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Forecasting August 29, Wednesday Course Structure Introduction Operations Strategy & Competitiveness Quality Management Strategic Decisions (some) Design of Products Process Selection Capacity and and Services and Design Facility Decisions Forecasting Tactical & Operational Decisions Forecasting Predict the next number in the pattern: a) 3.7, 3.7, 3.7, 3.7, 3.7, ? b) 2.5, 4.5, 6.5, 8.5, 10.5, ? c) 5.0, 7.5, 6.0, 4.5, 7.0, 9.5, 8.0, 6.5, ? Forecasting Predict the next number in the pattern: a) 3.7, 3.7, 3.7, 3.7, 3.7, 3.7 b) 2.5, 4.5, 6.5, 8.5, 10.5, 12.5 c) 5.0, 7.5, 6.0, 4.5, 7.0, 9.5, 8.0, 6.5, 9.0 Outline What is forecasting? Types of forecasts Time-Series forecasting Naïve Moving Average Exponential Smoothing Regression Good forecasts What is Forecasting? Process of predicting a future event based on historical data Educated Guessing Underlying basis of all business decisions Production Inventory Personnel Facilities Why do we need to forecast? In general, forecasts are almost always wrong. So, Throughout the day we forecast very different things such as weather, traffic, stock market, state of our company from different perspectives. Virtually every business attempt is based on forecasting. Not all of them are derived from sophisticated methods. However, “Best" educated guesses about future are more valuable for purpose of Planning than no forecasts and hence no planning. Importance of Forecasting in OM Departments throughout the organization depend on forecasts to formulate and execute their plans. Finance needs forecasts to project cash flows and capital requirements. Human resources need forecasts to anticipate hiring needs. Production needs forecasts to plan production levels, workforce, material requirements, inventories, etc. Importance of Forecasting in OM Demand is not the only variable of interest to forecasters. Manufacturers also forecast worker absenteeism, machine availability, material costs, transportation and production lead times, etc. Besides demand, service providers are also interested in forecasts of population, of other demographic variables, of weather, etc. Types of Forecasts by Time Horizon Quantitative Short-range forecast methods Usually < 3 months Job scheduling, worker assignments Detailed use of Medium-range forecast system 3 months to 2 years Sales/production planning Long-range forecast > 2 years Design of system New product planning Qualitative Methods Forecasting During the Life Cycle Introduction Growth Maturity Decline Qualitative models Quantitative models - Executive judgment - Time series analysis - Market research - Regression analysis -Survey of sales force -Delphi method Sales Time Qualitative Forecasting Methods Qualitative Forecasting Models Sales Delphi Executive Market Force Method Judgement Research/ Composite Survey Smoothing Qualitative Methods Briefly, the qualitative methods are: Executive Judgment: Opinion of a group of high level experts or managers is pooled Sales Force Composite: Each regional salesperson provides his/her sales estimates. Those forecasts are then reviewed to make sure they are realistic. All regional forecasts are then pooled at the district and national levels to obtain an overall forecast. Market Research/Survey: Solicits input from customers pertaining to their future purchasing plans. It involves the use of questionnaires, consumer panels and tests of new products and services. Qualitative Methods Delphi Method: As opposed to regular panels where the individuals involved are in direct communication, this method eliminates the effects of group potential dominance of the most vocal members. The group involves individuals from inside as well as outside the organization. Typically, the procedure consists of the following steps: Each expert in the group makes his/her own forecasts in form of statements The coordinator collects all group statements and summarizes them The coordinator provides this summary and gives another set of questions to each group member including feedback as to the input of other experts. The above steps are repeated until a consensus is reached. . Quantitative Forecasting Methods Quantitative Forecasting Time Series Regression Models Models 2. Moving 3. Exponential 1. Naive Average Smoothing a) simple a) level b) weighted b) trend c) seasonality Quantitative Forecasting Methods Quantitative Forecasting Time Series Regression Models Models 2. Moving 3. Exponential 1. Naive Average Smoothing a) simple a) level b) weighted b) trend c) seasonality Time Series Models Try to predict the future based on past data Assume that factors influencing the past will continue to influence the future Time Series Models: Components Random Trend Seasonal Composite Product Demand over Time Demand for product or service Year Year Year Year 1 2 3 4 Product Demand over Time Trend component Seasonal peaks Demand for product or service Actual Random demand line variation Year Year Year Year 1 2 3 4 Now let’s look at some time series approaches to forecasting… Borrowed from Heizer/Render - Principles of Operations Management, 5e, and Operations Management, 7e Quantitative Forecasting Methods Quantitative Time Series Models Models 2. Moving 3. Exponential 1. Naive Average Smoothing a) simple a) level b) weighted b) trend c) seasonality 1. Naive Approach Demand in next period is the same as demand in most recent period May sales = 48 → June forecast = 48 Usually not good 2a. Simple Moving Average Assumes an average is a good estimator of future behavior Used if little or no trend Used for smoothing A t + A t -1 + A t -2 + ... + A t -n 1 Ft 1 = n Ft+1 = Forecast for the upcoming period, t+1 n = Number of periods to be averaged At = Actual occurrence in period t A t + A t -1 + A t -2 + ... + A t -n 1 Ft 1 = n 2a. Simple Moving Average You’re manager in Amazon’s electronics department. You want to forecast ipod sales for months 4-6 using a 3-period moving average. Sales Month (000) 1 4 2 6 3 5 4 ? 5 ? 6 ? A t + A t -1 + A t -2 + ... + A t -n 1 Ft 1 = n 2a. Simple Moving Average You’re manager in Amazon’s electronics department. You want to forecast ipod sales for months 4-6 using a 3-period moving average. Sales Moving Average Month (000) (n=3) 1 4 NA 2 6 NA 3 5 NA 4 ? (4+6+5)/3=5 5 ? 6 ? 2a. Simple Moving Average What if ipod sales were actually 3 in month 4 Sales Moving Average Month (000) (n=3) 1 4 NA 2 6 NA 3 5 NA 4 ? 3 5 5 ? 6 ? 2a. Simple Moving Average Forecast for Month 5? Sales Moving Average Month (000) (n=3) 1 4 NA 2 6 NA 3 5 NA 4 3 5 5 ? (6+5+3)/3=4.667 6 ? 2a. Simple Moving Average Actual Demand for Month 5 = 7 Sales Moving Average Month (000) (n=3) 1 4 NA 2 6 NA 3 5 NA 4 3 5 5 ? 7 4.667 6 ? 2a. Simple Moving Average Forecast for Month 6? Sales Moving Average Month (000) (n=3) 1 4 NA 2 6 NA 3 5 NA 4 3 5 5 7 4.667 6 ? (5+3+7)/3=5 2b. Weighted Moving Average Gives more emphasis to recent data Ft 1 = w1A t + w 2 A t -1 + w 3A t -2 + ... + w n A t -n 1 Weights decrease for older data sum to 1.0 Simple moving average models weight all previous periods equally Ft 1 = w1A t + w 2 A t -1 + w 3A t -2 + ... + w n A t -n 1 2b. Weighted Moving Average: 3/6, 2/6, 1/6 Month Sales Weighted (000) Moving Average 1 4 NA 2 6 NA 3 5 NA 4 ? 31/6 = 5.167 5 ? 6 ? Ft 1 = w1A t + w 2 A t -1 + w 3A t -2 + ... + w n A t -n 1 2b. Weighted Moving Average: 3/6, 2/6, 1/6 Month Sales Weighted (000) Moving Average 1 4 NA 2 6 NA 3 5 NA 4 3 31/6 = 5.167 5 7 25/6 = 4.167 6 32/6 = 5.333 3a. Exponential Smoothing Assumes the most recent observations have the highest predictive value gives more weight to recent time periods Ft+1 = Ft + a(At - Ft) et Ft+1 = Forecast value for time t+1 Need initial At = Actual value at time t forecast Ft a = Smoothing constant to start. 3a. Exponential Smoothing – Example 1 Ft+1 = Ft + a(At - Ft) i Ai Week Demand 1 820 Given the weekly demand 2 775 data what are the exponential 3 680 smoothing forecasts for 4 655 periods 2-10 using a=0.10? 5 750 6 802 Assume F1=D1 7 798 8 689 9 775 10 3a. Exponential Smoothing – Example 1 Ft+1 = Ft + a(At - Ft) i Ai Fi Week Demand a = 0.1 0.6 1 820 820.00 820.00 2 775 820.00 820.00 3 680 F2815.50 a(A1–F1) =820+.1(820–820) = F1+ 793.00 4 655 801.95 725.20=820 5 750 787.26 683.08 6 802 783.53 723.23 7 798 785.38 770.49 8 689 786.64 787.00 9 775 776.88 728.20 10 776.69 756.28 3a. Exponential Smoothing – Example 1 Ft+1 = Ft + a(At - Ft) i Ai Fi Week Demand a = 0.1 0.6 1 820 820.00 820.00 2 775 820.00 820.00 3 680 815.50 793.00 F3 = F2+ a(A2–F2) =820+.1(775–820) 4 655 801.95 725.20 5 750 787.26 683.08=815.5 6 802 783.53 723.23 7 798 785.38 770.49 8 689 786.64 787.00 9 775 776.88 728.20 10 776.69 756.28 3a. Exponential Smoothing – Example 1 Ft+1 = Ft + a(At - Ft) i Ai Fi Week Demand a = 0.1 0.6 1 820 820.00 820.00 2 775 820.00 820.00 3 680 815.50 793.00 4 655 801.95 725.20 5 750 787.26 683.08 This process 6 802 783.53 723.23 continues 7 798 785.38 770.49 through week 8 689 786.64 787.00 10 9 775 776.88 728.20 10 776.69 756.28 3a. Exponential Smoothing – Example 1 Ft+1 = Ft + a(At - Ft) i Ai Fi Week Demand a = 0.1 a = 0.6 1 820 820.00 820.00 2 775 820.00 820.00 3 680 815.50 793.00 4 655 801.95 725.20 5 750 787.26 683.08 What if the 6 802 783.53 723.23 a constant 7 798 785.38 770.49 equals 0.6 8 689 786.64 787.00 9 775 776.88 728.20 10 776.69 756.28 3a. Exponential Smoothing – Example 2 Ft+1 = Ft + a(At - Ft) i Ai Fi Month Demand a = 0.3 a = 0.6 January 120 100.00 100.00 February 90 106.00 112.00 March 101 101.20 98.80 April 91 101.14 100.12 May 115 98.10 94.65 What if the June 83 103.17 106.86 a constant July 97.12 92.54 equals 0.6 August September 3a. Exponential Smoothing – Example 3 Company A, a personal computer producer purchases generic parts and assembles them to final product. Even though most of the orders require customization, they have many common components. Thus, managers of Company A need a good forecast of demand so that they can purchase computer parts accordingly to minimize inventory cost while meeting acceptable service level. Demand data for its computers for the past 5 months is given in the following table. 3a. Exponential Smoothing – Example 3 Ft+1 = Ft + a(At - Ft) i Ai Fi Month Demand a = 0.3 a = 0.5 January 80 84.00 84.00 February 84 82.80 82.00 March 82 83.16 83.00 April 85 82.81 82.50 May 89 83.47 83.75 What if the June 85.13 86.38 a constant July ?? ?? equals 0.5 3a. Exponential Smoothing How to choose α depends on the emphasis you want to place on the most recent data Increasing α makes forecast more sensitive to recent data Forecast Effects of Smoothing Constant a Ft+1 = Ft + a (At - Ft) or Ft+1 = a At + a(1- a) At - 1 + a(1- a)2At - 2 + ... w1 w2 w3 Weights a= Prior Period 2 periods ago 3 periods ago a a(1 - a) a(1 - a)2 a= 0.10 10% 9% 8.1% a= 0.90 90% 9% 0.9% To Use a Forecasting Method Collect historical data Select a model Moving average methods Select n (number of periods) For weighted moving average: select weights Exponential smoothing Select a Selections should produce a good forecast …but what is a good forecast? A Good Forecast Has a small error Error = Demand - Forecast Measures of Forecast Error et n a. MAD = Mean Absolute Deviation A t=1 t - Ft MAD = n n b. MSE = Mean Squared Error A t - Ft 2 t =1 MSE = n c. RMSE = Root Mean Squared Error RMSE = MSE Ideal values =0 (i.e., no forecasting error) n MAD Example A t=1 t - Ft = 40 =10 MAD = 4 n What is the MAD value given the forecast values in the table below? At Ft Month Sales Forecast |At – Ft| 1 220 n/a 2 250 255 5 3 210 205 5 4 300 320 20 5 325 315 10 = 40 n A t - Ft 2 t =1 = 550 =137.5 MSE/RMSE Example MSE = n 4 What is the MSE value? RMSE = √137.5 =11.73 At Ft Month Sales Forecast |At – Ft| (At – Ft)2 1 220 n/a 2 250 255 5 25 3 210 205 5 25 4 300 320 20 400 5 325 315 10 100 = 550 Measures of Error 1. Mean Absolute Deviation (MAD) n t At Ft et |et| et2 e MAD 1 t 84 = 14 Jan 120 100 20 20 400 n 6 -16 16 Feb 90 106 256 2a. Mean Squared Error -1 1 1 (MSE) Mar 101 102 n -10 10 100 et 2 April 91 101 MSE 1 1,446 17 17 289 n = 241 May 115 98 6 -20 20 400 2b. Root Mean Squared Error June 83 103 (RMSE) -10 84 1,446 An accurate forecasting system will have small MAD, RMSE MSE MSE and RMSE; ideally equal to zero. A large error may indicate that either the forecasting method used or the = SQRT(241) parameters such as α used in the method are wrong. Note: In the above, n is the number of periods, which is =15.52 Forecast Bias How can we tell if a forecast has a positive or negative bias? TS = Tracking Signal Good tracking signal has low values RSFE (actual t forecastt ) TS = = t MAD Mean absolute deviation MAD 30 Quantitative Forecasting Methods Quantitative Forecasting Time Series Regression Models Models 2. Moving 3. Exponential 1. Naive Average Smoothing a) simple a) level b) weighted b) trend c) seasonality Exponential Smoothing (continued) We looked at using exponential smoothing to forecast demand with only random variations Ft+1 = Ft + a (At - Ft) Ft+1 = Ft + a At – a Ft Ft+1 = a At + (1-a) Ft Exponential Smoothing (continued) We looked at using exponential smoothing to forecast demand with only random variations What if demand varies due to randomness and trend? What if we have trend and seasonality in the data? Regression Analysis as a Method for Forecasting Regression analysis takes advantage of the relationship between two variables. Demand is then forecasted based on the knowledge of this relationship and for the given value of the related variable. Ex: Sale of Tires (Y), Sale of Autos (X) are obviously related If we analyze the past data of these two variables and establish a relationship between them, we may use that relationship to forecast the sales of tires given the sales of automobiles. The simplest form of the relationship is, of course, linear, hence it is Sales of Autos (100,000) referred to as a regression line. Formulas y=a+bx where, xy n x y x y b x nx 2 2 x y a y bx Regression – Example y = a+ b X b xy n x y a y bx x nx 2 2 MonthAdvertising Sales X 2 XY January 3 1 9.00 3.00 February 4 2 16.00 8.00 March 2 1 4.00 2.00 April 5 3 25.00 15.00 May 4 2 16.00 8.00 June 2 1 4.00 2.00 July TOTAL 20 10 74 38 General Guiding Principles for Forecasting 1. Forecasts are more accurate for larger groups of items. 2. Forecasts are more accurate for shorter periods of time. 3. Every forecast should include an estimate of error. 4. Before applying any forecasting method, the total system should be understood. 5. Before applying any forecasting method, the method should be tested and evaluated. 6. Be aware of people; they can prove you wrong very easily in forecasting FOR JULY 2nd MONDAY READ THE CHAPTERS ON Forecasting Product and service design

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posted: | 9/21/2011 |

language: | English |

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