topic 2 -forecasting
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Operat ionsManagement
Top ic 2 – Forecast ing
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What is Forecasting?
Process of predicting afuture event
Can be any orcombination of:
Mathematical model
Intuitive
Hmm… you
gonna get an for
this subject
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Short-range forecast Up to 1 year but generally less than 3 months
used for planning purchasing, job scheduling,workforce levels, job assignments, production levels.
Medium-range forecast Generally spans from 3 months to 3 years
useful for sales planning, production planning andbudgeting, cash budgeting, and analyzing variousoperating plans.
Long-range forecast Generally 3 years or more
used in planning for new products, capitalexpenditures, facility location or expansion, and
R&D
Forecasting Time Horizons
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Types of Forecasts
Economic forecasts Address business cycle – inflation rate, money
supply, housing starts, etc.
Technological forecasts
Predict rate of technological progress
Impacts development of new products
Demand forecasts
Predict sales of existing products and services
We can also forecast the economy or the technology.
But for OM, demand forecasting the most relevant.
The forecast is the only estimate of demand until actual
demand becomes known.
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Importance of Forecasting
Human Resources – Hiring, training, laying offworkers
Capacity – Capacity shortages can result inundependable delivery, loss of customers,loss of market share
Supply Chain Management – Good supplierrelations and price advantage
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Seven Steps in Forecasting
1. Determine the use of the forecast
2. Select the items to be forecasted
3. Determine the time horizon of theforecast
4. Select the forecasting model(s)
5. Gather the data6. Make the forecast
7. Validate and implement results
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The Realities!
Forecasts are seldom perfect
Most techn iques assume anunder ly ing stabi l ity in the system
Product fam i ly and agg regated
forecasts are more accu rate than
indiv idual produc t forecasts
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Forecasting Approaches
Qualitative (subjective)
Forecast incorporates the decision maker’sintuition, emotion, personal experiences, and
value system in reaching a forecast.
Quantitative
Forecast use a variety of mathematical models/
techniques that rely on historical data and/orcausal variables to forecast demand.
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Forecasting Approaches
Used when situation is ‘stable’ and
historical data exist Existing products
Current technology
e.g., forecasting sales of color televisions
Quantitative Methods
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Qualitative methods
1. Jury of executive opinion – uses the opinion of a
small group of high level managers to form a group estimate
of demand.
2. Delphi method – using a group process that allowsexperts to make forecasts.
3. Sales force composite – based on salesperson’s
estimates of expected sales.
4. Consumer market survey – solicits inputs from
customers or potential customers regarding future
purchasing plans.
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Quantitative Methods
1. Naive approach
2. Moving averages3. Weighted Moving
Averages
4. Exponentialsmoothing
5. Trend projection
6. Linear regression
Time-SeriesModels
Associative Model
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uses a series of past data points to make aforecast. It is based on a sequence of evenly
spaced (weekly, monthly, quarterly, etc) data
points.
Predict on the assumption that the future is afunction of the past.
Forecast based only on past values, no other
variables important Look what happened over a period of time and use
a series of past data to make a forecast.
For example: to predict the sales of lawn mowers,
use the past sales to make the forecasts.
Time Series Models
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Components of Demand
D e m a
n d f o r p r o d u c t o r
s e r v i c e
| | | |
1 2 3 4
Year
Average demand
over four years
Seasonal peaks
Trendcomponent
Actualdemand
Randomvariation
Figure 4.1
Product demand charted over 4 years witha Growth Trend and Seasonality added:
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Persistent, overall upward or
downward pattern
Changes due to population,technology, age, culture, etc.
Typically several years duration
Trend Component
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Regular pattern of up and down
fluctuations
Due to weather, customs, etc.
Occurs within a single year
Seasonal Component
Number ofPeriod Length Seasons
Week Day 7Month Week 4-4.5Month Day 28-31Year Quarter 4Year Month 12
Year Week 52
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Erratic, unsystematic, ‘residual’
fluctuations
Due to random variation or unforeseenevents
Short duration and
nonrepeating
Random Component
M T W T F
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Naive Approach
Assumes demand in nextperiod is the same as
demand in most recent period e.g., If January sales were 68, then
February sales will be 68
Sometimes cost effective and efficient
Can be good starting point
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Moving average
Weighted moving average
Exponential smoothing
Techniques for Averaging
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Moving Average Method
Moving average =∑ demand in previous n periods
n
A forecasting method that uses an average of the ‘n’ most recent
periods of data to forecast the next period. Useful if we can assume
that market demands will stay fairly steady over time.
e.g. a 4-month moving average is found by summing the demand during
the past 4 months and dividing by 4. This practice tends to smooth out
short term irregularities in the data series.
Where n is the number of periods in the moving average.
The above is used as an estimate of the next period’s demand
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Moving Average Example
Storage shed sales at a Garden Supply shop are as shown in the following
Table.
Example 1:
Calculate the 3-month
moving average forecast.
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January 10
February 12 March 13
Apr i l 16
May 19
June 23Ju ly 26
Actual 3-MonthMonth Shed Sales Movin g Average
(12 + 13 + 16)/3 = 13 2 /3
(13 + 16 + 19)/3 = 16(16 + 19 + 23)/3 = 19 1 /3
Moving Average Example
10
12 13
(10 + 12 + 13)/3 = 11 2 /3
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Moving Average Example
e.g. the forecast for December is 20.7
The forecast for coming January is
(18+16+14)/3=16.0
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Graph of Moving Average
| | | | | | | | | | | |
J F M A M J J A S O N D
S h e
d
S a
l e s
30 –
28 –
26 –
24 –
22 –
20 –
18 –
16 –
14 – 12 –
10 –
Actual
Sales
MovingAverageForecast
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Weighted Moving Average
Weightedmoving average =
∑ (weight for per iod n ) x (demand in period n )
∑ weights
When a detectable trend or pattern is present, weights can be used to place
more emphasis on recent values. This makes forecasting techniques more
responsive to changes because more recent periods may be more heavily
weighted.
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Weighted Moving Average Ex:
Example 2 The shop in Example 1 decides to forecast storage shed sales by weighting the past 3 months as
follows:
Period Weight applied
Last month 3
2 months ago 2
3 months ago 1
_____________________________
Solution:
∑ (weights) = 6
Based on the weightings above, the forecast for any month
[(3 x Sales last month) + (2 x Sales 2 months ago) + (1 x Sales 3 months ago)]
= -------------------------------------------------------------------------------------------------∑ (weights)
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January 10
February 12
March 13
Apr i l 16May 19
June 23
Ju ly 26
Actual 3-Month Weigh ted
Month Shed Sales Movin g Average
[(3 x 16) + (2 x 13) + (12)]/6 = 141 /3
[(3 x 19) + (2 x 16) + (13)]/6 = 17
[(3 x 23) + (2 x 19) + (16)]/6 = 201 /2
Weighted Moving Average
10
12
13
[(3 x 13) + (2 x 12) + (10)]/6 = 121
/6
Weights Appl ied Per iod
3 Last month
2 Two months ago
1 Three mon ths ago
6 Sum of weights
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Weighted Moving Average Ex:
Note that in this situation more heavily weighting the latest month provides a much more
accurate projection.
Note also that moving averages are effective in smoothing out sudden fluctuations in the
demand pattern to provide stable estimates.
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Moving Average AndWeighted Moving Average
Note from the graph that both moving averages lag the actual demand. The
weighted moving average, however reacts more quickly to changes in
demand.
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Increasing n smooths the forecast but makes
it less sensitive to real changes in the data.
Cannot pick up trends very well. Because
they are averages, they will always stay
within past levels and will not predict
changes to either higher or lower levels.
Require extensive historical of past data.
Potential Problems With
Moving Average
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Exponential Smoothing
Is a weighted moving average forecasting technique
in which data points are weighted by an exponential
function. This technique involves little record keeping of past
data.
Easy to use.
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Exponential Smoothing
New forecast = Last period’s forecast
+ (Last period’s actual demand
– Last period’s forecast )
F t = F t – 1 + (A t – 1 - F t – 1)
where F t = new fo recast
F t – 1 = previous fo recast
= smooth ing (or weight ing)
constant (0 ≤ ≤ 1)
Remember This!!!!!!!!Basic exponential smoothing formula:
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Exponential Smoothing Example
Example 3
In January, a car dealer predicted February demand for 142 Ford Mustangs. Actual
February demand was 153. Using a smoothing constant chosen by management of α =0.20, forecast the March demand using the exponential smoothing model.
Solution:
Substituting into the formula above,
New forecast (for March demand),
FMac
= FFeb
+ α (AFeb
– FFeb
)
= 142 + 0.20 (153 – 142)
= 144.2
Therefore the March demand forecast for Ford Mustang is 144.
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Measuring Forecast Error
Forecast error (or Deviation) = Actual demand – Forecast demand= At - Ft.
Several measures in use:
•Mean absolute deviation (MAD)
•Mean squared error (MSE)
•Mean absolute percent error (MAPE)
∑ | Actual - Forecast |
MAD = ------------------------------
n
∑ (Forecast error)
2
MSE = ------------------------
n
n
100 ∑ | Actual i - Forecast i | / Actual i
MAPE = -------i=1--------------------------------------------
n
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Forecast Error Example:
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Exponential Smoothing Example
2Demand for the last four months was:
Predict demand for July using each of these methods:
(A)
1) A 3-period moving average
2) exponential smoothing with alpha equal to .20 (use naïve to
begin).
(B)
3) If the naive approach had been used to predict demand for April
through June, what would MAD have been for those months?
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Exponential Smoothing Example 2
Month Demand Forecast
March 6 -
April 8 6May 10 6 + 0.2(8 – 6) = 6.4
June 8 6.4 + 0.2(10 – 6.4) = 7.12
7.12 + 0.2(8 – 7.12) = 7.296
A) 1. (8+10+8)/3 = 8.33 (July Forecast)
2. Use naïve to begin
B)
Month March April May JuneDemand 6 8 10 8
Naïve - 6 8 10
Error - +2 +2 -2
MAD 6/3 = 2.0
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Moving Average
Weekly sales of ten-grain bread at the local organic food market are in the
table below. Based on this data, forecast week 9 using a five-week moving
average.
Other Examples
Week 1 2 3 4 5 6 7 8
Sales 415 389 420 382 410 432 405 421
(382+410+432+405+421)= 410.0
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Exponential Smoothing & MAD Jim's department at a local department store has tracked the sales of a product
over the last ten weeks. Forecast demand using exponential smoothing with
an alpha of 0.4, and an initial forecast of 28.0. Calculate MAD.
Other Examples
Period Demand1 24
2 23
3 26
4 36
5 26
6 30
7 32
8 26
9 25
10 28
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Period Demand Forecast Error Absolute
1 24 28.00
2 23 26.40 -3.40 3.40
3 26 25.04 0.96 0.96
4 36 25.42 10.58 10.58 5 26 29.65 -3.65 3.65
6 30 28.19 1.81 1.81
7 32 28.92 3.08 3.08
8 26 30.15 -4.15 4.15
9 25
28.49 -3.49 3.49 10 28 27.09 0.91 0.91
Total 2.64 32.03
Average 0.29 3.56
Bias MAD
Other Examples – Exponential Smoothing
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Other ExamplesProblems: Forecasting
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QUIZ 1
The docking rate of ships at the Northport varies monthly and the operationsmanager is attempting to test the use of exponential smoothing to determine the
effectiveness of the technique in forecasting. He begins the analysis in the
month of January and continues for an additional 5 months. The initial forecast
for January is 320. Actual data for the past 6 month are as follows:
The operation manager has decided on 2 values for a i.e. = 0.1 and a = 0.4.
Which of these alpha values will be more accurate? Explain why?