om3-1 mcgraw-hill/irwin operations management, seventh edition, by william j. stevenson copyright ©...
TRANSCRIPT
OM3-1
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Chapter 3
Forecasting
OM3-2
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
FORECAST:
• A statement about the future
• Used to help managers– Plan the system– Plan the use of the system
OM3-3
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Accounting Cost/profit estimates
Finance Cash flow and funding
Human Resources Hiring/recruiting/training
Marketing Pricing, promotion, strategy
MIS IT/IS systems, services
Operations Schedules, MRP, workloads
Product/service design New products and services
Uses of Forecasts
OM3-4
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
• Assumes causal systempast ==> future
• Forecasts rarely perfect because of randomness
• Forecasts more accurate forgroups vs. individuals
• Forecast accuracy decreases as time horizon increases
I see that you willget an A this semester.
OM3-5
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Elements of a Good Forecast
Timely
AccurateReliable
Mea
ningfu
l
Written
Easy
to u
se
OM3-6
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Steps in the Forecasting Process
Step 1 Determine purpose of forecast
Step 2 Establish a time horizon
Step 3 Select a forecasting technique
Step 4 Gather and analyze data
Step 5 Prepare the forecast
Step 6 Monitor the forecast
“The forecast”
OM3-7
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Forecast Accuracy
• Error - difference between actual value and predicted value
• Average Error (BIAS) – Any Problems!• Mean absolute deviation (MAD)
– Average absolute error
• Mean Absolute Percentage Error (MAPE)• Mean squared error (MSE)
– Average of squared error
• Tracking signal– Ratio of cumulative error and MAD
OM3-8
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
BIAS & MSE
BIAS = Actual forecast)n
(
MSE = Actual forecast)
-1
2n
(
OM3-9
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
MAD & MAPE
MAD = Actual forecastn
MAPE = |Actual - Forecast|)/Actualn
(
OM3-10
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Types of Forecasts
• Judgmental - uses subjective inputs
• Time series - uses historical data assuming the future will be like the past
• Associative models - uses explanatory variables to predict the future
OM3-11
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Judgmental Forecasts
• Executive opinions
• Sales force composite
• Consumer surveys
• Focus Groups
• Outside opinion
• Opinions of managers and staff– Delphi technique
OM3-12
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Time Series Forecasts
• Trend - long-term movement in data
• Seasonality - short-term regular variations in data
• Irregular variations - caused by unusual circumstances
• Random variations - caused by chance
OM3-13
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Forecast Variations
Trend
Irregularvariation
Cycles
Seasonal variations
908988
Figure 3-1
OM3-14
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
• Simple to use
• Virtually no cost
• Data analysis is nonexistent
• Easily understandable
• Cannot provide high accuracy
• Can be a standard for accuracy
Naïve Forecasts
OM3-15
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Techniques for Averaging
• Naïve forecasts
• Arithmetic Mean
• Moving Averages
• Weighted Moving Averages
• Exponential Smoothing
OM3-16
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Definitions
• At = Actual Demand in period t
• Ft = Forecast Demand in period t
• n = Number of past Observations
OM3-17
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
• Stable time series data– F(t) = A(t-1)
• Seasonal variations– F(t) = A(t-n)
• Data with trends– F(t) = A(t-1) + (A(t-1) – A(t-2))
Uses for Naïve Forecasts
OM3-18
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Naive Forecasts
Uh, give me a minute.... We sold 250 wheels lastweek.... Now, next week we should sell....
OM3-19
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Arithmetic Average
Ft+1 = n
Aii = 1n
OM3-20
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Techniques for Averaging
• Moving average
• Weighted moving average
• Exponential smoothing
OM3-21
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Simple Moving Average
600
700
800
900
1 2 3 4 5 6 7 8 9 10 11 12 13
Actual
MA3
MA5
Ft+1 = k
Aii = 1k
Figure 3-4
OM3-22
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Weighted Moving Average
• Ft+1 = At*wt + At-1*wt-1 + At-2*wt-2 + ….+ At-
k*wt-k
where: wi = 1
OM3-23
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Exponential Smoothing
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+1 = Ft + (At - Ft)Or
Ft+1 = At + (1-Ft
OM3-24
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Example 1
• A laundry has experienced the following past demand pattern for garment cleaning.
Period Annual Demand (kgs)
1 15
2 20
3 10
4 20
5 10
6 15
OM3-25
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Example 1 (cont.)
Forecast demand for period seven using:
a) Last period demand
b) The arithmetic average
c) Three period moving average
d) Weighted moving average with the weights as .2, .3, and .5
e) Exponential smoothing with = 0.1
OM3-26
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Period Actual Alpha = 0.1 Error Alpha = 0.4 Error1 422 40 42 -2.00 42 -23 43 41.8 1.20 41.2 1.84 40 41.92 -1.92 41.92 -1.925 41 41.73 -0.73 41.15 -0.156 39 41.66 -2.66 41.09 -2.097 46 41.39 4.61 40.25 5.758 44 41.85 2.15 42.55 1.459 45 42.07 2.93 43.13 1.87
10 38 42.36 -4.36 43.88 -5.8811 40 41.92 -1.92 41.53 -1.5312 41.73 40.92
Example of Picking a Smoothing Constant
OM3-27
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Picking a Smoothing Constant
35
40
45
50
1 2 3 4 5 6 7 8 9 10 11 12
Period
Dem
and .1
.4
Actual
OM3-28
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Common Nonlinear Trends
Parabolic
Exponential
Growth
Figure 3-5
OM3-29
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Linear Trend Equation
• b is similar to the slope. 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.
Yt = a + bt
0 1 2 3 4 5 t
Y
OM3-30
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Calculating a and b
b = n (ty) - t y
n t2 - ( t)2
a = y - b t
n
OM3-31
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Linear Trend Equation Example
t yW e e k t 2 S a l e s t y
1 1 1 5 0 1 5 02 4 1 5 7 3 1 43 9 1 6 2 4 8 64 1 6 1 6 6 6 6 45 2 5 1 7 7 8 8 5
t = 1 5 t 2 = 5 5 y = 8 1 2 t y = 2 4 9 9( t ) 2 = 2 2 5
OM3-32
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Linear Trend Calculation
y = 143.5 + 6.3t
a = 812 - 6.3(15)
5 =
b = 5 (2499) - 15(812)
5(55) - 225 =
12495-12180
275 -225 = 6.3
143.5
OM3-33
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Forecasting: Trend Adjustment
Example 22 (a). Using the data below, develop a linear regression line to capture the trend component and predict for quarter numbers 15, 16 and 17. 2 (b) Then, predict for the same periods using both the trend and seasonal components.
Quarter Number
t
Demand Y
Quarter Number
t
Demand Y
1 3.5 8 16 2 8 9 15.5 3 5.5 10 20 4 10 11 17.5 5 9.5 12 22 6 14 13 21.5 7 11.5 14 26
OM3-34
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Solution Example 2 (a) - Trend Equation
• Using Excel, the following can be obtained as the best fit line for Example 2 (a).
Y = 2.725 + 1.546t
OM3-35
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Forecasting: Seasonal Adjustments
• Seasonal Variations are regularly repeating upward or downward movements in series values that can be tied to recurring events.
• Examples include winter and summer clothing, ski equipment, rush hour traffic, restaurants, and customer service assistance.
•Additive vs. Multiplicative Models
OM3-36
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Forecasting: Seasonal Adjustments
•Use multiplicative method known as Ratio-to-Trend Method
Actual Observation
Trend Value
OM3-37
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Forecasting: Seasonal Adjustments
• Use the linear regression model to capture the trend component and forecast each past period.• Divide the actual observation by the trend value to obtain a ratio.• Average ratios of similar periods to obtain seasonal factors.• Multiply the trend forecasted value by the appropriate seasonal factors to obtain seasonally adjusted forecasts.• See example 2 (b)
OM3-38
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Associative Forecasting
• Predictor variables - used to predict values of variable interest
• Regression - technique for fitting a line to a set of points
• Least squares line - minimizes sum of squared deviations around the line
OM3-39
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Associative Forecasting
• Again, the least squares line equation is used:
y = a + b(x)
where,
y = Predicted (dependent) variable
x = Predictor (independent) variable
b = Slope of the line
a = Value of y, when x=0 (or the y intercept)
OM3-40
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Associative Forecasting
Then,
22 xxn
yxxynb
)()(
))(()(
and
n
xbya
)(
OM3-41
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Associative Forecasting
• Coefficient of Correlation (r): The coefficient of correlation r is a relative measure of such a relationship between two variables.
• Coefficient of Determination (r2)
• It is a statistic that indicates how well a regression line explains or fits the observed data.
• -1 < r < +1
• r > 0 implies positive correlation
• r < 0 implies negative correlation
OM3-42
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Associative Forecasting
• -1 < r < +1
• r > 0 implies positive correlation
• r < 0 implies negative correlation
• R can be calculated by using the following equation:
2222 yynxxn
yxxynr
)()(.)()(
))(()(
OM3-43
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Associative Forecasting
• Control Limits on the Forecast Value
Upper Limit = Forecast Value + z (Syx)
Lower Limit = Forecast Value – z (Syx)
where, z is the standard normal deviate and
2n
xybyayS
2
yx
)()(
OM3-44
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Linear Model Seems Reasonable
0
10
20
30
40
50
0 5 10 15 20 25
X Y7 152 106 134 15
14 2515 2716 2412 2014 2720 4415 347 17
Computedrelationship
OM3-45
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Tracking Signal
• Tracking Signal is a measurement that indicates whether the forecast average is keeping pace with any genuine upward or downward changes in demand
OM3-46
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Tracking Signal
Tracking signal = (Actual-forecast)
MAD
Tracking signal = (Actual-forecast)Actual-forecast
n
OM3-47
McGraw-Hill/IrwinOperations Management, Seventh Edition, by William J. StevensonCopyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
Forecasting
Tracking Signal
• ExampleWeek Forecast Actual Deviation
(Actual – Forecast)
Running Sum of (Actual-
Forecast)
Absolute Deviation
Sum of Absolute Deviation
MAD TS
1 100 95 -5 -5 5 5 5 -12 102 105 3 -2 3 8 4 -0.53 98 110 12 10 12 20 6.66666667 1.54 96 94 -2 8 2 22 5.5 1.454545455 101 106 5 13 5 27 5.4 2.407407416 100 107 7 20 7 34 5.66666667 3.52941176