session 10 forecasting
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8/9/2019 Session 10 Forecasting
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PRODUCTION & OPERATIONS
MANAGEMENTDr. Partha Priya Datta
Associate Professor of Operations Management
Chair, Visionary Leadership in Manufacturing
ppdatta@iimcal.ac.in
Office: M-202, NAB,
Tel: 765
mailto:ppdatta@iimcal.ac.inmailto:ppdatta@iimcal.ac.in
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Principles of Forecasting
Many types of forecasting models that differ in complexity
and amount of data & way they generate forecasts:
1. Forecasts are rarely perfect
2. Forecasts are more accurate for grouped data than for individualitems
3. Forecast are more accurate for shorter than longer time periods
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Three Building Blocks
3
Source: PRTM.com
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• Qualitative
– Sales force composite / Grass Roots
– Market Research / Consumer market surveys & interviews
– Jury of Executive Opinion / Panel Consensus – Delphi Method
– Historical Analogy - DVDs like VCRs
– Naïve approach
• Quantitative
– Time Series Analysis
– Causal Relationships
– Simulation
Types of Forecasts
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Selection of Forecasting Methods
Method Data Requirements Applications Relative
Cost
Moving
Averages
At least two years of data Short-range
forecasts
Low
ExponentialSmoothing Well adapted to computerapplications, at least two
years of data
Short-rangeforecasts Low
Decomposition Aggregate data, at least
two years of data
Medium-range
forecasts
Medium
Causal
Forecasting
Large volume of data Short to medium
range
Medium
to High
Qualitative
Forecasting
Large volume of expert
judgments, surveys, Not
enough quantitative data
Long range
forecasts
Medium
to High
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6
Time Series Patterns
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Time Series Models
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• Simple Mean:• The average of all available data - good for level patterns
• Moving Average:• The average value over a set time period
(e.g.: the last four weeks)
• Each new forecast drops the oldest data point & adds a new observation• More responsive to a trend but still lags behind actual data
F t = Forecast for the coming period
n = Number of periods to be averaged
At-i = Actual occurrence in the past period for up to “n” periods
n
A A A F
nt t t
t
...
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Time Series Models contd..
• Weighted Moving Average:
• All weights must add to 100% or 1.00
e.g. Ct .5, Ct-1 .3, Ct-2 .2 (weights add to 1.0)
• Allows emphasizing one period over others; above indicates
more weight on recent data (Ct=.5)
• Differs from the simple moving average that weighs all periodsequally - more responsive to trends
tt1t ACF
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Time Series Models contd..
Exponential Smoothing:
• Most frequently used time series method because of ease of
use and minimal amount of data needed
• Need just three pieces of data to start:
• Last period’s forecast (Ft)
• Last periods actual value ( At)
• Select value of smoothing coefficient, a ,between 0 and 1.0
• If no last period forecast is available, average the last few
periods or use naive method
• Higher a values (e.g. .7 or .8) may place too much weight on
last period’s random variation
tt1t Fα1αAF
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Compare MAF and ESF
Period
20 21 22 23 24 25 26 27 28
5-period MAF
weights
0% 0% 0% 20% 20% 20% 20% 20% ----
ESF weights(a.3 2% 4% 5% 7% 10% 15% 21% 30% ----
Ft = aAt-1 + (1-aFt-1
F28 = 0.3xA27 + 0.7xF27
F27 = 0.3xA26 + 0.7xF26
F28 = 0.3xA27 + 0.7x(0.3xA26 + 0.7xF26
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Seasonality problem: a university must develop forecasts for the next year’s quarterly
enrollments. It has collected quarterly enrollments for the past two years. It has also
forecast total enrollment for next year to be 90,000 students. What is the forecast for
each quarter of next year?
Quarter Year 1 SeasonalIndex
Year2
SeasonalIndex
Avg.Index
Year3
Fall24000 ? 26000 ? ? 27450
Winter 23000 ? 22000 ? ? ?
Spring 19000 ? 19000 ? ? ?
Summer 14000 ? 17000 ? ? ?
Total 80000 ? 84000 ? ? ?
Average ? ? ?
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Seasonality problem: a university must develop forecasts for the next year’s quarterly enrollments. It
has collected quarterly enrollments for the past two years. It has also forecast total enrollment for
next year to be 90,000 students. What is the forecast for each quarter of next year?
Quarter Year 1 SeasonalIndex
Year2
SeasonalIndex
Avg.Index
Year3
Fall24000 1.2 26000 1.23 1.22 27450
Winter 23000 1.15 22000 1.05 1.1 24750
Spring 19000 0.95 19000 0.91 0.93 20925
Summer 14000 0.7 17000 0.81 0.75 16875
Total 80000 4 84000 4 4 90000
Average 20000 21000 22500
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Problem 1
Qtr Yr1-
Q1
Yr1-
Q2
Yr1-
Q3
Yr1-
Q4
Yr2-
Q1
Yr2-
Q2
Yr2-
Q3
Yr2-
Q4
Actual 525 605 755 675 580 675 850 740
Trend 628.2 641.8 655.4 668.9 682.5 696.1 709.7 723.3
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Given the following quarterly demand data and trend values, what is the seasonal factor
for quarter II?
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Problem 2The following equation summarizes the trend portion of quarterly sales ofwardrobes over a long cycle. Sales also exhibit seasonal variations.
F t = 40 – 6 .5t + 2t 2
Where
F t =Unit Sales
t=0 at the 1st quarter of 2004
The seasonal indexes for each quarter are given belowQuarter Index
1 1.1
2 1.0
3 0.6
4 1.3
Using the information given, select the forecast of sales (rounded to the nextinteger) for the first quarter of 2008 from the choices given.
a) 192;
b) 493;
c) 432;
d) 336;
e) none of the above
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Problem 3
A shoe manufacturer, using exponential smoothing with a =
0.1, has developed a January forecast of 400 units for a
ladies’ shoe. This brand has seasonal indexes of 0.80,
0.90, and 1.20, respectively, for the first 3 months of the
year. Assuming that actual sales were 344 units in Januaryand 414 units in February, what would be the seasonalized
March forecast? Assume a multiplicative time series model.
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Problem 4
Month
Jan
Feb
Mar
Apr
May
Jun
July
Aug
Sep
Oct
Nov
Dec
S.I.
0.86
0.96
1.2
1.44
1.22
1.06
0.99
0.93
0.89
1.1
3
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Using seasonal indices Apple’s Citrus Fruit Farm ships boxed fruits anywhere in the
world. Using the following information, forecast shipments for the first five months of
next year .
However, for the first two months the S.I. data is misplaced and you only have actual
shipment data for January for last 3 years, which are 300, 400 and 500. Also you know
that the average actual monthly shipment is 500 over the last 3 years. For February youdo not have any information on actual shipments. The trend portion of the demand is
projected using monthly forecast equation: Ft=402+3t, where t=0 for January of last
year and Ft is the number of shipments.
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The Bias Statistic to Determine Forecasting Error
• The ideal Bias/Mean Error is zero which would meanthere is no forecasting error
• Positive Bias means on average under-forecasting
• Bias indicates compensation actions
n
)F(A
=Bias
n
1=t
tt
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1814 J 201 S i 10 (Ch 18) F i (P h P D )
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The MAD Statistic to Determine Forecasting Error
• The ideal MAD is zero which would mean there is noforecasting error
• The larger the MAD, the less the accurate the resultingmodel
• Gives us the size of compensation
MAD =
A - F
n
t tt=1
n
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1914 J 2015 S i 10 (Ch 18) F ti (P th P D tt )
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Tracking Signal
• The Tracking Signal or TS is a measure that
measures whether forecasting model is working• If >4 or
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MAD, RSFE and TSMont
h
Demand
Forecast
Actua
l
Deviatio
n
RSFE Abs
Dev
Sum
of Abs
Dev
MAD TS
1 1000 950 -50 -50 50 50 50 -1
2 1000 1070 70 20 70 120 60 .33
3 1000 1100 100 120 100 220 73.3 1.64
4 1000 960 -40 80 40 260 65 1.2
5 1000 1090 90 170 90 350 70 2.46 1000 1050 50 220 50 400 66.7 3.3
2014 January 2015 Session 10 (Ch.18): Forecasting (Partha P. Datta)
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