Forecasting
THE FIRST STEP FOR DEMAND
PLANNING
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Intro
Vs.
¿Why do I need to forecast demand?
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Intro
–
In Pull processes: Plan for inventory levels and capacity
– In Push processes: Plan for Production & wharehousing,
logistics
In supply chains, forecasting is essential for the
estimation of future demand
It is the first step of a supply chain manager
in order to plan & scale all other activities
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Forecasting basics
Beware of how you use the forecast!!!
Case 1: Sales for next semester
are expected to be between 100
and 1900 units monthly
Case 2: Sales for next semester are
expected to be between 900 and
1100 units monthly
Average expected monthly sales: 1000
However…. Supply chain policies should be
very different
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Forecasting basics
Better short term than long term
Case 1: Ice cream shop forecasting for next week
Case 2: Ice cream shop forecasting for next month or
semester
In general, short-term forecasts are more precise than long
term forecasts, because they use more accurate information
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Forecasting basics
Always easier to aggregate demand (SKU families, geography, etc.)
Case 1: Annual Coca-Cola sales in Uruguay vs Daily Coca-Cola Light sales in
Montevideo
Case 2: Students entering the University in Uruguay in 2022 vs number of
students entering at FIUM in 2022
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Forecasting basics
There is no best system to forecast
Usually, the further up in the value chain, the more distorted the
information
Most planners/managers usually prefer a range of acceptable
values rather than a single value.
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Factors affecting the demand
• Historic demand
• Product lead time
• Marketing campaigns or promotions
• Economic and political issues
• Other competitors
Observed Demand = Systematic component + random component (noise)
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Beware: You have to be skeptical with a forecast
that has no error with respect to the historical
demand!!!
Basic steps
1. Understand the purpose of the forecast
2. Understand the relative importance of forecasting demand in the supply
chains and integrate it into planning
3. Understand and identify the different segments, products, customers
4. Establish the main factors influencing demand
5. Select the most proper technique for forecasting and run the forecast
6. Select and calculate error and performance metrics
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Different methods
Judgmental (Qualitative)
Causal
Subjective, based on human
judgements. Products with little or
no historical information.
Correlation with certain specific factors.
Look for that correlation and estimate
demand from regressions
Time series
Simulation
Historical demand to predict
future demand. Simple methods
that serve for stable products or
as a basis for other methods.
Seeks to mimic consumer
behavior to predict future
scenarios
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Time series definition
• Series of observations over time of some quantity of interest, measured at
constant intervals of time (X1, X2, X3,…)
Daily
Monthly
Bi-annually
Annually
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Possible components of Time-series
Constant Level (L)
Seasonality (S)
Trend (T)
All together
Important: Remember that all observed demand will always have random error
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Basic Notation
Origin: t: when I do the forecast
Time horizon k: for which period I am forecasting
Ft,t+k is the forecast at period t for period t+k:
Ft,t+k = E [Xt+k | Xt, Xt-1, Xt-2,….,X1]
Example:
If t=10, k=4 , then F10,14 is the forecast for t=14 conducted at the end of period t=10 (using
data point until X10): F10,14 = E [X14 | X10, X9, … ,X1]
4
0
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2
4
6
8
10
12
14
16
FORECASTING METHODS FOR A CONSTANT-LEVEL MODEL
• The simplest model to make a forecast using time-series is to assume only a
constant-level model
• Four alternative forecastig methods:
Last-Value Forecast
Averaging Forecast
Moving-Average Forecast
Exponential Smoothing Forecast
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Last Value Forecast (Naïve method)
Model: Xt = Lt + εt
Our model is trying to estimate the Level (L) at time t.
By interpreting t as the current time, the last-value forecasting procedure
uses the value of the time series observed at time t (xt) as the forecast at
time t+1.
Therefore, Ft+1 = xt
It is worth considering when the underlying assumption about the constant-level model is
“shaky” and the process is changing so rapidly that anything before time t is almost
irrelevant or misleading
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Averaging Forecast
Model: Xt = Lt + εt
Our model is trying to estimate the Level (L) at time t.
This method uses all the data points in the time series and simply averages
these points. Thus, the forecast of what the next data point will turn out to be
is:
Ft+1 =
𝑡 𝑥𝑖
𝑖=1 𝑡
This estimate is an excellent one if the process is entirely stable
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Moving Average Forecast
Model: Xt = Lt + εt
Our model is trying to estimate the Level (L) at time t.
This method averages the data for only the last n periods as the forecast for
the next period:
Ft+1 =
𝑥𝑖
𝑡
𝑖=𝑡−𝑛+1 𝑛
The moving-average estimator combines the advantages of the last value and averaging
estimators in that it uses only recent history, and it uses multiple observations
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Exponential Smoothing Forecast
This forecasting method is just a weighted sum of the last observation xt and
the preceding forecast Ft for the period just ended.
Ft+1= αxt + (1-α)Ft
where α(0 ≤ α ≤ 1) is called the smoothing constant
Because of this recursive relationship between Ft+1 and Ft, alternatively Ft+1 can be
expressed as
Ft+1= αxt + α(1-α)xt-1 + α(1-α)2xt-2 + α(1-α)3xt-3 + … + α(1-α)nxt-n
Another alternative form for the exponential smoothing technique is given by:
Ft+1= Ft + α(xt – Ft)
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Exponential smoothing
¿What happens for different values of α?
If α=0 then: Ft+1= Ft
the forecast turns into the averaging forecast method (using all historical data)
If α=1 then: Ft+1= xt
the forecast turns into de Last value method (only considering last data point available)
If 0<α<1 then: Ft+1= αxt + α(1-α)xt-1 + α(1-α)2xt-2 + … + α(1-α)nxt-n
the forecast turns into a smoothing average, considering all data points, but gives less weigth
to older information
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Comparing the four constant level forecasting methods
Consider Ft+1= ΣwiDi with D being the actual demand points
Di
D0
Último valor Promedio total histórica Promedio Móvil (N períodos) Suavizado exponencial
wi
wi
wi
wi
0
1/t
0
D1
0
1/t
0
D2
0
1/t
0
D3
0
1/t
0
…
0
1/t
0 si i<t-N; 1/N si i≥t-N
α(1-α) Dt-i
Dt-2
0
1/t
1/N
α(1-α)2Dt-2
Dt-1
0
1/t
1/N
α(1-α)Dt-1
Dt
1
1/t
1/N
α
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i
INCORPORATING SEASONAL EFFECTS
It is fairly common for a time series to have a seasonal pattern with higher values at
certain times of the year than others. In other words, the level changes according to the
“season” in which we are.
Repetitive pattern appearing every certain periodic cycles, e.g., seasonal months in the
year, seasonal days in the week, hours in the day, etc.
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Example of seasonal effects
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Example of seasonal effects
First, we need to adjust data point to remove the effect of seasonal patterns. To remove
the seasonal effects from the time series shown in Fig. 27.3, each of these average
daily call volumes needs to be divided by the corresponding seasonal factor given in
Table 27.2.
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The General Procedure to forecast using seasonal factors
1. Compute seasonal factors S
2. Adjust each value in the time series using the seasonal factors
3. Select a time series forecasting method
4. Apply this method to the seasonally adjusted time series to obtain a forecast of
the next seasonally adjusted value (or values)
5. Multiply this forecast by the corresponding seasonal factor to obtain a forecast
of the next actual value (without seasonal adjustment).
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Forecast error
Every demand value has an error component.
A good forecast should capture only the systematic part of the demand (and not the error)
The error should be considered within the forecast error, and it is important to measure it to:
o See that the selected method correctly predicts the demand pattern
o Take it into account when calculating risks and contingency plans
E=F-D
The error should be calculated with a term at least equal to the lead time we will have to be
able to solve any problem
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Accuracy and Bias
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Forecast error metrics
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Exercise (constant level)
“La Rinconada” Port
The operational manager of the port terminal of Puerto La Rinconada wants to try different
methods to update the forecasts of grain discharge from ships. You are requested to examine
the moving average (N=3), Last value, and simple exponential smoothing with alpha 0.10
and alpha 0.50. Graph and compare using MAD. Select the most appropriate method.
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Month
Past sales (tons)
September
October
November
December
January
February
March
April
May
180
168
159
175
190
205
180
182
?
Incorporating Linear Trend into Forecasting models
Suppose that the generating process of the observed time series can be represented by
a linear trend superimposed with random fluctuations
General Model: Xi = A + B*i + ε i
Our Forecast should try to estimate A and B as best as possible
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Incorporating Linear Trend into Forecasting models
Modelo Holt’s (double smoothing):
We define Tt+1 as the exponential smoothing estimate of the trend factor B at time t+1, given the
observed values, X1= x1, X2= x2, . . . , Xt= xt.
Given Tt+1, the forecast of the value of the time series at time t+1 (Ft+1) is obtained simply by adding
Tt+1 to the formula for Ft+1
seen for simple exponential smoothing:
Ft+1= xt + (1- )Ft + Tt+1
Then, we could use the following formula in order to update the forecasted trend:
Tt+1= (α(xt-xt-1) + (1- α)(Ft – Ft-1)) + (1- )Tt
0<α<1
0<β<1
This method requires two initial estimates:
• x0= initial estimate of the expected value of the time series (A) if the conditions just prior to
beginning forecasting were to remain unchanged without any trend
• T1 =initial estimate of the trend of the time series (B) just prior to beginning forecasting
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Example (double smoothing)
A manufacturer of music players notes that their demand has been increasing in the last 6
months. It has the following data. You want to forecast your future demand for period 7 using
double exponential smoothing with alpha = 0.1 and beta = 0.2.
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Month
Units sold (miles)
1
8415
2
8732
3
9014
4
9808
5
10413
6
11961
Exercise (double smoothing)
Factory “Blue ducks"
The factory manager for blue ducks wants to forecast the demand for his main product which is
blue duck shaped pop machines. The manager suspects that the latest data reflects a positive
trend in the data. You want to test Holt's method using alpha 0.2 and beta 0.4
.
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Month
Demand (units sold)
1
2
3
4
5
6
7
8
9
10
12
17
20
19
24
21
31
28
36
?
0
