Production and Operations Management: Manufacturing and Services
McGraw-Hill/Irwin Copyright 2009 by The McGraw-Hill Companies, Inc. All rights res Chapter 15 Demand Management and Forecasting 15-3 OBJECTIVES Demand Management Qualitative Forecasting Methods Simple & Weighted Moving Average Forecasts Exponential Smoothing Simple Linear Regression Web-Based Forecasting 15-4 Demand Management Independent Demand: Finished Goods Dependent Demand: Raw Materials, Component parts, Sub-assemblies, etc. A
C(2) B(4) D(2) E(1) D(3) F(2) 15-5 Independent Demand: What a firm can do to manage it? Can take an active role to influence demand Can take a passive role and simply respond to demand 15-6 Types of Forecasts Qualitative (Judgmental) Quantitative Time Series Analysis Causal Relationships Simulation
15-7 Components of Demand Average demand for a period of time Trend Seasonal element Cyclical elements Random variation Autocorrelation 15-8 Finding Components of Demand Seasonal Seasonalvariation variation Sales x x x x xx x x xx x x x
x x x x x x x x x x x x xxxx 1 2 x x x x 3 Year x x x
x x x x x x x x 4 Linear Linear x x Trend Trend x 15-9 Qualitative Methods Executive Judgment Historical analogy Grass Roots Qualitative
Market Research Methods Delphi Method Panel Consensus 15-10 Delphi Method l. Choose the experts to participate representing a variety of knowledgeable people in different areas 2. Through a questionnaire (or E-mail), obtain forecasts (and any premises or qualifications for the forecasts) from all participants 3. Summarize the results and redistribute them to the participants along with appropriate new questions 4. Summarize again, refining forecasts and conditions, and again develop new questions 5. Repeat Step 4 as necessary and distribute the final results to all participants 15-11 Time Series Analysis Time series forecasting models try to predict the future based on past
data You can pick models based on: 1. Time horizon to forecast 2. Data availability 3. Accuracy required 4. Size of forecasting budget 5. Availability of qualified personnel 15-12 Simple Moving Average Formula The simple moving average model assumes an average is a good estimator of future behavior The formula for the simple moving average is: A + A + A +...+A A + A + A +...+A t-1 t-2 t-3
t-n t-1 t-2 t-3 t-n FFtt == nn Ft = Forecast for the coming period N = Number of periods to be averaged A t-1 = Actual occurrence in the past period for up to n periods 15-13 Simple Moving Average Problem (1) Week 1 2 3 4 5 6 7 8 9 10 11 12 Demand 650 678
720 785 859 920 850 758 892 920 789 844 A + A + A +...+A A + A + A +...+A t-1 t-2 t-3 t-n t-1 t-2 t-3 t-n FFtt == nn
Question: Question: What What are are the the 33week week and and 6-week 6-week moving moving average average forecasts forecasts for for demand? demand? Assume Assume you you only only have have 33 weeks weeks and and 66 weeks weeks of of actual actual demand demand data data for for the the respective respective forecasts
howthe the lines linessmooth smooth out outto toreveal reveal the theoverall overallupward upward trend trend in in this thisexample example 1000 Demand 900 Demand 800 3-Week 700 6-Week 600 500 1 2 3 4 5 6 7 8 9 10 11 12
Week Note Notehow howthe the 3-Week 3-Weekisis smoother smootherthan than the theDemand, Demand, and and6-Week 6-Weekisis even evensmoother smoother 15-16 Simple Moving Average Problem (2) Data Week 1 2 3 4 5 6 7
Demand 820 775 680 655 620 600 575 Question: Question: What What is is the the 33 week week moving moving average average forecast forecast for for this this data? data? Assume Assume you you only only have have 33 weeks weeks and
and 55 weeks weeks of of actual actual demand demand data data for for the the respective respective forecasts forecasts 15-17 Simple Moving Average Problem (2) Solution Week 1 2 3 4 5 6 7 Demand 820 775 680 655
620 600 575 3-Week 5-Week F4=(820+775+680)/3 =758.33 758.33 703.33 651.67 625.00 F6=(820+775+680 +655+620)/5 =710.00 710.00 666.00 15-18 Weighted Moving Average Formula While While the the moving moving average average formula formula implies
implies an an equal equal weight weight being being placed placed on on each each value value that that isis being being averaged, averaged, the the weighted weighted moving moving average average permits permits an an unequal unequal weighting weighting on on prior prior time time periods periods The The formula formula for for the the moving moving average
average is: is: FFt t == w + w A t-2 ++ w +...+w A t-n w11A At-1 w33A At-3 t-1 + w22 At-2 t-3 +...+wnn At-n wwt ==weight weightgiven givento totime timeperiod periodt t t occurrence occurrence(weights (weightsmust mustadd addto toone) one) nn ww ==11 i=1
i=1 ii 15-19 Weighted Moving Average Problem (1) Data Question: Question:Given Giventhe theweekly weeklydemand demandand andweights, weights,what whatisis th the theforecast forecastfor forthe the44thperiod periodor orWeek Week4? 4? Week 1 2 3 4
Demand 650 678 720 Weights: t-1 .5 t-2 .3 t-3 .2 Note Notethat thatthe theweights weightsplace placemore moreemphasis emphasison onthe the most mostrecent recentdata, data,that thatisistime timeperiod periodt-1 t-1 15-20 Weighted Moving Average Problem (1) Solution
Week 1 2 3 4 Demand Forecast 650 678 720 693.4 F4 = 0.5(720)+0.3(678)+0.2(650)=693.4 15-21 Weighted Moving Average Problem (2) Data Question: Question:Given Giventhe theweekly weeklydemand demandinformation informationand and weights, weights,what whatisisthe theweighted weightedmoving movingaverage averageforecast
4 5 Demand Forecast 820 775 680 655 672 F5 = (0.1)(755)+(0.2)(680)+(0.7)(655)= 672 15-23 Exponential Smoothing Model FFtt == FFt-1 + (A F ) + (A F t-1 t-1 t-1 t-1 t-1) Where : Ft Forcast value for the coming t time period Ft - 1 Forecast value in 1 past time period At - 1 Actual occurance in the past t time period
Alpha smoothing constant 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 15-24 Exponential Smoothing Problem (1) Data Week 1 2 3 4 5 6 7 8 9 10 Demand 820 775 680 655 750 802 798 689 775
Question: Question: Given Given the the weekly weekly demand demand data, data, what what are are the the exponential exponential smoothing smoothing forecasts forecasts for for periods periods 2-10 2-10 using using =0.10 =0.10 and and =0.60? =0.60? Assume Assume FF11=D =D11 15-25
Exponential Smoothing Problem (2) Data Question: What What are are Week Demand Question: the exponential exponential 1 820 the smoothing forecasts forecasts 2 775 smoothing for periods periods 2-5 2-5 using using 3 680 for =0.5? 4 655 aa =0.5? 5 Assume Assume FF11=D =D11 15-28 Exponential Smoothing Problem (2) Solution F1=820+(0.5)(820-820)=820
Week 1 2 3 4 5 Demand 820 775 680 655 F3=820+(0.5)(775-820)=797.75 0.5 820.00 820.00 797.50 738.75 696.88 15-29 The MAD Statistic to Determine Forecasting Error nn MAD MAD == AA --FF
t=1 t=1 tt tt 1 MAD 0.8 standard deviation 1 standard deviation 1.25 MAD nn The ideal MAD is zero which would mean there is no forecasting error The larger the MAD, the less the accurate the resulting model 15-30 MAD Problem Data Question: Question: What What isis the the MAD MAD value value given given the the forecast forecast values values in in the
220 250 210 300 325 Forecast Abs Error n/a 255 5 205 5 320 20 315 10 40 nn MAD MAD== AA --FF t=1 t=1 tt nn tt
40 == 40 ==10 44 10 Note Notethat thatby byitself, itself,the theMAD MAD only onlylets letsus usknow knowthe themean mean error errorin inaaset setof offorecasts forecasts 15-32 Tracking Signal Formula The Tracking Signal or TS is a measure that indicates whether the forecast average is keeping pace with any genuine upward or
downward changes in demand. Depending on the number of MADs selected, the TS can be used like a quality control chart indicating when the model is generating too much error in its forecasts. The TS formula is: RSFE RSFE Running Running sum sum of of forecast forecast errors errors TS == TS == MAD Mean MAD Mean absolute absolute deviation deviation 15-33 Simple Linear Regression Model The Thesimple simplelinear linearregression regression
model modelseeks seeksto tofit fitaaline line through throughvarious variousdata dataover over time time Yt = a + bx Y a 0 1 2 3 4 5 x (Time) Is Isthe thelinear linearregression regressionmodel model Yt is the regressed forecast value or dependent
variable in the model, a is the intercept value of the the regression line, and b is similar to the slope of the regression line. 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. 15-34 Simple Linear Regression Formulas for Calculating a and b aa == yy-- bx bx -- n(y)(x) xy n(y)(x) xy bb == 22 22 n(x)) xx -- n(x 15-35 Simple Linear Regression Problem Data Question: Question:Given Giventhe thedata databelow,
15-36 Answer: Answer: First, First,using using the thelinear linear regression regressionformulas, formulas,we we can cancompute computea aand andb b Week Week*Week Sales Week*Sales 1 1 150 150 2 4 157 314 3 9 162 486
4 16 166 664 5 25 177 885 3 55 162.4 2499 Average Sum Average Sum xy --5(162.4)(3) 63 xy--n( n(y)(x) y)(x) 2499 2499 5(162.4)(3) 63= 6.3 bb== == 10 = 6.3 55 5
( 9 ) x n(x ) 55 5(9 ) 10 x - n(x ) 22 22 aa== yy--bx bx==162.4 162.4--(6.3)(3) (6.3)(3)==143.5 143.5 15-37 The resulting regression model is: Yt = 143.5 + 6.3x Sales Now if we plot the regression generated forecasts against the actual sales we obtain the following chart: 180 175
170 165 160 155 150 145 140 135 Sales Forecast 1 2 3 Period 4 5 15-38 Web-Based Forecasting: CPFR Collaborative Planning, Forecasting, and Replenishment (CPFR) a Web-based tool used to coordinate demand forecasting, production and purchase planning, and inventory replenishment between supply chain trading partners. Used to integrate the multi-tier or n-Tier supply
chain, including manufacturers, distributors and retailers. CPFRs objective is to exchange selected internal information to provide for a reliable, longer term future views of demand in the supply chain. CPFR uses a cyclic and iterative approach to derive consensus forecasts. 15-39 Web-Based Forecasting: Steps in CPFR 1. Creation of a front-end partnership agreement. 2. Joint business planning 3. Development of demand forecasts 4. Sharing forecasts 5. Inventory replenishment 15-40 Question Bowl Which of the following is a classification of a basic type of forecasting? a. Transportation method b. Simulation c. Linear programming d. All of the above e. None of the above
Answer: b. Simulation (There are four types including Qualitative, Time Series Analysis, Causal Relationships, and Simulation.) 15-41 Question Bowl Which of the following is an example of a Qualitative type of forecasting technique or model? a. Grass roots b. Market research c. Panel consensus d. All of the above e. None of the above Answer: d. All of the above (Also includes Historical Analogy and Delphi Method.) 15-42 Question Bowl Which of the following is an example of a Time Series Analysis type of forecasting technique or model? a. Simulation b. Exponential smoothing c. Panel consensus d. All of the above e. None of the above
Answer: b. Exponential smoothing (Also includes Simple Moving Average, Weighted Moving Average, Regression Analysis, Box Jenkins, Shiskin Time Series, and Trend Projections.) 15-43 Question Bowl Which of the following is a reason why a firm should choose a particular forecasting model? a. Time horizon to forecast b. Data availability c. Accuracy required d. Size of forecasting budget e. All of the above Answer: e. All of the above (Also should include availability of qualified personnel .) 15-44 Question Bowl Which of the following are ways to choose weights in a Weighted Moving Average forecasting model? a. Cost b. Experience c. Trial and error d. Only b and c above
e. None of the above Answer: d. Only b and c above 15-45 Question Bowl Which of the following are reasons why the Exponential Smoothing model has been a well accepted forecasting methodology? a. It is accurate b. It is easy to use c. Computer storage requirements are small d. All of the above e. None of the above Answer: d. All of the above 15-46 Question Bowl The value for alpha or must be between which of the following when used in an Exponential Smoothing model? a. 1 to 10 b. 1 to 2 c. 0 to 1 d. -1 to 1
e. Any number at all Answer: c. 0 to 1 15-47 Question Bowl Which of the following are sources of error in forecasts? a. Bias b. Random c. Employing the wrong trend line d. All of the above e. None of the above Answer: d. All of the above 15-48 Question Bowl Which of the following would be the best MAD values in an analysis of the accuracy of a forecasting model? a. 1000 b. 100 c. 10 d. 1 e. 0 Answer: e. 0
15-49 Question Bowl If a Least Squares model is: Y=25+5x, and x is equal to 10, what is the forecast value using this model? a. 100 b. 75 c. 50 d. 25 e. None of the above Answer: b. 75 (Y=25+5(10)=75) 15-50 Question Bowl Which of the following are examples of seasonal variation? a. Additive b. Least squares c. Standard error of the estimate d. Decomposition e. None of the above Answer: a. Additive (The other type is of seasonal variation is Multiplicative.) 15-51
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