Operations Management “Forecasting” Hardianto Iridiastadi, Ph.D.
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Operations Management“Forecasting”
Hardianto Iridiastadi, Ph.D.
•Demand Management•Qualitative Forecasting
Methods•Simple & Weighted Moving
Average Forecasts•Exponential Smoothing•Simple Linear Regression•Web-Based Forecasting
OBJECTIVES
Demand Management
A
B(4) C(2)
D(2) E(1) D(3) F(2)
Dependent Demand:Raw Materials, Component parts,Sub-assemblies, etc.
Independent Demand:Finished Goods
Independent Demand: What a firm can do to manage it?
• Can take an active role to influence demand
• Can take a passive role and simply respond to demand
Types of Forecasts
• Qualitative (Judgmental)
• Quantitative– Time Series Analysis– Causal Relationships– Simulation
Components of Demand
• Average demand for a period of time
• Trend• Seasonal element• Cyclical elements• Random variation• Autocorrelation
Finding Components of Demand
1 2 3 4
x
x xx
xx
x xx
xx x x x
xxxxxx x x
xx
x x xx
xx
xx
x
xx
xx
xx
xx
xx
xx
x
x
Year
Sal
es
Seasonal variationSeasonal variation
Linear
Trend
Linear
Trend
Qualitative Methods
Grass Roots
Market Research
Panel Consensus
Executive Judgment
Historical analogy
Delphi Method
Qualitative
Methods
Delphi Method
l. Choose the experts to participate representing a variety of knowledgeable people in different areas
2. Through a questionnaire (or E-mail), obtain forecasts (and any premises or qualifications for the forecasts) from all participants
3. Summarize the results and redistribute them to the participants along with appropriate new questions
4. Summarize again, refining forecasts and conditions, and again develop new questions
5. Repeat Step 4 as necessary and distribute the final results to all participants
Time Series Analysis
• Time series forecasting models try to predict the future based on past data
• You can pick models based on:1. Time horizon to forecast2. Data availability3. Accuracy required4. Size of forecasting budget5. Availability of qualified personnel
Simple Moving Average Formula
F = A + A + A +...+A
ntt-1 t-2 t-3 t-nF =
A + A + A +...+A
ntt-1 t-2 t-3 t-n
• The simple moving average model assumes an average is a good estimator of future behavior
• The formula for the simple moving average is:
Ft = Forecast for the coming period N = Number of periods to be averagedA t-1 = Actual occurrence in the past period for up to “n” periods
Simple Moving Average Problem (1)
Week Demand1 6502 6783 7204 7855 8596 9207 8508 7589 892
10 92011 78912 844
F = A + A + A +...+A
ntt-1 t-2 t-3 t-nF =
A + A + A +...+A
ntt-1 t-2 t-3 t-n
Question: What are the 3-week and 6-week moving average forecasts for demand?
Assume you only have 3 weeks and 6 weeks of actual demand data for the respective forecasts
Question: What are the 3-week and 6-week moving average forecasts for demand?
Assume you only have 3 weeks and 6 weeks of actual demand data for the respective forecasts
Week Demand 3-Week 6-Week1 6502 6783 7204 785 682.675 859 727.676 920 788.007 850 854.67 768.678 758 876.33 802.009 892 842.67 815.33
10 920 833.33 844.0011 789 856.67 866.5012 844 867.00 854.83
F4=(650+678+720)/3
=682.67F7=(650+678+720 +785+859+920)/6
=768.67
Calculating the moving averages gives us:13
500
600
700
800
900
1000
1 2 3 4 5 6 7 8 9 10 11 12
Week
Dem
and
Demand
3-Week
6-Week
Plotting the moving averages and comparing them shows how the lines smooth out to reveal the overall upward trend in this example
Plotting the moving averages and comparing them shows how the lines smooth out to reveal the overall upward trend in this example
Note how the 3-Week is smoother than the Demand, and 6-Week is even smoother
Note how the 3-Week is smoother than the Demand, and 6-Week is even smoother
Simple Moving Average Problem (2) Data
Week Demand1 8202 7753 6804 6555 6206 6007 575
Question: What is the 3 week moving average forecast for this data?
Assume you only have 3 weeks and 5 weeks of actual demand data for the respective forecasts
Question: What is the 3 week moving average forecast for this data?
Assume you only have 3 weeks and 5 weeks of actual demand data for the respective forecasts
Simple Moving Average Problem (2) Solution
Week Demand 3-Week 5-Week1 8202 7753 6804 655 758.335 620 703.336 600 651.67 710.007 575 625.00 666.00
F4=(820+775+680)/3
=758.33F6=(820+775+680 +655+620)/5 =710.00
Weighted Moving Average Formula
F = w A + w A + w A +...+w At 1 t-1 2 t-2 3 t-3 n t-nF = w A + w A + w A +...+w At 1 t-1 2 t-2 3 t-3 n t-n
w = 1ii=1
n
w = 1ii=1
n
While the moving average formula implies an equal weight being placed on each value that is being averaged, the weighted moving average permits an unequal weighting on prior time periods
While the moving average formula implies an equal weight being placed on each value that is being averaged, the weighted moving average permits an unequal weighting on prior time periods
wt = weight given to time period “t” occurrence (weights must add to one)
wt = weight given to time period “t” occurrence (weights must add to one)
The formula for the moving average is:The formula for the moving average is:
Weighted Moving Average Problem (1) Data
Weights: t-1 .5t-2 .3t-3 .2
Week Demand1 6502 6783 7204
Question: Given the weekly demand and weights, what is the forecast for the 4th period or Week 4?
Question: Given the weekly demand and weights, what is the forecast for the 4th period or Week 4?
Note that the weights place more emphasis on the most recent data, that is time period “t-1”
Note that the weights place more emphasis on the most recent data, that is time period “t-1”
Weighted Moving Average Problem (1) Solution
Week Demand Forecast1 6502 6783 7204 693.4
F4 = 0.5(720)+0.3(678)+0.2(650)=693.4
Weighted Moving Average Problem
(2) Data
Weights: t-1 .7t-2 .2t-3 .1
Week Demand1 8202 7753 6804 655
Question: Given the weekly demand information and weights, what is the weighted moving average forecast of the 5th period or week?
Question: Given the weekly demand information and weights, what is the weighted moving average forecast of the 5th period or week?
Weighted Moving Average Problem (2) Solution
Week Demand Forecast1 8202 7753 6804 6555 672
F5 = (0.1)(755)+(0.2)(680)+(0.7)(655)= 672
Exponential Smoothing Model
• Premise: The most recent observations might have the highest predictive value
• Therefore, we should give more weight to the more recent time periods when forecasting
Ft = Ft-1 + (At-1 - Ft-1)Ft = Ft-1 + (At-1 - Ft-1)
constant smoothing Alpha
period epast t tim in the occurance ActualA
period past time 1in alueForecast vF
period t timecoming for the lueForcast vaF
:Where
1-t
1-t
t
Exponential Smoothing Problem (1) Data
Week Demand1 8202 7753 6804 6555 7506 8027 7988 6899 775
10
Question: Given the weekly demand data, what are the exponential smoothing forecasts for periods 2-10 using =0.10 and =0.60?
Assume F1=D1
Question: Given the weekly demand data, what are the exponential smoothing forecasts for periods 2-10 using =0.10 and =0.60?
Assume F1=D1
Week Demand 0.1 0.61 820 820.00 820.002 775 820.00 820.003 680 815.50 793.004 655 801.95 725.205 750 787.26 683.086 802 783.53 723.237 798 785.38 770.498 689 786.64 787.009 775 776.88 728.20
10 776.69 756.28
Answer: The respective alphas columns denote the forecast values. Note that you can only forecast one time period into the future.
Answer: The respective alphas columns denote the forecast values. Note that you can only forecast one time period into the future.
Exponential Smoothing Problem (1) Plotting
500
600
700
800
900
1 2 3 4 5 6 7 8 9 10
Week
Dem
and
Demand
0.1
0.6
Note how that the smaller alpha results in a smoother line in this example
Note how that the smaller alpha results in a smoother line in this example
Exponential Smoothing Problem (2) Data
Question: What are the exponential smoothing forecasts for periods 2-5 using a =0.5?
Assume F1=D1
Question: What are the exponential smoothing forecasts for periods 2-5 using a =0.5?
Assume F1=D1
Week Demand1 8202 7753 6804 6555
Exponential Smoothing Problem (2) Solution
Week Demand 0.51 820 820.002 775 820.003 680 797.504 655 738.755 696.88
F1=820+(0.5)(820-820)=820 F3=820+(0.5)(775-820)=797.75
The MAD Statistic to Determine Forecasting Error
MAD = A - F
n
t tt=1
n
MAD =
A - F
n
t tt=1
n
1 MAD 0.8 standard deviation
1 standard deviation 1.25 MAD
• The ideal MAD is zero which would mean there is no forecasting error
• The larger the MAD, the less accurate the resulting model
MAD Problem Data
Month Sales Forecast1 220 n/a2 250 2553 210 2054 300 3205 325 315
Question: What is the MAD value given the forecast values in the table below?
Question: What is the MAD value given the forecast values in the table below?
MAD Problem Solution
MAD = A - F
n=
40
4= 10
t tt=1
n
MAD =
A - F
n=
40
4= 10
t tt=1
n
Month Sales Forecast Abs Error1 220 n/a2 250 255 53 210 205 54 300 320 205 325 315 10
40
Note that by itself, the MAD only lets us know the mean error in a set of forecasts
Note that by itself, the MAD only lets us know the mean error in a set of forecasts
Tracking Signal Formula
• The Tracking Signal or TS is a measure that indicates whether the forecast average is keeping pace with any genuine upward or downward changes in demand.
• Depending on the number of MAD’s selected, the TS can be used like a quality control chart indicating when the model is generating too much error in its forecasts.
• The TS formula is:
TS =RSFE
MAD=
Running sum of forecast errors
Mean absolute deviationTS =
RSFE
MAD=
Running sum of forecast errors
Mean absolute deviation
Simple Linear Regression Model
Yt = a + bx0 1 2 3 4 5 x (Time)
YThe simple linear regression model seeks to fit a line through various data over time
The simple linear regression model seeks to fit a line through various data over time
Is the linear regression modelIs the linear regression model
a
Yt is the regressed forecast value or dependent variable in the model, a is the intercept value of the the regression line, and b is similar to the slope of the regression line. However, since it is calculated with the variability of the data in mind, its formulation is not as straight forward as our usual notion of slope.
Simple Linear Regression Formulas
for Calculating “a” and “b”
a = y - bx
b =xy - n(y)(x)
x - n(x2 2
)
a = y - bx
b =xy - n(y)(x)
x - n(x2 2
)
Simple Linear Regression Problem Data
Week Sales1 1502 1573 1624 1665 177
Question: Given the data below, what is the simple linear regression model that can be used to predict sales in future weeks?
Question: Given the data below, what is the simple linear regression model that can be used to predict sales in future weeks?
Week Week*Week Sales Week*Sales1 1 150 1502 4 157 3143 9 162 4864 16 166 6645 25 177 8853 55 162.4 2499
Average Sum Average Sum
b =xy - n(y)(x)
x - n(x=
2499 - 5(162.4)(3)=
a = y - bx = 162.4 - (6.3)(3) =
2 2
) ( )55 5 9
63
106.3
143.5
b =xy - n(y)(x)
x - n(x=
2499 - 5(162.4)(3)=
a = y - bx = 162.4 - (6.3)(3) =
2 2
) ( )55 5 9
63
106.3
143.5
Answer: First, using the linear regression formulas, we can compute “a” and “b”
Answer: First, using the linear regression formulas, we can compute “a” and “b”
35
Yt = 143.5 + 6.3x
180
Period
135140145150155160165170175
1 2 3 4 5
Sal
es
Sales
Forecast
The resulting regression model is:
Now if we plot the regression generated forecasts against the actual sales we obtain the following chart:
36
Questions
• Ready…., Set…., Go….
Question
Which of the following is a classification of a basic type of forecasting?
a. Transportation methodb. Simulationc. Linear programmingd. All of the abovee. None of the above
Answer: b. Simulation (There are four types including Qualitative, Time Series Analysis, Causal Relationships, and Simulation.)
Question
Which of the following is an example of a “Qualitative” type of forecasting technique or model?
a. Grass rootsb. Market researchc. Panel consensusd. All of the abovee. None of the above
Answer: d. All of the above (Also includes Historical Analogy and Delphi Method.)
Question
Which of the following is an example of a “Time Series Analysis” type of forecasting technique or model?
a. Simulationb. Exponential smoothingc. Panel consensusd. All of the abovee. None of the above
Answer: b. Exponential smoothing (Also includes Simple Moving Average, Weighted Moving Average, Regression Analysis, Box Jenkins, Shiskin Time Series, and Trend Projections.)
Question
Which of the following is a reason why a firm should choose a particular forecasting model?
a. Time horizon to forecastb. Data availabilityc. Accuracy requiredd. Size of forecasting budgete. All of the above
Answer: e. All of the above (Also should include “availability of qualified personnel” .)
Question
Which of the following are ways to choose weights in a Weighted Moving Average forecasting model?
a. Costb. Experiencec. Trial and errord. Only b and c abovee. None of the above
Answer: d. Only b and c above
Question
Which of the following are reasons why the Exponential Smoothing model has been a well accepted forecasting methodology?
a. It is accurateb. It is easy to usec. Computer storage requirements
are smalld. All of the abovee. None of the above
Answer: d. All of the above
Question
The value for alpha or α must be between which of the following when used in an Exponential Smoothing model?
a. 1 to 10b. 1 to 2c. 0 to 1d. -1 to 1e. Any number at all
Answer: c. 0 to 1
Question
Which of the following are sources of error in forecasts?
a. Biasb. Randomc. Employing the wrong trend
lined. All of the abovee. None of the aboveAnswer: d. All of the above
Question
Which of the following would be the “best” MAD values in an analysis of the accuracy of a forecasting model?
a. 1000b. 100c. 10d. 1e. 0
Answer: e. 0
Question
If a Least Squares model is: Y=25+5x, and x is equal to 10, what is the forecast value using this model?
a. 100b. 75c. 50d. 25e. None of the aboveAnswer: b. 75 (Y=25+5(10)=75)
Question
Which of the following are examples of seasonal variation?
a. Additiveb. Least squaresc. Standard error of the
estimated. Decompositione. None of the above
Answer: a. Additive (The other type is of seasonal variation is Multiplicative.)
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