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Forecasting
y
Section Demand Objectives After completing this section, you should be able to: 1. List the features of a good forecast. 2. Outline the steps in the forecasting process. 3. Compare and contrast qualitative and quantitative approaches to forecasting. 4. Identify three qualitative forecasting methods. 5. Briefly describe averaging techniques, trend and seasonal techniques and regression analysis, and solve typical problems. 6. Describe two measures of forecast accuracy. 7. Describe two ways of evaluating and controlling forecasts.
5-1
Demand Forecasting
y
Features of Forecasts 1. Causal System. Forecast techniques generally assume that the
same underlying causal system that existed in the past will continue to exist in the future. 2. Forecast Error. Forecasts are rarely perfect; actual results usually differ from predicted values. 3. Group Forecasts. Forecasts for groups of items tend to be more accurate than forecasts for individual items because forecasting errors among items in a group usually have a canceling effect. 4. Accuracy and Time. Forecast accuracy decreases as the time period covered by the forecast (i.e. the time horizon) increases. Generally, short-term forecasts must deal with fewer uncertainties than long-term forecasts.
5-2
Demand Forecasting
y
Forecast Process The process of forecasting has four clearly definable steps: 1. Determine the purpose of the forecast. The use to which the forecast will be used will determine both the technique to be used and the frequency with which the forecast has to be updated. 2. Establish a time horizon. How far forward are we interested in forecasting? Next week? Next month? Next year? Next 20 years? The choice of horizon affects the choice of technique and this, in turn, determines the amount of data and effort needed to prepare the forecast. 3. Prepare the forecast. This involves four steps: a. Identify the assumptions in the forecast model you propose to use. b. Gather the data. 5-3
Demand Forecasting
y
Types of Forecasts
1. Qualitative - consists mainly of subjective inputs such as human factors, personal opinions or hunches which may be difficult or impossible to quantify. 2. Quantitative - involve the extension of historical data or development of associative models. Time Series - extension of historical data by identifying patterns in the past that might reasonably be expected to continue in the future. Causal models - development of an association between the variable we are interested in forecasting and one or more variables that might explain the variable of interest.
5-4
Demand Forecasting
C la s s ific a tio n o f F o r e c a s tin g M o d e ls
F o r e c a s tin g
S ta tis tic a l
T im e S e r ie s M o d e ls T ren d P r o je c tio n
M o v in g A verages
S im p le M o v in g A v era g es W e ig h te d M o v in g A v erages S im p le E x p o n e n tia l S m o o th in g
J u d g e m e n ta l
E xp ert O p in io n M arket S u rveys D e lp h i M eth o d
C a u sa l o r R e g r e ssio n M o d e ls S m o o th in g M eth o d s
T ren d an d S ea so n a l
E x p o n e n tia l S m o o th in g
E x p o n e n tia l S m o o th in g w ith T r e n d E x p o n e n tia l S m o o th in g w ith S e a s o n a l V a r ia tio n E x p o n e n tia l S m o o th in g w ith T r e n d a n d S e a s o n a l
5-5
Demand Forecasting
Operations Forecasting: Uses and Methods
Uses of Forecasting for Operations
Location
Time Horizon
Long
Accuracy Required
Medium
Management Level
Top
Forecasting Methods
Qualitative and Causal
Capacity Planning: Facilities Equipment Scheduling / MRP Long Medium Short Medium High Highest Top Middle Lower Qual. & Causal Causal & T.S. Time Series
Order Processing
Short
Highest
Lower
Time Series
5-6
Demand Forecasting
y
Qualitative Forecasting Methods
Executive Opinion. Forecasts that are based on the judgment and experience of managers. Sales Force Composite. Forecasts compiled from estimates of demand made by members of a company's sales force Consumer Surveys. A forecasting method that seeks input from customers regarding future purchasing plans for existing products or services. Market Research. This method tests hypothesis about new products or services or new markets for existing products or services. Delphi Method. A forecasting technique using a group process that allows experts to make forecasts.
5-7
Demand Forecasting
y
Quantitative Forecasting Methods
These can be broken into two main categories: 1. Time Series (TS) Models. A forecasting approach in which future values of a series can be estimated from past values of the series. Driving forward by looking at the rear view mirror. Types of TS models include:
Simple Average / Moving Average / Weighted Moving Average Exponential Smoothing: Single, Trend, Seasonal, and Trend and Seasonal
Trend Projection 2. Associative (Causal) Models. A forecasting method which identifies related variables that can be used to predict values of the variable of interest. The essential element is the development of an equation that summarizes the effects of predictor variables. The primary method of analysis is known as regression.
5-8
Demand Forecasting
y
Time Series Models A time series is a time-ordered sequence of observations taken at regular intervals over a period of time. Analysis of a time series requires an identification of the underlying behaviour of the series. This behaviour may have four patterns: 1. Trend refers to a gradual, long-term movement in the data. Population shifts, changing incomes and cultural changes often account for such movements. 2. Seasonality refers to short-term, fairly regular variations that are generally related to weather factors or to human-made factors such as holidays. 3. Cycles are wavelike variations of more than one year's duration. These are often related to a variety of economic and political factors. 5-9 4. Irregular variations are due to unusual
Demand Forecasting
Application of Forecasting Methods
Combination of Components in the Series
No trend (horizontal trend), no seasonal variation; i.e. a stable variation with random fluctuation
Objectives
To average out randomness and find average To determine seasonal pattern and project it or average out seasonality Short term projection
Models Often Appropriate
Simple moving average Weighted moving average Single exponential smoothing Simple moving average Time series decomposition Double exponential smoothing Time series decomposition Triple exponential smoothing Time series decomposition Simple linear regression Curvilinear regression Multiple regression
No trend, but seasonal variation
Trend, but no seasonal variation Long term projection Trend and seasonal variation To project trend and seasonal variation around it To identify variables that "explain" level of demand
Patterns of changes not related to time
5 - 10
Demand Forecasting
Seasonal Variations
700 600 500 400 300 200 Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 2000 2001 2002 2003 2004 2005
The data in the graph is monthly sales for a six-year period. Each year is graphed on top of the preceding one. Question: What time series patterns exist in this data?
5 - 11
Demand Forecasting
y
Time Series: Averaging Techniques 1. Naive Forecasts - a naive forecast for any period equals the previous period's actual value. Although it appears simplistic, it is a legitimate forecasting technique:
it has virtually no cost forecasts are quick and easy to prepare easy to understand can be used for seasonal data (e.g. sales for this December equal sales for preceding December)
2. Moving Average - a forecasting technique that use a number of the most recent actual data values in generating a forecast. There are two types: a. Simple moving average = SMA = i Ai / n
where i = the "age" of the data n = the number of periods in the moving average
5 - 12
Demand Forecasting
b. Weighted moving average = WMA = i Ai Wi
where Wi = the relative weight of each data point in the moving average Note that the sum of all weights , Wi , must equal 1.
For both the SMA and the WMA, a key issue is how many data points will be used to calculate the average. A large number of data points results in a smooth average: a small number of data points means the the model responds very quickly to the most recent changes. If responsiveness in important, a simple moving average with relatively few data points, or a weighted moving average with a heavy weight on recent data, should be used. A decision maker must weigh the risk of responding quickly to what might be random fluctuations in the 5 - 13 data against the risk of responding slowly to real
Demand Forecasting
3. Exponential Smoothing - This is a special case of a weighted moving average in which the weights are determined by mathematical formula, rather than assigned by the decision maker. Each new forecast is based on a percentage of the Ft + 1 = aDt + (1-a)Ft previous period's demand and a percentage of the previous period's forecast. That is:
where Ft+1 = forecast of the time series for period t + 1 Dt = actual value of the time series for period t Ft = forecast value for the time series for period t a = smoothing constant (0 1)
5 - 14
Demand Forecasting
Alpha () is a weighting factor with values between zero and one. The sensitivity forecast of adjustments is determined by this smoothing constant. The closer is to zero, the slower the forecast will be to adjust to forecast errors (i.e. the greater the smoothing). Conversely, the closer the value of is to 1.00, the greater the sensitivity and the less the smoothing. Commonly used values of range from .05 to .50.
Impact of a Values on the Weight Attached to Observations in a Time Series Weight Attached To Dt Dt-1 Dt-2 Dt-3 Dt-4 Dt-5 Dt-6 Dt-7 Values .1 .1000 .0900 .0810 .0729 .0656 .0590 .0531 .0478 .2 .2000 .1600 .1280 .1024 .0819 .0655 .0524 .0419 .3 .3000 .2100 .1470 .1029 .0720 .0504 .0353 .0247 .4 .4000 .2400 .1440 .0864 .0518 .0311 .0187 .0112 .5 .5000 .2500 .1250 .0625 .0313 .0156 .0078 .0039
5 - 15
Demand Forecasting
Simple Moving Average - Illustration
Compute a three-period simple moving average forecast given demand for gizmos for the last five periods: Period 1 2 3 4 5 Age 5 4 3 2 1 Demand 42 40 43 40 41
Solution = Forecast for Period 6 MA3 = (43 + 40 + 41) / 3 = 41.33
If actual demand in period 6 is 39, the forecast for period 7 will be: MA3 = (40 + 41 + 39) / 3 = 40.00 Note that in a moving average, as each new actual value becomes available, the forecast is updated by adding the newest value and dropping the oldest and then recomputing the average. Therefore, the forecast "moves" by reflecting only the most recent values.
3-Period Moving Average
50 45 Demand 40 35 30 25 2 4 6 8 10 12 14 16 Period 18 20 22 24 26 28 30 MA3 Demand
5 - 16
Demand Forecasting
y
Exponential Smoothing Models
1. Simple Model - assumes the time series is flat with no trend or seasonality.
t+1 t t
F
= D + (1-)F
t t t-1 t-1 2. Exponential Smoothing for Trend - assumes the time series has a long term linear trend. Trend may exhibit growth or decline. A = D + (1-)(A + T ) t t t-1 t-1
T = (A - A ) + (1 - )T
t+1 t t
3. Exponential Smoothing for Trend and Seasonal - assumes the time series t t t-L t-1 t-1 F = A + variation. Seasonal variation has both a long-term trend and seasonalT should occur at approximately the same time each year and be of the A = ( D / I ) + (1-)(A + T ) same degree. t t t-1 t-1 T = (A - A ) + (1 - )T
t t t t-L
I = (D /A ) + (1- )R
5 - 17
Demand Forecasting
Simple Exponential Smoothing: An Illustration 2
t Actual Demand
170 210 190 230 180 160 200 180 220 200 180 190 200
2
Forecast a = .1
170.0 170.0 174.0 175.6 181.0 180.9 178.8 181.0 180.9 184.8 186.1 185.7 186.1 187.5
Error
t t
Error
t t 2
(D - F )
0.0 40.0 16.0 54.4 -1.0 -20.9 21.2 -1.0 39.1 15.2 -6.1 4.3 13.9
Forecast a = .3
170.0 170.0 182.0 184.4 198.1 192.7 182.9 188.0 185.6 195.9 197.1 192.0 191.4 194.0
Error
t t
Error
t t 2
1 2 3 4 5 6 7 8 9 10 11 12 13
(D - F )
0.0 1600.0 256.0 2959.4 1.1 438.3 447.6 0.9 1531.8 231.8 39.7 18.8 193.2
(D - F )
0.0 40.0 8.0 45.6 -18.1 -32.7 17.1 -8.0 34.4 4.1 -17.1 -2.0 8.6
(D - F )
0.0 1600.0 64.0 2079.4 326.9 1066.4 293.8 64.0 1183.3 16.6 293.9 4.0 73.9
Sum of the errors = (Dt-Ft) = 174.9 Sum of the absolute errors
t t
Sum of the errors = (Dt-Ft) = 79.9 Sum of the absolute errors
t t
= |D -F | = 233.4
= |D -F | = 235.7
5 - 18
Demand Forecasting
SIMPLE EXPONENTIAL SMOOTHING MODEL ACTUAL vs. FORECAST
240 220 200 180 160 140 120 1 2 3 4 5 6 7 8 9 10 11 12 13
Original Demand
a = .3 a = .1
5 - 19
Demand Forecasting
Exponential Smoothing With Trend: An Illustration
Dt (in '000s of tons)
216.00 229.00 255.00 219.00 239.00 275.00 315.00 297.00 286.00 314.00
t
0 1 2 3 4 5 6 7 8 9 10
At (average)
205.00 216.00 227.40 241.75 246.30 253.39 265.98 284.22 295.84 302.95 313.91
Tt (trend)
11.00 11.00 11.04 11.37 10.69 10.33 10.55 11.32 11.35 10.93 10.93
Ft (forecast) At+Tt
216.00 227.00 238.44 253.12 256.99 263.72 276.53 295.55 307.19 313.88
Dt-Ft (error)
0.00 2.00 16.56 -34.12 -17.99 11.28 38.47 1.45 -21.19 0.12
|Dt-Ft| (absolute error)
0.00 2.00 16.56 34.12 17.99 11.28 38.47 1.45 21.19 0.12
(Dt-Ft)^2 (squared error)
0.00 4.00 274.23 1164.39 323.54 127.26 1479.97 2.11 449.07 0.01
A(t) + T(t) = F(t) 205 + 11 = 216 216 + 11 = 227
Sum of Forecast Errors Sum of Absolute Forecast Errors Sum of Squared Forecast Errors - 3.42 143.18 3824.59
Assume A = 205; T = 11; = .2; = .1
5 - 20
Demand Forecasting
TREND EXPONENTIAL SMOOTHING MODEL ACTUAL vs FORECAST
350
D(t) F(t)
300
Demand 250
200
150 1 2 3 4 5 6 7 8 9 10
Time Period
5 - 21
Demand Forecasting
Exponential Smoothing With Trend and Seasonal: An Illustration
t
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Dt (in At Tt units) (average) (trend)
4800 4100 6000 6500 5800 5200 6800 7400 6000 5600 7500 7800 6300 5900 8000 8400
It (seasonal ratio)
0.90 0.80 1.10 1.20 0.96 0.84 1.12 1.20 0.96 0.86 1.13 1.19 0.95 0.86 1.14 1.19
Ft (forecast) [At+Tt]*It-L+K
Dt-Ft (error)
|Dt-Ft| (absolute error)
(Dt-Ft)^2 (squared error)
5500 5689 5889 6016 6123 6227 6393 6552 6639 6715 6832 6969 7080
0 47 85 96 99 100 116 127 117 107 109 116 115
[A(t) + T(t)] x I(t-3) = F(t) (5500 + 0) x 0.90 = 4950 (5689 + 47) x 0.80 = 4589
4950 4589 6572 7334 5971 5324 7259 8044 6497 5858 7843 8428 6835 6296 8457 8958
850 611 228 66 29 276 241 -244 -197 42 157 -28 2030
850 611 228 66 29 276 241 244 197 42 157 28 2970
722500 373457 52104 4367 849 75911 58115 59764 38811 1727 24772 804 1413181
5 - 22
Demand Forecasting
TREND AND SEASONAL EXPONENTIAL SMOOTHING MODEL ACTUAL vs FORECAST
10000 9000 8000 7000
D(t) F(t)
Orders
6000 5000 4000 3000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Time periods
5 - 23
Demand Forecasting
y
Trend Projection: An Alternative to Exponential Smoothing
Whazzit? A method of taking time series data and separating (decomposing) it into
one or more components of trend, seasonal, cyclical, and random variation. Once the data has been "decomposed", we can estimate the values of the individual components and use these estimates to predict future values of the time series. 1. Calculate an annual moving average. 2. Centre the moving average. 3. Divide the centered moving average into the demand values. This is the seasonal-random component. 4. Average the seasonal-random component for the same time period in successive years. This average is the seasonal factor for the time period. 5. Divide each actual demand value by its seasonal factor. This produces deseasonalized demand. 6. Regress deseasonalized demand against time and calculate the trend value and the constant term. 7. Develop a trend forecast. 8. Multiply the trend forecast by the seasonal factor. This is the actual forecast.
Steps:
5 - 24
Demand Forecasting
Trend Projection: An Illustration
Centered Seasonal Moving Moving Random Seasonal Average Average Component Factor
5350 5600 5875 6075 6300 6350 6450 6625 6725 6800 6875 7000 7150 0.932 0.838 1.093 1.143 0.932 0.838 1.093 1.143 0.932 0.838 1.093 1.143 0.932 0.838 1.093 1.143
Year
Year 1
Quarter
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
Time Period
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Sales
4800 4100 6000 6500 5800 5200 6800 7400 6000 5600 7500 7800 6300 5900 8000 8400
Deseasonalized Sales
5149 4894 5488 5685 6222 6207 6219 6472 6436 6684 6860 6822 6758 7043 7317 7347
Year 2
Year 3
Year 4
5475 5738 5975 6188 6325 6400 6538 6675 6763 6838 6938 7075
1.096 1.133 0.971 0.840 1.075 1.156 0.918 0.839 1.109 1.141 0.908 0.834
(Step 1 )
( Step 2 )
( Step 3 )
( Step 4 )
( Step 5 )
5 - 25
Demand Forecasting
Regression Output: Constant = 5099.5 Std Err of Est = 212.6531 R Squared = 0.920804 No. of Observations = 16 Degrees of Freedom = 14 X Coefficient(s) Std Err of Coef. ( Step 6 ) 147.1397 11.53273 Trend Forecast: T(17) = 5100 + 147(17) = 7601 T(18) = 5100 + 147(18) = 7748 T(19) = 5100 + 147(19) = 7895 T(20) = 5100 + 147(20) = 8042 Quarterly Forecast: F(17) = 7601 x .932 = 7084 F(18) = 7748 x .838 = 6493 F(19) = 7895 x 1.093 = 8629 F(20) = 8042 x 1.143 = 9192
( Step 7 )
( Step 8 )
5 - 26
Demand Forecasting
TREND PROJECTION MODEL DESEASONALIZED DATA
Sales Deseasonalized Sales
9000 8000 7000
Quantity 6000
5000 4000 3000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Time Periods
5 - 27
Demand Forecasting
TREND PROJECTION MODEL ACTUAL vs FORECAST
10000 9000 8000 7000
Actual Forecast
Quantity
6000 5000 4000 3000 1 3 5 7 9 11 13 15 17 19
Quarters
5 - 28
Demand Forecasting
Demand Forecasting- Additional Illustration # 1
National Mixer Inc. sells can openers. Monthly sales for a seven-month period were as follows:
Month Feb Mar Apr May Jun Jul Aug a. Plot the monthly data on a sheet of graph paper.
Sales 20 18 15 20 18 22 20
b. Forecast September sales volume using each of the following: (1) A linear trend equation. (2) A five-month moving average. (3) Exponential smoothing with a smoothing constant (a) equal to .20, and a March forecast of 19. (4) The naive approach c. Which method seems least appropriate? Why? d. What does the use of the term sales rather than demand presume?
5 - 29
Demand Forecasting
Demand Forecasting- Additional Illustration # 2
a. Develop a linear trend equation for the following data on freight car loadings, and use it to predict loadings for periods 11 through 14.
Year 1 2 3 4 5 6
Number(`00) 00 220 245 280 275 300 310
Year 7 8 9 10 11 12
Number(`00) 350 360 400 380 420 450
b. Use trend-adjusted exponential smoothing with a = .3 and b = .2 to smooth the data. Forecast periods 11 through 14.
5 - 30

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/ NAME: YOUR_NAME/ STUDENT_ID: UW_ID/ A10Q3

W. Alabama - SE - 101

Thursday, October 23, 2004 Jane Smith SE 101 Teaching Assistant E2-1318 University of Waterloo 200 University Avenue West Waterloo, Ontario N2L 3G1 Dr. J. Atlee Director of Software Engineering Software Engineering Davis Centre University of Waterloo

W. Alabama - ARTS - 306

Sergei Eisenstein:Principle of the Montage in October: Ten Days that Shook the WorldThe Montage as Syntagm Eisenstein called montage "the hieroglyph of the intellectual cinema." Combinations of shots create what is graphically inexpressible in a

W. Alabama - ARTS - 306

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W. Alabama - CO - 351

Dan Moniz's question:-In step 2 of the Network Simplex Method, after we push flow along acycle C in T + uv, could it be that only arc uv is saturated or empty?(So that no arc in the tree could be removed for the update?)Response:--Yes, it

East Los Angeles College - IE - 294

Play and the Emergence of Literacy Nigel Hall(Chapter 1 in Christie, J. (ed) (1991) Play and Early Literacy Development, Albany: State University of New York Press)Introduction Both play and literacy have long been central concerns of educators, a