to use time series
(Q/P). All of these approaches are explained before. The related results are shown for A class SKUs
in Blendax and Pantene brand.
For Blendax A class SKUs:
Blendax
A class SKUs
SKU-1
SKU-2
SKU-3
SKU-4
SKU-5
SKU-6
SKU-7
SKU-8
REG-Model
58.34
43.83
55.83
47.23
43.24
42.64
53.82
53.17
MAPE (Mean Absolute Percentage Error)
P&G Forecast
Q/P Time Series
Sin(Pi(log))-Model
90.49
269
66.89
59.92
107
42.83
56.54
77.84
70.13
55.22
260
59.27
61.87
68.8
50.54
56.71
72.2
51.20
58.11
134
57.75
52.47
122
61.43
From the table above, for A class SKUs of the Blendax, the results obtained by multiplying
the weekly brand basis forecast value with the GDF split values are better than the current forecasts
of the firm for seven SKUs. It is noted that the output of regression model is selected to be
multiplied with the GDF SKU split values. The regression output (brand basis weekly forecast) is
used due to having lowest MAPE values in the weekly split stage. Below in Graph-5, weekly
absolute percentage error of SKU-12 of Blendax is shown. It is noted that SKU-12 is one of the SKU
of Blendax having high sales volume.
300
Absolute Percentage Error (%) for SKU-12
250
200
Regression APE
150
Current APE
100
50
%
0
1 2 3 4 5 6 7 8 9 10111213141516171819202122232425262728293031323334
Weeks 2008
Graph-4: Weekly absolute percentage error of SKU-12 of Blendax.
The graph-5 below shows the actual shipment of SKU-12, current shipment forecasts and
shipment forecasts generated from the model we set.
30
Actual vs. Forecasted Shipments
25
20
Model forecast
15
Actual shipments
Current forecast
10
5
MSU
0
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29 31 33 35
Weeks 2008
Graph-5: The actual shipment of SKU-12, current shipment forecasts and shipment forecasts.
For Pantene A class SKUs:
Pantene
A class SKUs
MAPE (Mean Absolute Percentage Error)
Reg-Model
P&G
Log-Model
SKU-1
SKU-2
SKU-3
SKU-4
SKU-5
SKU-6
SKU-7
112.26
105.05
36.41
44.78
88.32
54.69
49.53
103.41
118.30
64.96
71.73
69.70
73.07
86.48
118.78
103.67
38.08
47.31
89.52
55.27
51.42
From the table above, for A class SKUs of the Pantene, the results obtained by multiplying
the weekly brand basis forecast value with the GDF split values are better than the current forecasts
of the firm for five SKUs. It is noted that the output of regression model is selected to be multiplied
with the GDF SKU split values. The regression output (brand basis weekly forecast) is used due to
having lowest MAPE values in the weekly split stage. Time series (Q/P) methods are also tried for
these seven SKUs of Pantene. However, results of this method are not good. As a result we skip this
method. Below in graph-6, weekly absolute percentage error of SKU-6 of Pantene is shown. It is
noted that SKU-6 is one of the SKU of Pantene having high sales volume.
450
Absolute Percentage Error (%)
400
350
300
250
Reg-model
200
Current system
150
100
50
%
0
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29 31 33 35
Graph-6: Weekly absolute percentage error of SKU-6 of Pantene.
Weeks 2008
Graph-7, below shows the actual shipment of SKU-6, current shipment forecasts and
shipment forecasts generated from the model we set.
100
Actual vs. Forecasted Shipments
90
80
70
60
Model forecasts
50
Current forecasts
40
Actual shipments
30
20
10
MSU
0
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29 31 33 35 37 39
Weeks 2008
Graph-7: The actual shipment of SKU-6, current shipment forecasts and shipment forecasts
One of our solution approaches to SKU split stage is to use regression model for each SKUs.
However, due to having some limitations we stated before, we decide not to use this approach.
Although we decide not to use this approach, we try this approach to one of SKUs of Blendax and
Pantene. The results of this approach are as follows:
For one of the A class SKU of Blendax:
The graph-8 below shows the actual shipment values of one of the A class Blendax SKU and
forecasted shipment generated from SKU regression.
40
35
30
25
Actual
20
Forecast
15
Weeks
10
MSU
5
0
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55
Graph-8: Actual shipment values of Blendax SKU and SKU regression forecast.
MAPE (Mean Absolute Percentage Error)
SKU Regression
Reg-Model
Current System
865.55
42.14
51.84
As seen on the table above, MAPE value of SKU regression is very high. However, by using
regression model used in the weekly split stage and then by multiplying its output with the GDF
split, we get lowest MAPE value.
For one of the A class SKU of Pantene:
The graph-9 below shows the actual shipment values of one of the A class Blendax SKU and
forecasted shipment generated from SKU regression.
30
Actual vs. Forecasted Shipments
25
20
Actual
15
Forecast
10
5
MSU
Weeks 2008
0
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55
Graph-9: Actual shipment values of Pantene SKU and SKU regression forecast.
MAPE (Mean Absolute Percentage Error)
Reg-Model
SKU regression
Current System
33.51
62.10
68.81
As seen from the table above, although SKU regression gives better MAPE value for this A
class SKU than the current system, it is still worse than the output generated from multiplying the
regression weekly forecast with the GDF SKU split. It has 33.51% MAPE value.
One another measure we use is WAPE (weighted absolute percentage error) for SKU
forecast. WAPE is calculated as follows:
  SHP
n
WAPE 
i
* APEi 
i 1
n
 SHP
i
i 1
In this formula, SHP is the shipment value and APE is the absolute percentage error.
By weighting each SKUs’ absolute percentage error with the shipment amount of each SKU,
WAPE is obtained. For Blendax, WAPE of each week is shown on the graph-10, below.
300
Weighted Absolute Percentage Error for Blendax (%)
250
200
Model WAPE
150
Current WAPE
100
50
%
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
Weeks 2008
Graph-10: WAPE values of P&G’s current system and model constructed for Blendax.
It is noted that we use absolute percentage errors generated from regression model while
calculating WAPE measure. We use regression model due to having lowest MAPE value. Only
during June and July, WAPE measure of regression model worse than the current system WAPE
value.
For Pantene, WAPE of each week is shown on the graph-11, below.
400
Weighted Absolute Percentage Error for Blendax (%)
350
300
250
Model WAPE
200
Current System WAPE
150
100
50
%
0
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29 31 33
Weeks 2008
Graph-11: WAPE values of P&G’s current system and model constructed for Pantene.
It is noted that we use absolute percentage errors generated from regression model
while calculating WAPE measure. We use regression model due to having lowest MAPE
value. Only during July, WAPE measure of regression model worse than the current system
WAPE value.
7.) JUSTFY – serhat
CONCLUSION
In the spring semester final report, project team has explained the relevant processes,
the problem situation of the system and also specified the system in order to clarify problem
definition. After that, three different modeling approaches –regression model, mathematical
model, time-series method- is expressed with their formulations and charts. Moreover the
verification and validation analysis are made to support the reliability of the models. Finally,
the outputs of the related models are exhibited and compared with current forecasting method
in order to proof the best model as regression model. The accurate model gives the lower
mean absolute percentage error than the other ones that is generally gives closest numbers to
the target percentage error level. In conclusion, the benefits from the new model approach are
expressed basically.
APPENDIX C
Actual shipments of Blendax ShamCond Basic Norm 750 ml:
MSU
30
Actual Shipments
25
20
15
Actual shipments
10
5
0
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55
Weeks 2008
Actual shipments of Pantene Antidand 750 ml:
MSU
40
Actual Shipments
35
30
25
20
Actual Shipments
15
10
5
0
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53
Weeks 2008
APPENDIX B
Monthly actual shipment and monthly forecast for Blendax
300000
250000
200000
150000
100000
Forecast
Shipment
50000
0
Monthly forecast and monthly forecast for Pantene
600
500
400
300
forecast
shipment
200
100
May 06
June 06
Jul 06
Aug 06
Sep 06
Oct 06
Nov 06
Dec 06
Jan 07
Feb 07
Mar 07
Apr 07
May 07
Jun 07
Jul 07
Aug 07
Sep 07
Oct 07
Nov 07
Dec 07
Jan 08
Feb 08
Mar 08
Apr 08
May 08
Jun 08
Jul 08
Aug 08
0
APPENDIX A
Hair Care Category
Graph-A: Hair care category market share in Turkey for the period from 2006 to 2008.