Homework for Operation and supply chain Management

Description

Review the attached Word document with your homework assignment for this module. Complete the homework by typing your response in the Word document and uploading it to this assignment. Questions may be posted on the Q&A discussion forum.

I attached below :

1- homework qestion

2- Powerpoint module

INFO 564 Homework Assignment 5
This work must be done completely in EXCEL. Answer each question on a separate tab. Label
each tab appropriately. You can copy and paste the data given into an Excel worksheet.
South Shore Construction builds permanent docks and seawalls along the southern shore of
Long Island, New York. The following data show quarterly sales revenues (in $’000s) for the
past 5 years.
Quarter
1
2
3
4
Year 1
20
100
175
13
Year 2
37
136
245
26
Year 3
75
155
326
48
Year 4
92
202
384
82
Year 5
176
282
445
181
Question 1
Plot this data with quarters from years 1-5 on the horizontal axis. What components do you
see in this time series?
Question 2
Ignore any trend or seasonality in the data.
a. Suppose the company uses moving averages to make forecasts. Make forecasts all the
way through Q4 Year 5. Assume the company uses (i) 3-quarterly moving averages and
(ii) 4-quarterly moving averages.
b. Compare the two sets of forecasts from (a) on the basis of Mean Absolute Percent
Deviation. Which is more accurate – 3 quarterly moving average or 4 quarterly moving
average?
c. On a line chart plot the time series along with the forecasts from the method you select
in (b).
Question 3
Ignore any trend or seasonality in the data.
a. Suppose the company uses weighted moving averages to make forecasts. What are the
forecasts starting with Q4 Year 1 all the way through Q4 Year 5? Assume the company
uses (i) 3-quarterly moving averages with weights 0.6, 0.3, and 0.1 and (ii) 4-quarterly
moving averages with weights 0.4, 0.3, 0.2, and 0.1. In both cases the most weight is
given to the most recent quarter and the least to the oldest quarter in the moving
average.
b. Compare the two sets of forecasts from (a) on the basis of Mean Absolute Percent
Deviation. Which is more accurate – 3 quarterly weighted moving average or 4
quarterly weighted moving average?
c. On a line chart plot the time series along with the forecasts from the method you select
in (b).
Question 4
Again ignore any trend or seasonality in the data.
a. Suppose the company uses exponential smoothing to make forecasts. What are the
forecasts for periods Q2 Year 1 through Q4 Year 5 assuming (i) alpha = 0.3 and (ii) alpha
= 0.7? In both cases assume that the forecast for Q1 Year 1 was 25 units.
b. Compare the two sets of forecasts from (a) on the basis of Mean Absolute Percent
Deviation. Which is more accurate – alpha of 0.3 or alpha of 0.7?
c. On a line chart plot the time series along with the forecasts from the method you select
in (b)
Question 5
Now make adjustments for trend and seasonality.
a. Quantify the trend in the time series. What does the trend equation tell you?
b. Quantify the seasonality in the time series by calculating seasonality indexes. What do
these indexes tell you?
c. Using the trend and the seasonality information from (a) and (b) make forecasts from
Q1 Year 1 through Q4 Year 5.
d. Calculate the Mean Absolute Percent Deviation for the forecasts in (c).
e. On a line chart plot the time series along with the forecasts from (c).
Question 6
Using the most accurate method of all of the above,
a. Make forecasts for the four quarters of Year 6.
b. Plot these forecasts on the same line chart as the time series.
c. Summarize in a few lines your findings from your answers to Q1 through Q6b.
INFO 564
Operations & Supply Chain Management
Module 5a: Measuring Forecast Accuracy
Copyright 2017 Montclair State University
Forecast Accuracy
• Measured retrospectively based on past forecasts and
their errors
• Error = Actual – Forecast
• Also referred to as deviation
• Common measures are functions of past errors
• Mean Error (also called bias)
• Mean Absolute Error (MAE)
• Mean Absolute Percent Error (MAPE)
Mean Error
• Suppose we made forecasts for 5 past
periods and wish to measure their
accuracy.
• Error = Actual – Forecast
• Mean error is the average of the errors
in the 5 periods.
• Tells us that on average we are underforecasting by 1.2 units.
• Caveat: Small mean error does not
necessarily mean accurate forecasts
• Large negative errors in some periods could
cancel out large positive errors in others
Period
1
2
3
4
5
Actual
22
29
29
26
26
Forecast
25
26
26
28
21
Mean Error =
Error
-3
3
3
-2
5
1.2
Doesn’t seem to be of same
magnitude as the errors.
Mean Absolute Error
• Very popular measure
• Absolute Error ignores the sign
associated with error.
• Mean Absolute Error averages
the absolute errors.
• More reliable measure of
forecast errors.
• Forecasts are typically off by 3.2
units
• But is 3.2 big or small? MAE
does not tell us
Period
1
2
3
4
5
Actual
22
29
29
26
26
Forecast
25
26
26
28
21
Error
-3
3
3
-2
5
Absolute
Error
3
3
3
2
5
Mean Absolute Error =
Is of same magnitude
as the errors.
3.2
Mean Absolute Percent Error
• Absolute Percent Error = Absolute
Error ÷ Actual
• Mean Absolute Percent Error =
average of all the Absolute
Percent Errors.
• On average, forecasts are off by
about 12.2% of actual.
• Provides estimate of the relative
size of forecast error
• Another popular measure of
forecast accuracy
Period
1
2
3
4
5
Actual
22
29
29
26
26
Forecast
25
26
26
28
21
Error
-3
3
3
-2
5
Absolute
Absolute
Error
Percent Error
3
13.6%
3
10.3%
3
10.3%
2
7.7%
5
19.2%
Mean Absolute Percent Error =
12.2%
Forecasts off typically by
about 12.2% of actual values.
In Conclusion…
• Three very common measures of forecast accuracy
• Mean Error (also called bias)
• Mean Absolute Error (MAE)
• Mean Absolute Percent Error (MAPE)
• Found in all forecasting software
• Other measures available for specialized situations
• Can be used to compare different forecasting methods
• All based on past performance
• No guarantee of future performance of forecasts
INFO 564
Operations & Supply Chain Management
Module 5b: Patterns in Time-Series Data
Closing Price of Stock
Closing Price $
What are Time Series?
80
60
40
20
0
• Data collected over time
2
3
4
5
6
Week
7
8
9
10
Daily High Temperature
Temperature (F)
Monthly energy bills
Yearly college enrollment
Daily closing value of the DJIA
Hourly temperatures in a given
zip-code
• Quarterly earnings of a
company
90
88
86
84
82
80
78
76
74
1
2
3
4
5
6
7
8
Laptop Sales
3500
Sales (Units)




1
3000
2500
2000
1500
9 10 11 12
Patterns in Time Series: Randomness
• No pattern
• Seemingly random small ups
and downs in the time series
• Too many small causes that
contribute
• Difficult to forecast
• Impact reduced by averaging
1200
1100
# of Calls
• Movement not too big
compared with general level of
the series
Number of Calls to Help Center
1000
900
800
700
600
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
Day
Patterns in Time Series: Trend
• The spikes are random ups
and downs
• Useful for forecasting
• If we can assume trend will
continue
Temperature (F)
• Upward: cloud services, Alexa,
electric cars, battery life
• Downward: compact discs, stickshifts, cash
Daily High Temperature
90
88
86
84
82
80
78
76
74
1
2
3
4
5
6
7
8
9
10
11
12
10
11
12
Day
Bank Balance ($)
6000
5000
Dollars
• Trend: sustained upward or
downward movement
4000
3000
2000
1000
0
1
2
3
4
5
6
7
End of Week
8
9
Patterns in Time Series: Seasonality
Laptop Sales
• Often products and services
exhibit seasonal demand
• Randomness is present.
2500
2000
1500
1000
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
• Patterns can repeat annually,
monthly, weekly, even daily.
• If pattern can be expected to
continue, can use in forecasting.
• Pattern is not perfectly repeated.
3000
# of Laptops
• Some periods are consistently high,
some consistently low
• Christmas trees, school supplies,
vacation travel, business travel,
construction, etc.
3500
Patterns in Time Series: Cycles
•Cycles are like seasonality, but they repeat over much longer periods
•Correspond with business cycles, economic cycles
•Relevant in medium-term (3-5 years) and long-term (5 or more
years) forecasting
•Require lots of past data to recognize these patterns
Year-1
Year-2
Year-3
Year-4
Year-5
Year-6
Year-7
Year-8
Year-9
Using the Patterns for Forecasting
• Time-series can exhibit one or more of these patterns.
• Recognizing patterns – trends, seasonality, cyclicality
– allows us to use them for forecasting
• We have to be able to quantify them.
• Assumption: these patterns will hold in the future.
• Cyclicality is hard to recognize and quantity
• Only occasionally used in time-series forecasting
INFO 564
Operations & Supply Chain Management
Module 5c: Forecasting with Moving Averages
Example
Month
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan
Feb
Mar
Apr
Demand
988
978
1059
1013
1092
948
1002
952
958
1029
978
917
944
955
998
1017
• Past demand for a product is given in the time-series on the left.
• A graph of the series is shown below:
Demand
1200
1100
1000
900
800
700
600
500
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr
• The series shows no trend or seasonality
• Only random ups and downs.
• What is our forecast for the next period, May?
Approach – Moving Averages
• Forecast for May based on a moving average of recent data
• Example:
• 3-month moving average: Average of demand in February, March,
and April
• = (955+998+1017)/3 = 990 units
• 6-month moving average: Average of demand from November
through April
• = (978+917+…+1017)/6 = 968 units
• Moving averages assume only recent periods are relevant.
• Older periods may be ignored safely
• Reasonable assumption in real life
Moving Averages: Impact of Period
• Graph shows demand, 3-month, and
6-month moving average forecasts
• 3-month moving average forecasts more
responsive to actual demand
• 6-month moving average forecasts less
responsive to demand
• Which is better?
• Longer periods dampen random fluctuations
(good) but also dampen trends (bad)
• Shorter periods respond to random
fluctuations (bad) and to trends (good)
Demand & Forecasts
1050
1000
950
900
850
800
750
700
Jan
Feb
Mar
Apr
Demand
• We want forecasts to ignore random
fluctuations but highlight trends
May
Jun
3-Mth MA
Jul
Aug
6-Mth MA
Sep
Oct
How to pick a period for moving averages?
• Experience, knowledge, instinct
OR…
• Use past data to experiment
• 3-month moving average forecasts
have a MAD of 37
• 6-month moving average forecasts
have a MAD of 36
• 6-month moving averages seem
slightly superior
• May be the choice going forward
Month
Jul
Aug
Sep
Oct
Nov
Dec
Jan
Feb
Mar
Apr
Demand
1002
952
958
1029
978
917
944
955
998
1017
3-Mth MA Abs Dev
1017
15
1014
62
967
9
971
58
980
1
988
72
975
31
947
9
939
59
966
52
37
MAD
6-Mth MA Abs Dev
1013
11
1015
64
1011
53
994
35
997
18
978
61
973
28
963
8
964
34
970
47
36
MAD
Weighted Moving Averages
• Simple moving averages assume equal importance (weight) of
each period used to compute the moving average.
• We could give different weights to different periods
• In a 3-month weighted moving average, 60% to the most recent
period, 30% to the one before, and 10% to the oldest period.
May forecast = 0.6*1017+0.3*998+0.1*955 = 1005 units
• Weights are subjective
• Most recent period is considered the most important and gets most
weight
• Oldest period is least important and gets the least weight
• Add up to 1
Summary
• Moving averages are appropriate when the time-series shows
no trend or seasonality
• Subjective considerations
• Averaging period
• Weighting if any
• Moving averages are reactive
• When there is trend moving averages will always lag behind
• Easy to understand
• Easy to implement on a spreadsheet
INFO 564
Operations & Supply Chain Management
Module 5d: Forecasting with Exponential Smoothing
Exponential Smoothing
• A weighted-average forecasting method
• Forecasts are a series of adjustments to previous forecasts
• New Forecast = Old Forecast + Adjustment
• Adjustment depends on forecast error
• All past periods are used in calculating the new forecast
• Unlike moving averages
• Given declining weights; most recent period the most.
• A subjective parameter, denoted α, is used to perform the
weighting
• α is between 0 and 1
Basic Idea
• Ft+1 = Forecast for period t+1
(upcoming period)
• Ft= Forecast for period t
(period that just ended)
• At= Actual demand for period t
Now
Ft
Period t+1
Period t
Ft+1
At
Adjustment
Ft+1= Ft + α(At – Ft)
Thus Ft+1 is Ft plus a portion of
the forecast error.
May also be written as:
Ft+1 = αAt + (1-α)Ft
Easier for calculation
Example
Suppose α = 0.4
Forecast for
April=30
• FMay = FApr + α(AApr-FApr)
= 30+0.4*(25-30) = 28
Actual for
April=25
• FJun = FMay + α(AMay-FMay)
Forecast for
May=28
= 28+0.4*(29-28) = 28.4
Actual for
May=29
= 28.4+0.4*(32-28.4) = 29.84
Forecast for
June=28.4
Actual for
June=32
Forecast for
July=29.84
• FJul = FJun + α(AJun-FJun)
• And so on…
Effect of α
• Alternate form Ft+1 = αAt + (1-α)Ft
• Can interpret Ft+1 as a weighted average of At and Ft
• α is the weight given to At, 1-α the weight given to Ft
• Large values of α give more weight to actual demand At
• Forecasts become more responsive to actual demand
• Small values of α give less weight to At
• Forecasts less responsive to actual demand
Effect of α
Forecasts
Month
Exponential Smoothing Forecasts
Demand Alpha=0.2 Alpha=0.8
988
1000
1000
1150
Feb
978
998
990
1100
Mar
1059
994
980
1050
Apr
1013
1007
1043
May
1092
1008
1019
Jun
948
1025
1077
Jul
1002
1009
974
Aug
952
1008
996
Sep
958
997
960
Oct
1029
989
959
Nov
978
997
1015
Dec
917
993
986
Jan
944
978
931
Feb
955
971
942
Mar
998
968
953
Apr
1017
974
989
* Forecasts for this January are
assumed numbers
Units Demand
Jan*
1000
950
900
850
800
750
700
Jan
Feb
Mar
Apr
May
Jun
Demand
Jul
Aug
Sep
Alpha = 0.2
Oct
Nov
Dec
Jan
Feb
Mar
Alpha=0.8
Forecasts with the smaller value of α are much steadier than with the larger
value of α
Apr
Picking a value of α
• Judgment, experience, intuition
• Using value of α that works well on past
data
• Table on right, forecasts for past periods
using α=0.2 and α=0.8.
• α=0.2 provides more accurate forecasts
(smaller MAD)
• Going forward, α=0.2 may be a better value
than α=0.8.
• Can also experiment with other values to
obtain best value.
• No guarantee that this value will work
well in the future
Month
Demand
Alpha=0.2
Abs.Dev Alpha=0.8
Abs.Dev
Jan
988
1000
12.4
1000
12.4
Feb
978
998
20.0
990
12.5
Mar
1059
994
65.6
980
79.1
Apr
1013
1007
6.1
1043
30.6
May
1092
1008
83.8
1019
72.8
Jun
Jul
948
1002
1025
1009
77.0
7.3
1077
974
129.4
28.4
Aug
952
1008
56.3
996
44.8
Sep
958
997
38.4
960
2.3
Oct
1029
989
40.0
959
70.2
Nov
978
997
18.4
1015
36.3
Dec
917
993
76.3
986
68.8
Jan
944
978
33.7
931
13.5
Feb
955
971
15.8
942
13.8
Mar
998
968
30.1
953
45.6
Apr
1017
974
43.5
989
28.5
39.0
43.1
MAD
MAD
Advantages of Exponential Smoothing
• More accurate than more sophisticated methods
• Easy to use and understand
• Easy to adjust importance given to actual demand through α
• Nested mechanism means that all past periods are used in making a
forecast
• FNov depends on AOct and FOct. FOct depends on ASep and FSep. FSep depends on
AAug and FAug, and so on.
• Thus FNov depends on AOct, ASep, AAug, and so on.
• No period is ignored
• More importance is given to more recent data
• Included in all popular forecasting packages
INFO 564
Operations & Supply Chain Management
Module 5e: Trend in Time Series
Example – # of Passengers
• Weekly number of passengers
carried by a bus service
reveals an upward trend.
• How to quantify this trend?
• Trend in this instance seems
linear
• A straight line with random
departures from it
#
Week Pass
1
305
2
302
3
380
4
372
5
452
6
404
7
424
8
408
9
533
10
522
11
510
12
588
13
604
14
581
15
585
16
617
# of Passengers
700
600
500
400
300
200
100
0
1
2
3
4
5
6
7
8
9
Week
10
11
12
13
14
15
16
Example – # of Passengers
• Weekly number of passengers
carried by a bus service
reveals an upward trend.
• How to quantify this trend?
• Trend in this instance seems
linear
• A straight line with random
departures from it
#
Week Pass
1
305
2
302
3
380
4
372
5
452
6
404
7
424
8
408
9
533
10
522
11
510
12
588
13
604
14
581
15
585
16
617
# of Passengers
700
600
500
400
300
200
100
0
1
2
3
4
5
6
7
8
9
Week
10
11
12
13
14
15
16
Quantifying Trend
• A line is described by a slope and
an intercept
• Y = bX + a
• b: slope, a: intercept
• The slope b measures the rate at
which the line climbs or falls – trend
• How to find slope and intercept?
• Line of best fit
• Formula for b and a
• Software
• Spreadsheet
# of Passengers
700
600
500
400
300
200
100
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Week
• The line of best fit above is
# of Passengers = b(Week) + a
• b captures the trend: the rate at which the
number of passengers is increasing each
week.
16
Trendline with EXCEL
Put mouse cursor on plot
and Left Click.
Trendline with EXCEL
Right Click and select Add
Trendline…
Trendline with EXCEL
Check
these.
Trend Line
• y = 21.41x + 292.2
• # of Passengers = 21.41*Week # + 292.2
• Interpretation
• The number of passengers increases at the rate of 21.4 (slope) each
week starting from a base of about 292 passengers
• The line can be used for forecasting by “projecting the trend”
• Simply substitute the future Week # into the equation.
Forecasts for Weeks 17-20
Week Forecast
17
656
18
678
19
699
20
720
=21.41*18+292.2
= 678 (rounded)
# of Passengers
800
700
y = 21.41x + 292.2
600
500
400
300
200
100
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20
Week
• Careful! You shouldn’t use the equation
to forecast too far into the future.
• Large forecasting errors can result.
• The estimates of slope and intercept are
valid only for a few periods beyond the
data
• Recalculate slope and intercept as fresh
data arrives
Summary
• Quantify trend using the slope of the line of best fit
• Spreadsheets can do this for us easily
• Trendline feature in Excel; also Excel functions: SLOPE and
INTERCEPT
• Statistical software
• Use estimate of slope and intercept to make forecasts
• Trends need not always be linear
• Spreadsheets provide other options: logarithmic, exponential,
quadratic, etc.
• Shouldn’t project trend too far
INFO 564
Operations & Supply Chain Management
Module 5f: Quantifying Seasonality
Seasonality
• Patterns that repeat every week, month, quarter, or year
• Christmas trees, vacation travel, construction, clothing, etc.
• Usually associated with seasons, not always
• “Back to school” supplies, # of defects in cars built on Mondays,
absenteeism on Fridays, demand for tax accountants
• Extent of seasonality measured through a seasonality index
• Seasonality index of 1.30 for December means December sales are
30% higher than average monthly sales.
• Ignoring seasonality can lead to large forecasting errors
Example: Monthly Sales of Laptops
Month
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Year1
2452
2272
2725
2637
2626
2790
2951
2986
2398
2522
2317
2518
Year2
2348
2203
2842
2491
2552
2856
2937
2976
2452
2588
2319
2480
Year3
2233
2114
2673
2543
2632
2857
2924
3119
2488
2566
2332
2445
Monthly Sales of Laptops
3500
3000
2500
2000
1500
1000
Jan
Feb
Mar
Apr
May
Year1
Jun
Jul
Year2
Aug
Sep
Oct
Nov
Dec
Year3
Clearly laptop sales are seasonal with high sales in August, and low sales
in February
Calculating Seasonality Indexes
Month
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Year1
Year2
2452
2348
2272
2203
2725
2842
2637
2491
2626
2552
2790
2856
2951
2937
2986
2976
2398
2452
2522
2588
2317
2319
2518
2480
Overall Average =
Year3
2233
2114
2673
2543
2632
2857
2924
3119
2488
2566
2332
2445
2588
Monthly
Average
2344
2196
2747
2557
2603
2834
2937
3027
2446
2559
2323
2481
Sales in August are 17% higher than average. Sales in
February are 15% lower than average.
Seasonality
Index
0.91
0.85
1.06
0.99
1.01
1.10
1.14
1.17
0.95
0.99
0.90
0.96
• Calculate overall average sales per
month – average of 36 numbers
• Calculate monthly average sales for
each month – average of 3 numbers
• Seasonality Index = monthly average ÷
overall average
• Seasonality indexes must add up to the
number of periods – 12 in this
example.
• One of many ways of calculating
seasonality indexes
Seasonality Indexes in Forecasting
• Forecasts are usually forecasts of average sales for a
particular period
• When seasonality is present, averages can be very misleading
• Months of typically high sales will see low forecasts – shortages of
product, labor, capacity, and other resources
• Months of typically low sales will see high forecasts – excess of
product, labor, capacity, and other resources
• Forecasts of average sales must be adjusted for seasonality
• Average Forecast * Seasonality Index
INFO 564
Operations & Supply Chain Management
Module 5g: Forecasting When Trend
and Seasonality Are Present
Example – Sales of Laptops
Year-1
Year-2
Year-3
Jan
2473
2624
2764
Feb
2314
2500
2666
Mar
2789
3160
3246
Apr
2722
2831
3137
May
2732
2913
3248
Jun
2917
3238
3494
Jul
3100
3340
3582
Aug
3156
3401
3798
Sep
2589
2898
3189
Oct
2734
3055
3288
Nov
2551
2807
3075
Dec
2773
2990
3209
Sales of Laptops
4000
3500
3000
Units
Month
2500
Increasing trend
Seasonality
Randomness
2000
1500
1000
Jan
Feb
Mar
Apr
May
Year-1
Jun
Year-2
Jul
Aug
Year-3
Sep
Oct
Nov
Dec
2473
2314
2789
2722
2732
2917
3100
3156
2589
2734
2551
2773
2624
2500
3160
2831
2913
3238
3340
3401
2898
3055
2807
2990
2764
2666
3246
3137
3248
3494
3582
3798
3189
3288
3075
3209
Example – Sales of Laptops Continued
• Another way of identifying the trend and
seasonality is to plot the data as one time
series.
• Trend and patterns that repeat each year are
clearly seen
Laptop Sales
4000
3500
3000
2500
2000
1500
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Units
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Sales (Units)
Month
Multiplicative Decomposition – A 4-Step
Process
• Calculate seasonality indexes
• Quantifies seasonality
• Draw a trend-line through the data
• Estimates slope (trend) and intercept
• Project the trend into the future periods
• Trend forecast
• Adjust trend forecast with seasonality index
• Final forecast
Calculating Seasonality Indexes
Month
Year-1
Year-2
Year-3
Jan
2473
2624
2764
Feb
2314
2500
2666
Mar
2789
3160
3246
Apr
2722
2831
3137
May
2732
2913
3248
Jun
2917
3238
3494
Jul
3100
3340
3582
Aug
3156
3401
3798
Sep
2589
2898
3189
Oct
2734
3055
3288
Nov
2551
2807
3075
Dec
2773
2990
3209
Overall Average =
2981
Monthly
Average
2620
2493
3065
2897
2964
3216
3341
3452
2892
3026
2811
2991
Seasonality
Index
0.88
0.84
1.03
0.97
0.99
1.08
1.12
1.16
0.97
1.02
0.94
1.00
12.00
Estimating Trend
Laptop Sales
4000
y = 21.231x + 2587.9
3500
3000
2500
Slope = 31.23 units per month
Intercept = 2588 units
2000
Dec
Oct
Nov
Sep
Aug
Jul
Jun
Apr
May
Mar
Jan
Feb
Dec
Nov
Oct
Sep
Jul
Aug
Jun
May
Apr
Mar
Feb
Jan
Dec
Oct
Nov
Sep
Aug
Jul
Jun
Apr
May
1500
Mar
2473
2314
2789
2722
2732
2917
3100
3156
2589
2734
2551
2773
2624
2500
3160
2831
2913
3238
3340
3401
2898
3055
2807
2990
2764
2666
3246
3137
3248
3494
3582
3798
3189
3288
3075
3209
Jan

Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Feb
Units
Sales (Units)
Month
Project Trend
• Laptop Sales = 21.23*Period + 2588
• Suppose we want to make forecasts for the next four months.
• Project trend to the first four months of year 4 (periods 37 – 40)
Period Month
Trend
Forecast
37
January
3374
38
February
3395
39
March
3416
40
April
3437
=21.23*37 + 2588
Final Forecasts
• Adjust trend forecasts with seasonality indexes
Period Month
Trend Seasonality
Final
Forecast
Index Forecast
37
January
3373
0.88
2968
38
February
3395
0.84
2852
39
March
3416
1.03
3518
40
April
3437
0.97
3334
=3395*0.84
Final Forecasts
Laptop Sales
4000
y = 18.128x + 2627.4
• The dotted line represents
trend projections for those
four periods.
3000
2500
2000
1500
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan
Feb
Mar
April
Sales (Units)
3500
• The last four points (in red)
are forecasts.
Summary
• When trend and seasonality are present we estimate
each component separately
• The final forecast is a product of the trend component
and the seasonality adjustment
• Randomness is handled through the averaging
process
• Many versions of multiplicative decomposition
• This is the simplest

We offer the bestcustom writing paper services. We have done this question before, we can also do it for you.

Why Choose Us

  • 100% non-plagiarized Papers
  • 24/7 /365 Service Available
  • Affordable Prices
  • Any Paper, Urgency, and Subject
  • Will complete your papers in 6 hours
  • On-time Delivery
  • Money-back and Privacy guarantees
  • Unlimited Amendments upon request
  • Satisfaction guarantee

How it Works

  • Click on the “Place Order” tab at the top menu or “Order Now” icon at the bottom and a new page will appear with an order form to be filled.
  • Fill in your paper’s requirements in the "PAPER DETAILS" section.
  • Fill in your paper’s academic level, deadline, and the required number of pages from the drop-down menus.
  • Click “CREATE ACCOUNT & SIGN IN” to enter your registration details and get an account with us for record-keeping and then, click on “PROCEED TO CHECKOUT” at the bottom of the page.
  • From there, the payment sections will show, follow the guided payment process and your order will be available for our writing team to work on it.