Operations Management (2) Forecasting Lessons 1 and 2 Prof. Upendra Kachru Prediction Prediction Reflects judgment after taking all considerations into account Based on intuition Involves anticipated changes in future that may or may not happen Based on unique representations It can be biased No error analysis Prof. Upendra Kachru Operations Management Forecasting Forecasting Involves the projection of the past into the future Estimating the demand on the basis of factors that generated the demand Based on theoretical model It is objective Error Analysis is possible Results are replicable Prof. Upendra Kachru Operations Management A forecast is an estimate of a future event achieved by systematically combining and casting forward , in a predetermined way, data about the past. DEFINING FORECASTING Prof. Upendra Kachru Operations Management Forecasting vs. Prediction Forecasting Involves the projection of the past into the future Prediction Reflects management’s judgment after taking all considerations into account Estimating the demand on the basis of factors that generated the demand Involves anticipated changes in future that may or may not generate the demand Based on intuition It can be biased No error analysis Based on unique representations Based on theoretical model It is objective Error Analysis is possible Results are replicable Prof. Upendra Kachru Operations Management Forecasting is the start of any planning activity. The main purpose of forecasting is to estimate the occurrence, timing or magnitude of future events. WHY FORECASTING? Prof. Upendra Kachru Operations Management The Decision making Cycle The decision making cycle reflects how organizations use forecasting to reduce the impact of market forces on a business. Forecasts help management take into account external factors that impact operations and reduce the uncertainty. Prof. Upendra Kachru Operations Management Decision Types requiring Forecasting Types of Decision Short term Medium term Long term Planning Strategies & facilities Specific demand Aggregate demand Forecasting horizon in years Prof. Upendra Kachru Operations Management Demand Forecasting Demand Forecasting is the activity of estimating the quantity of a product or service that consumers will purchase. Demand forecasting involves techniques including both formal and informal methods. Demand forecasting may be used in making scheduling decisions, in assessing future capacity requirements, or in making decisions on whether to enter a new market. Prof. Upendra Kachru Operations Management 9 Types of Demand Aggregate Planning is concerned with aggregate demand i.e. the amount of a particular economic good or service that a consumer or group of consumers will want to purchase (at a given price). Independent Demand: Finished Goods A B(4) C(2) Dependent Demand: Raw Materials, Component parts, Sub-assemblies, etc. D(2) E(1) D(3) F(2) Prof. Upendra Kachru Operations Management 10 Demand and Costs The firm should be able to forecast ideal levels of inventory. The relative cost of holding either too much or too little inventory might be different from the ideal levels because of poor forecasts of demand. If demand were less than expected, the firm would incur extra inventories and the cost of holding them. If demand were greater than expected, the firm would incur back-order or shortage cost and the possible opportunity costs of lost sales or a lower volume of activity. Prof. Upendra Kachru Operations Management Demand Management Do I manage demand ? Do I live with it? Demand management describes the process of influencing the volume of consumption of the product or service through management decision so that firms can use their resources and production capacity more effectively. Prof. Upendra Kachru Operations Management Independent Demand Can take an active role to influence demand. For example, air conditioner manufactures offer discounts for their products in winter , when demand for the products falls. Demand management is also used to spread demand more evenly. Telephone companies, world over, offer discounts for calls made during late hours or at night. What to do? Prof. Upendra Kachru Can take a passive role and simply respond to demand 13 Operations Management Determining the use of the forecast--what are the objectives? Select the items to be forecast Determine the time horizon of the forecast Select the forecasting model(s) Collect the data Validate the forecasting model Make the forecast Implement the results Prof. Upendra Kachru Eight Steps to Forecasting Operations Management Types of Forecasts Quantitative Time Series Analysis Exponential Method Regression Analysis Simulation/ Scenario Planning Qualitative (Judgmental) Prof. Upendra Kachru 15 Operations Management Time Series 1. Extrapolation 2. Moving average Method Exponential Method 1. Simple Exponential Method 2. Double Exponential Method 3. Triple Exponential Method Regression Analysis 1. Simple Regression Analysis 2. Multiple Regression Analysis Quantitative Approach Prof. Upendra Kachru Operations Management Time Series There are five basic patterns in which demand varies with time that have been identified: Horizontal Trend Seasonal Cyclical Random Prof. Upendra Kachru Operations Management Graphical Representation Linear Trend Cyclical Seasonal/ Cyclical Demand (units) Turning Points Constant Time Prof. Upendra Kachru Operations Management Moving Average Method The general formula for moving average is: Ft+1 = (At + At-1 + At-2 + At-3 + ……+ At-n+1) / n Where: Ft+1 is the moving average for the period t+1, At, At-1, At-2, At-3 etc. are actual values for the corresponding period, and ‘n’ is the total number of periods in the average Or it can be written as: A t-1 + A t-2 + A t-3 +...+A t- n Ft = n Prof. Upendra Kachru Operations Management Simple Moving Average Problem 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 t-1 + A t-2 + A t-3 +...+A t- n Ft = n Question: What are the 3week and 6-week moving average forecasts for demand? Assuming you only have 3 weeks and 6 weeks of actual demand data for the respective forecasts Prof. Upendra Kachru Operations Management Calculating the moving averages gives us: Week 1 2 3 4 5 6 7 8 9 10 11 12 Demand 3-Week 6-Week 650 F4=(650+678+720)/3 678 =682.67 720 F7=(650+678+720 +785+859+920)/6 785 682.67 859 727.67 =768.67 920 788.00 850 854.67 768.67 758 876.33 802.00 892 842.67 815.33 920 833.33 844.00 789 856.67 866.50 844 867.00 854.83 Operations Management ©The McGraw-Hill Companies, Inc., 2004 Prof. Upendra Kachru Weighted Moving Average While the moving average formula implies an equal weight being placed on each value that is being averaged, the weighted moving average permits an unequal weighting on prior time periods The general formula for the weighted moving average then changes to: Ft+1 = [(wtAt + wt-1At-1 + wt-2At-2 + wt-3At-3 + ……+ wt-n+1At-n+1) / n Where: Ft+1 is the weighted moving average for the period t+1, wt is the weighing factor, and ∑nt=1 wt = 1 Prof. Upendra Kachru Operations Management The formula for the moving average can also be written as: Ft = w 1 A t -1 + w 2 A t - 2 + w 3 A t -3 + ...+ w n A t - n wt = weight given to time period “t” occurrence (weights must add to one) w i=1 n i =1 Question: Given the weekly demand and weights, what is the forecast for the 4th period or Week 4? Week 1 2 3 4 Demand 650 678 720 Weights: t-1 .5 t-2 .3 t-3 .2 Note that the weights place more emphasis on the most recent data, that is time period “t-1” Prof. Upendra Kachru Operations Management 23 Problem 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 Prof. Upendra Kachru Operations Management 24 Exponential method is a technique that is applied to time series data, either to produce smoothed data for presentation, or to make forecasts. 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 Exponential Method Prof. Upendra Kachru Operations Management Exponential Smoothing Model The exponential relationship be written as: Ft+1 = α Dt + (1 - α) Ft Where: Dt is the actual value Ft is the forecasted value α is the weighting factor, which ranges from 0 to 1 t is the current time period. The variance is given by: (Dt - Ft+1)2 / n = Variance Prof. Upendra Kachru Operations Management 26 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: Given the weekly demand data, what are the exponential smoothing forecasts for periods 2-10 using a=0.10 and a=0.60? Assume F1=D1 Which is a better choice? Prof. Upendra Kachru Operations Management 27 Answer: The respective alphas columns denote the forecast values. Note that you can only forecast one time period into the future. Week 1 2 3 4 5 6 7 8 9 10 Prof. Upendra Kachru Demand 820 775 680 655 750 802 798 689 775 0.1 0.6 F3=775x0.1 + (1820.00 820.00 0.1)x820 =815.50 820.00 815.50 801.95 787.26 783.53 785.38 786.64 776.88 776.69 820.00 793.00 725.20 683.08 723.23 770.49 787.00 728.20 756.28 28 Operations Management Which one? Demand 820 775 0.1 820.00 820.00 D-W 0.00 -45.00 (D-W)2 0.00 2025.00 0.6 820.00 820.00 D-W 0.00 -45.00 (D-W)2 0 2025 680 655 750 802 798 689 775 815.50 801.95 787.26 783.53 785.38 786.64 776.88 -135.50 -146.95 -37.26 18.47 12.62 -97.64 -1.88 18360.25 21594.30 1387.94 341.16 159.35 9533.35 3.52 53404.87 793.00 725.20 683.08 723.23 770.49 787.00 728.20 -113.00 -70.20 66.92 78.77 27.51 -98.00 46.80 12769 4928.04 4478.286 6204.398 756.6461 9603.436 2190.348 42955.15 Answer: Variance0.3 = 6675.61 and Variance0.6 = 5369.39. alpha as 0.6 is a better choice Prof. Upendra Kachru Therefore Operations Management 29 Plotting the Solution Note how that the smaller alpha results in a smoother line in this example 900 Demand 800 700 600 500 1 2 3 4 5 6 7 8 9 10 Week Demand 0.1 0.6 Prof. Upendra Kachru Operations Management 30 Exponential Smoothing & Simple Moving Average An exponentially weighted moving average with a smoothing constant a, corresponds roughly to a simple moving average of length (i.e., period) n, where α and n are related by: α = 2/(n+1) OR n = (2 - α)/ α. Prof. Upendra Kachru Operations Management Double and Triple Smoothing An exponential smoothing over an already smoothed time series is called doubleexponential smoothing. It applies the process of exponential smoothing to a time series that is already exponentially smoothened. This is used when trends are not stationary. In the case of nonlinear trends it might be necessary to extend it even to a tripleexponential smoothing. Triple Exponential Smoothing is better at handling parabola trends and is normally used for such data. Prof. Upendra Kachru Operations Management Double Exponential Smoothing What happens when there is a definite non-stationary trend? A trendy clothing boutique has had the following sales over the past 6 months: 1 2 3 4 5 6 510 512 528 530 542 552 560 550 540 530 520 510 500 490 480 1 2 3 Actual Forecast Demand 4 Month 5 6 7 8 9 10 Prof. Upendra Kachru Operations Management All forecasts have errors. However, the ‘error’ in a forecast should be within confidence limits. The error can be measured by or described by the standard error, the mean absolute deviation, or the variance. Forecasting Errors Prof. Upendra Kachru Operations Management Source of forecast errors: Forecast inadequate Model may beAccuracy Irregular variations Incorrect use of forecasting technique Random variation Key to validity is randomness Accurate models: random errors Invalid models: nonrandom errors Key question: How to determine if forecasting errors are random? Prof. Upendra Kachru Operations Management Error measures Error - difference between actual value and predicted value • • • Mean Absolute Deviation (MAD) - Average absolute error Mean Squared Error (MSE) Average of squared error Mean Absolute Percent Error (MAPE) - Average absolute percent error Prof. Upendra Kachru Operations Management MAD, MSE, and MAPE MAD = Actual forecast n MSE = ( Actual forecast) n -1 2 MAPE Prof. Upendra Kachru Actual Forecast 100 Actual n Operations Management MAD Characteristics 1 MAD 0.8 standard deviation 1 standard deviation 1.25 MAD The ideal MAD is zero which would mean there is no forecasting error When the error is less than three standard deviations, it is considered as an acceptable forecast. σ = √ (π/2) x MAD ≈ 1.25 MAD Where „σ‟ is the standard deviation The larger the MAD, the less the accurate the resulting model Prof. Upendra Kachru 38 Operations Management MAD Problem (1) Question: What is the MAD value given the forecast values in the table below? Month 1 2 3 4 5 Prof. Upendra Kachru Sales Forecast 220 n/a 250 255 210 205 300 320 325 315 Operations Management 39 Solution Month 1 2 3 4 5 Sales 220 250 210 300 325 σ = 1.25 MAD = 12.5; 3 σ =37.5 All readings are within limits Forecast Abs Error n/a 255 5 205 5 20 320 315 10 40 A MAD = t=1 n t - Ft n 40 = = 10 4 Note that by itself, the MAD only lets us know the mean error in a set of forecasts Prof. Upendra Kachru Operations Management Example (2) Period Actual Forecast 1 217 215 2 213 216 3 216 215 4 210 214 5 213 211 MAD = 22/8 = 2.75 6 219 214 7 216 217 8 212 216 (A-F) 2 -3 1 -4 2 5 -1 -4 -2 |A-F| 2 3 1 4 2 5 1 4 22 (A-F)^2 4 9 1 16 4 25 1 16 76 (|A-F|/Actual)*100 0.92 1.41 0.46 1.90 0.94 2.28 0.46 1.89 10.26 MAD= MSE= MAPE= 2.75 10.86 1.28 MSE = 76/7 = 10.86 MAPE = 10.26/8 = 10.86 Operations Management Prof. Upendra Kachru Deseasoning Demand: Seasonal Index Seasonal index represents the extent of seasonal influence for a particular segment of the year. The calculation involves a comparison of the expected values of that period to the grand mean. The formula for computing seasonal factors is: Si = Di/D, where: Si = the seasonal index for ‘i’ th period, Di = the average values of ‘i’ th period, D = grand average, i = the ith seasonal period of the cycle Prof. Upendra Kachru 42 Operations Management Actual ProblemStep 4: Dividewith the sales (Col. 2) Step 2: Add data in Col. 2 and 5. Then divide by „2‟ seasonal factor The sales data for two(Col. 7) are given with the sales data years aggregated in periods of two months. Month, 2003 Jan – Feb Mar – Apr May – June Jul – Aug Sept – Oct Nov – Dec Total Sales 109.0 104.0 150.0 170.0 120.0 100.0 753 Deseasoned Demand 125.29 125.30 126.05 125.00 126.32 125.00 Month, 2004 Jan – Feb Mar – Apr Sales 115.0 112.0 Average 112.0 108.0 Seasonal Deseasoned factor 0.87 0.83 Demand 132.18 130.12 133.61 133.82 132.63 132.50 May – 159.0 June Jul – Aug Sept – Oct Nov – Dec 182.0 126.0 106.0 800 154.5 Step 3: Divide Col. 6 1.19 112/129.42 = 0.87 176.0 1.36 123.0 103.0 0.95 0.80 Step 1: Add data in Col. 2 and divide by „n‟. Then add data in Col. 2 and divide by „n‟. Determine the average. (753/6 + 800/6)/2 = (125.5 + 133.33)/2 = 129.42 Prof. Upendra Kachru Operations Management Tracking Signals 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 MAD‟s 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: (Actual demand - Forecast demand) i 1 n i MAD Prof. Upendra Kachru Operations Management 44 Control Charts A control chart is: A visual tool for monitoring forecast errors Used to detect non-randomness in errors Forecasting errors are in control if All errors are within the control limits No patterns, such as trends or cycles, are present Prof. Upendra Kachru Operations Management Controlling the forecast Prof. Upendra Kachru Operations Management Control charts Control charts are based on the following assumptions: when errors are random, they are Normally distributed around a mean of zero. Standard deviation of error is 95.5% of data in a normal distribution is within 2 standard deviation of the mean MSE 99.7% of data in a normal distribution is within 3 standard deviation of the mean Upper and lower control limits are often determine via 0 2 MSE or 0 3 MSE Prof. Upendra Kachru Operations Management Example Compute 2s control limits for forecast errors to determine if the forecast is accurate. s MSE 3.295 2 s 6.59 Errors are all between -6.59 and +6.59 No pattern is observed Therefore, according to control chart criterion, forecast is reliable (Refer Slide 42) 5.41 3.41 1.41 -0.59 0 -2.59 10 -4.59 -6.59 Prof. Upendra Kachru Operations Management Regression Analysis Regression Analysis is a method of predicting the value of one variable based on the value of other variables. It reflects the casual relationship underlying the demand being forecast and an independent variable. Prof. Upendra Kachru Operations Management Regression analysis is of two types: (a) Simple Linear Regression: A regression using only one predictor is called a simple regression, and (b)Multiple Regressions: Where there are two or more predictors, multiple regression analysis is employed. Regression Analysis There are two types of variables, one that is being forecasted and one from which the forecast is made. The first one is known as the dependent variable, the latter as the independent variable. Operations Management Prof. Upendra Kachru Simple Regression Analysis The functional relationship between the two can be visualized within a system of coordinates where the dependent variable is shown on the y and independent variable on the x-axis. yt=f(x) or yt = a + bx Where: ‘yt’ is the dependent variable ‘a’ is the Y intercept ‘b’ is the slope of the line, and ‘x’ is the time period Prof. Upendra Kachru Operations Management The simple linear regression model seeks to fit a line through various data over time Y a 0 1 2 3 4 5 x (Time) yt = a + bx Is the linear regression 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. Prof. Upendra Kachru 52 Operations Management Simple Linear Regression Formulas For Calculating “a” and “b” a = y - bx xy - n(y)(x) x - n(x ) 2 2 b= Prof. Upendra Kachru Operations Management 53 Problem Question: Given the data below, what is the simple linear regression model that can be used to predict sales in future weeks? Week 1 2 3 4 5 Prof. Upendra Kachru Sales 150 157 162 166 177 Operations Management 54 55 Answer: First, using the linear regression formulas, we can compute “a” and “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 - n( y)(x) = 2499 - 5(162.4)(3) 63 = 6.3 b= 55 5( 9 ) 10 x - n(x ) 2 2 a = y - bx = 162.4 - (6.3)(3) = 143.5 Prof. Upendra Kachru Operations Management 55 56 The resulting regression model is: yt = 143.5 + 6.3x 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 1 Prof. Upendra Kachru Sales Sales Forecast 2 3 Period 4 5 Operations Management 56 Correlation Analysis Correlation analysis measures the degree of relationship between normally distributed dependent and independent variables and is signified by the correlation coefficient ‘r’. Mathematically, correlation coefficient is defined by: r = 1Sxy Sy 2 2 Where: Syx2 is the standard error of the estimated regression equation of the ‘y’ values on ‘x’, and Sy2 is the standard error for the ‘y’ values Prof. Upendra Kachru Operations Management Multiple Regression With multiple regressions, we can use more than one predictor. The forecast takes the form: Y = β0 + β1 X1 + β2 X2 + . . .+ βn Xn, Where: β0 is the intercept, and β1, β2, . . . βn are coefficients representing the contribution of the independent variables X1, X2,..., Xn. Prof. Upendra Kachru Operations Management The Gillette Story & Demand Management Gillette is one of the best practitioners of demand management in the consumer goods space. With manufacturing plants in 51 locations in 20 countries, Gillette caters to the need of more than 200 countries around the world. Globally, Gillette's portfolio of brands is organized into five business units: Blades and Razors, Personal Care, Oral Care, Duracell, and Braun. Operations Management Prof. Upendra Kachru Gillette Story In terms of volumes. Overall, Gillette was a $10 billion company. Out-of-stocks represented a large revenue loss. A 10 percent stock out rate could cost the company up to $1 billion. The opportunity afforded by higher fill rates, even when discounted 50, 60 or 90 percent, could still be worth $100 million. The challenge was to bridge supply and demand, especially as the manufacturer usually does not control replenishment. Operations Management Prof. Upendra Kachru Gillette Story The key performance indicators which Gillette uses are forecast accuracy and case fill rates. Gillette made significant improvements in forecast accuracy, from 40 percent in 2001 to 65 percent in 2003. In the case of fill rate it improved from 80 percent in 2001 to 96 percent in 2003. . Prof. Upendra Kachru Operations Management Gillette Story How did Gillette make these improvements? Gillette restructured its organization to improve the bridge between supply and demand. Next, Gillette identified 11 key elements which it had to improve in order to improve overall value chain performance. These elements included: increase in service levels, reduction in inventory, and improved costs. Operations Management Prof. Upendra Kachru Gillette Story It worked with customers to map processes across company boundaries to avoid a gap between Gillette's processes and the customer's processes. The key element that has made these initiatives possible is Collaborative Planning, Forecasting, and Replenishment (CPFR), data synchronization (UCCNET) and Auto ID. Prof. Upendra Kachru Operations Management Gillette Story Gillette standardized the company's approach to forecasting across regions, customer-based forecasting for promotions, and redesigned some parts of the company's warehouse and transportation strategy to improve transit time to customers. The Gillette story is the story of a company that had to undergo restructuring in 2001 due to large drop in its profit. It highlights how new techniques such as CPFR have reinforced the traditional models of demand planning and forecasting. Operations Management Prof. Upendra Kachru Collaborative Planning Forecasting and Replenishment (CPFR) CPFR is forecasting based on the concept of supply chain management. It is a business model that takes a holistic approach to supply chain management and information exchange among trading partners. It uses common metrics, standard language, and firm agreements to improve supply chain efficiencies for all participants. Prof. Upendra Kachru Operations Management Collaborative Planning Forecasting and Replenishment (CPFR) In other words, CPFR is based on considering the entire supply chain or partnerships as a single unit and the sharing of information between the links in the chain. The objective is to collectively, as members of the supply chain, meet the needs of the final consumer. This is accomplished by supplying the right product at the right place, right time and right price to the customer. Operations Management Prof. Upendra Kachru CPFR usually begins with identifying a ‘forecasting champion’. The forecasting champion can be it a single person, a department, or a firm. A forecast collaboration group is formed with each organization choosing its member in this group. Group members should represent a variety of functional areas including sales, marketing, logistics/operations, finance, and information systems. Prof. Upendra Kachru Operations Management Prof. Upendra Kachru Operations Management Prof. Upendra Kachru Operations Management Prof. Upendra Kachru Operations Management Collaborative Planning Forecasting and Replenishment (CPFR) The driving premise of CPFR is that all supply chain participants develop a synchronized forecast. A company can collaborate with numerous other supply network members both upstream and downstream in the supply network. Every participant in a CPFR process — supplier, manufacturer, distributor, retailer — can view and amend forecast data to optimize the process from end to end. Operations Management Prof. Upendra Kachru 1.Specialand analyze the Forecast Identify Long-Term organizational issues Methodologies that will provide the decision focus 2. Specify the key decision factors 3. Identify and analyze the key environmental forces 4. Establish the scenario logics 5. Select and elaborate the scenario 6. Interpret the scenario for their decision implications Prof. Upendra Kachru Scenario Planning Operations Management Qualitative approach – (Judgmental) Historical Analogy Method Executive Opinion Method Survey Methods The Delphi Method Prof. Upendra Kachru Operations Management Qualitative Approaches Usually based on judgments about causal factors that underlie the demand of particular products or services Do not require a demand history for the product or service, therefore are useful for new products/services Approaches vary in sophistication from scientifically conducted surveys to intuitive hunches about future events Operations Management Executive Opinion Method Technique Manager’s Opinion Executive’s Opinion Sales Force Composite Number in Sample Low Sales High Sales 40.7% 40.7% 29.6% 27 39.6% 41.6% 35.4% 48 Prof. Upendra Kachru Operations Management How to choose the right Tool Prof. Upendra Kachru Operations Management Prof. Upendra Kachru Operations Management Prof. Upendra Kachru Operations Management Validating Model Whatever be the type of analysis you make, it is essential that the model you choose provides satisfaction on these two critical questions: •Is the model adequate? •Is the model stable? Prof. Upendra Kachru Operations Management Forecast control Using Standard Computer Programs Delphi Method Read at Home Prof. Upendra Kachru Operations Management Exercise Design a Delphi Study on what should be the type of learning in a 3 year (part time) management program. Please explain the logic behind the design. Prof. Upendra Kachru Operations Management Operations Management (2) Click to edit company slogan .