Operations Management Forecasting Chapter 4

Examples Predict the next number in the pattern:

Examples Predict the next number in the pattern: a) 3.7, 3.7, 3.7, 3.7, 3.7, y = 3.7 b) 2.5, 4.5, 6.5, 8.5, 10.5, y = 0.5 + 2x c) 5.0, 7.5, 6.0, 4.5, 7.0, 9.5, 8.0, 6.5, y = 4.5 + 0.5x + ci c1 = 0; c2 = 2; c3 = 0; c4 = -2; etc

Outline What is Forecasting? Types of Forecasts. Time horizons. Life cycle. Types of Forecasts. Eight Steps in the Forecasting System. Forecasting Approaches: Overview of Qualitative Methods. Overview of Quantitative Methods.

Outline - Continued Time-Series Forecasting: Moving Averages. Exponential Smoothing. Trend Projection. Associative Forecasting Methods: Regression and Correlation Analysis. Monitoring and Controlling Forecasts. Forecasting in the Service Sector.

What is Forecasting? Art and science of predicting future events. Underlying basis of all business decisions. Production & Inventory. Personnel & Facilities. Focus on forecasting demand. Sales will be $200 Million!

Types of Forecasts by Time Horizon Short-range forecast: Usually < 3 months. Job scheduling, worker assignments. Medium-range forecast: 3 months to 3 years. Sales & production planning, budgeting. Long-range forecast: > 3 years. New product planning, facility location. At this point, it may be useful to point out the “time horizons” considered by different industries. For example, some colleges and universities look 30 to fifty years ahead, industries engaged in long distance transportation (steam ship, railroad) or provision of basic power (electrical and gas utilities, etc.) also look far ahead (20 to 100 years). Ask them to give examples of industries having much shorter long-range horizons.

Short- vs. Long-term Forecasting Medium & Long range forecasts: Long range for design of system. Deal with comprehensive issues. Support management decisions regarding planning. Short-term forecasts: To plan detailed use of system. Usually use quantitative techniques. More accurate than longer-term forecasts. At this point it may be helpful to discuss the actual variables one might wish to forecast in the various time periods.

Influence of Product Life Cycle Stages of introduction and growth require longer forecasts than maturity and decline. Forecasts useful in projecting: staffing levels, inventory levels, and factory capacity (expansion and contraction), as product passes through life cycle stages. This slide introduces the impact of product life cycle on forecasting The following slide, reproduced from chapter 2, summarizes the changing issues over the product’s lifetime for those faculty who wish to treat the issue in greater depth.

Forecasting During the Life Cycle Hard to forecast. Need long-range forecasts. Often use qualitative models. Introduction Growth Maturity Decline Sales Forecasting critical, both for future magnitude and growth rate. Long-range forecasts still important. Easier to forecast. Use quantitative models. Hard to forecast, but forecasting is less important. Time

Eight Steps in Forecasting Determine the use of the forecast. Select the items to be forecast. Determine the time horizon of the forecast. Select the forecasting model(s). Gather the data. Make the forecast. Validate and implement results. Monitor forecasts and adjust when needed. A point to be made here is that one requires a forecasting “plan,” not merely the selection of a particular forecasting methodology.

Realities of Forecasting Assumes future will be like the past (causal factors will be the same). Forecasts are imperfect. Forecasts for groups of product are more accurate than forecasts for individual products. Accuracy decreases with length of forecast. This slide provides a framework for discussing some of the inherent difficulties in developing reliable forecasts. You may wish to include in this discussion the difficulties posed by attempting forecast in a continuously, and rapidly changing environment where product life-times are measured less often in years and more often in months than ever before. One might wish to emphasize the inherent difficulties in developing reliable forecasts.

Forecasting Approaches Qualitative Methods Quantitative Methods Used when little data or time exist. New products & technology. Long time horizon. Major changes expected. Involves intuition, experience. Example: forecasting for e-commerce sales. Used when situation is ‘stable’ & historical data exist. Existing products & current technology. No significant changes expected. Involves mathematical techniques. Example: forecasting sales of color televisions. This slide distinguishes between Quantitative and Qualitative forecasting. If you accept the argument that the future is one of perpetual, and perhaps significant change, you may wish to ask students to consider whether quantitative forecasting will ever be sufficient in the future - or will we always need to employ qualitative forecasting also. (Consider Tupperware’s ‘jury of executive opinion.’)

Overview of Qualitative Methods Jury of executive opinion. Combine opinions from executives. Sales force composite. Aggregate estimates from salespersons. Delphi method. Query experts interatively. Consumer market survey. Survey current and potential customers. This slide outlines several qualitative methods of forecasting. Ask students to give examples of occasions when each might be appropriate. The next several slides elaborate on these qualitative methods.

Jury of Executive Opinion Seek opinions/estimates from small group of high-level managers working together. Combines managerial experience with statistical models. Relatively quick. ‘Group-think’. Leader may dominate. Ask your students to consider other potential disadvantages. (Politics?)

Sales Force Composite Each salesperson projects their sales. Aggregate projections at district & national levels. Sales rep’s know customers. Must not reward inaccurate forecasts. May over- or under-forecast to acquire more resources. Sales You might ask your students to consider what problems might occur when trying to use this method to predict sales of a potential new product.

Delphi Method Iterative group process. 3 types of people: Decision makers. Staff. Respondents. Reduces ‘group-think’. Takes time. Respondents Staff (Make forecast) (Provide input to decision makers) Decision Makers (Administer) You might ask your students to consider whether there are special examples where this technique is required. ( Questions of technology transfer or assessment, for example; or other questions where information from many different disciplines is required.)

Consumer Market Survey How many hours will you use the Internet next week? Ask customers about purchasing plans. Relatively simple. What consumers say, and what they actually do are often different. You might discuss some of the difficulties with this technique. Certainly there is the issue that what consumers say is often not what they do. There are other problems such as that consumers sometime wish to please the surveyor; and for unusual, future, products, consumers may have a very imperfect frame of reference within which to consider the question.

Quantitative Forecasting Methods Time Series Associative Models Models A point you may wish to make here is that only in the case of linear regression are we assuming that we know “why” something happened. General time-series models are based exclusively on “what” happened in the past; not at all on “why.” Does operating in a time of drastic change imply limitations on our ability to use time series models? Moving Exponential Trend Linear Average Smoothing Projection Regression

What is a Time Series? Set of evenly spaced numerical data. From observing response variable at regular time periods. Forecast based only on past values. Assumes that factors influencing past will continue influence in future. Example: Year: 1 2 3 4 5 Sales: 78.7 63.5 89.7 93.2 92.1 This and subsequent slide frame a discussion on time series - and introduce the various components.

Time Series Components Trend Seasonal Cyclical Random

Product Demand over 4 Years Demand for product or service This slide illustrates a typical demand curve. You might ask students why it is important to know more than simply the actual demand over time. Why, for example, would one wish to be able to break out a “seasonality” factor? Year 1 Year 2 Year 3 Year 4

Product Demand over 4 Years Trend component Seasonal peaks Demand for product or service Cyclic component Actual demand line This slide illustrates a typical demand curve. You might ask students why it is important to know more than simply the actual demand over time. Why, for example, would one wish to be able to break out a “seasonality” factor? Random variation Year 1 Year 2 Year 3 Year 4

Trend Component Persistent, overall upward or downward pattern. Due to population, technology etc. Several years duration. Time

Seasonal Component Regular pattern of up & down fluctuations. Due to weather, customs etc. Occurs within 1 year. Quarterly, monthly, weekly, etc. Time Demand Summer

Cyclical Component Repeating up & down movements. Due to interactions of factors influencing economy. Usually 2-10 years duration. Year Demand Cycle

Random Component Erratic, unsystematic, ‘residual’ fluctuations. Due to random variation or unforeseen events. Union strike Tornado Short duration & non-repeating.

General Time Series Models Any value in a time series is a combination of the trend, seasonal, cyclic, and random components. Multiplicative model: Yi = Ti · Si · Ci · Ri Additive model: Yi = Ti + Si + Ci + Ri This slide introduces two general forms of time series model. You might provide examples of when one or the other is most appropriate.

Naive Approach Demand in next period is the same as demand in most recent period. e.g., If May sales were 48, then June sales will be 48. Sometimes cost effective & efficient. Usually not good. This slide introduces the naïve approach. Subsequent slides introduce other methodologies.

 Moving Average Method MA is a series of arithmetic means. Used if little or no trend. Used often for smoothing. MA n   Demand in previous periods At this point, you might discuss the impact of the number of periods included in the calculation. The more periods you include, the closer you come to the overall average; the fewer, the closer you come to the value in the previous period. What is the tradeoff?

Moving Average Example You’re manager of a museum store that sells historical replicas. You want to forecast sales (in thousands) for months 4 and 5 using a 3-period moving average. Month 1 4 Month 2 6 Month 3 5 Month 4 ? Month 5 ?

Moving Average Forecast Month Response Y i Moving Total (n=3) Average 1 4 NA 2 6 3 5 ? 4+6+5=15 15/3=5

Moving Average Graph 95 96 97 98 99 00 Sales 2 4 8 Actual Forecast 3 1 6 This slide shows the resulting forecast. Students might be asked to comment on the useful ness of this forecast. Month

Actual Demand for Month 4 = 3 Response Y i Moving Total (n=3) Average 1 4 NA 2 6 3 5 4+6+5=15 15/3 = 5 ?

Moving Average Graph 95 96 97 98 99 00 Sales 2 4 8 Actual Forecast 3 1 6 This slide shows the resulting forecast. Students might be asked to comment on the useful ness of this forecast. Month

Moving Average Forecast Month Response Y i Moving Total (n=3) Average 1 4 NA 2 6 3 5 15 7 6+5+3=14 14/3=4.667 ?

Moving Average Graph 95 96 97 98 99 00 Sales 2 4 8 Actual Forecast 3 1 6 This slide shows the resulting forecast. Students might be asked to comment on the useful ness of this forecast. Month

Actual Demand for Month 5 = 7 Response Y i Moving Total (n=3) Average 1 4 NA 2 6 3 5 15 7 6+5+3=14 14/3=4.667 ?

Moving Average Graph 95 96 97 98 99 00 Sales 2 4 8 Actual Forecast 3 1 6 This slide shows the resulting forecast. Students might be asked to comment on the useful ness of this forecast. Month

Moving Average Forecasts Month Response Y i Moving Total (n=3) Average 1 4 NA 2 6 3 5 4+6+5=15 15/3=5.0 7 6+5+3=14 14/3=4.667 ? 5+3+7=15

Moving Average Graph 95 96 97 98 99 00 Sales 2 4 8 Actual Forecast 3 1 6 This slide shows the resulting forecast. Students might be asked to comment on the useful ness of this forecast. Month

Weighted Moving Average Method Gives more emphasis to recent data. Weights decrease for older data. Weights sum to 1.0. May be based on intuition. Sum of digits weights: numerators are consecutive. 3/6, 2/6, 1/6 4/10, 3/10, 2/10, 1/10 This slide introduces the “weighted moving average” method. It is probably most important to discuss choice of the weights. WMA = Σ [(Weight for period n) (Demand in period n)] ΣWeights

Weighted Moving Average: 3/6, 2/6, 1/6 Month Response Y i Weighted Moving Average 1 4 NA 2 6 3 5 31/6 = 5.167 ? ? ?

Weighted Moving Average: 3/6, 2/6, 1/6 Month Response Y i Weighted Moving Average 1 4 NA 2 6 3 5 31/6 = 5.167 7 ? 25/6 = 4.167 32/6 = 5.333

Moving Average Methods Increasing n makes forecast: Less sensitive to changes. Less sensitive to recent data. Weights control emphasis on recent data. Do not forecast trend well. Require historical data. These points should have been brought out in the example, but can be summarized here.

Moving Average Graph Demand Time Actual This slide illustrates graphically the results of the example forecast. Time

Moving Average Graph Large n Small n Demand Time Actual This slide illustrates graphically the results of the example forecast.

Weighted Moving Average Graph Time Demand Actual Large weight on recent data Small weight on recent data This slide illustrates graphically the results of the example forecast.

Exponential Smoothing Method Form of weighted moving average. Weights decline exponentially. Most recent data weighted most. Requires smoothing constant (). Usually ranges from 0.05 to 0.5 Should be chosen to give good forecast. Involves little record keeping of past data. This slide introduces the exponential smoothing method of time series forecasting. The following slide contains the equations, and an example follows.

Exponential Smoothing Equation Ft = Ft-1 + (At-1 - Ft-1) Ft = Forecast value for time t At-1 = Actual value at time t-1  = Smoothing constant Need initial forecast Ft-1 to start. Could be given or use moving average. You may wish to discuss several points: - this is just a moving average wherein every point in included in the forecast, but the weights of the points continuously decrease as they extend further back in time. - the equation actually used to calculate the forecast is convenient for programming on the computer since it requires as data only the actual and forecast values from the previous time point. - we need a formal process and criteria for choosing the “best” smoothing constant.

Exponential Smoothing Example You want to forecast product demand using exponential smoothing with  = .10. Suppose in the most recent month (month 6) the forecast was 175 and the actual demand was 180. Month 6 180 Month 7 ? Month 8 ? Month 9 ? Month 10 ? This slide begins an exponential smoothing example.

Exponential Smoothing - Month 7 Ft = Ft-1 + α (At-1 - Ft-1) Forecast, F t Month Actual ( α = .10) 6 180 175.00 (Given) 7 ? 175.00 + .10(180 - 175.00) = 175.50 8 ? 9 ? 10 ? 11 ?

Exponential Smoothing - Month 8 Ft = Ft-1 + α (At-1 - Ft-1) Actual Forecast, F t ( α = .10) 180 175.00 (Given) 168 175.00 + .10(180 - 175.00) = 175.50 ? 175.50 + .10(168 - 175.50) = 174.75 Month 6 7 8 9 10 11

Exponential Smoothing Solution Ft = Ft-1 + α (At-1 - Ft-1) Actual Forecast, F t ( α = .10) 180 175.00 (Given) 168 175.00 + .10(180 - 175.00) = 175.50 159 175.50 + .10(168 - 175.50) = 174.75 ? 174.75 + .10(159 - 174.75) = 173.18 Month 6 7 8 9 10 11 This slide illustrates the result of the steps used to make the forecast desired in the example. In the PowerPoint presentation, there are additional slides to illustrate the individual steps.

Exponential Smoothing Solution Ft = Ft-1 + α (At-1 - Ft-1) Actual Forecast, F t ( α = .10) 180 175.00 (Given) 168 175.00 + .10(180 - 175.00) = 175.50 159 175.50 + .10(168 - 175.50) = 174.75 175 174.75 + .10(159 - 174.75) = 173.18 190 ? 173.36 + .10(190 - 173.36) = 175.02 Month 6 7 8 9 10 11 This slide illustrates the result of the steps used to make the forecast desired in the example. In the PowerPoint presentation, there are additional slides to illustrate the individual steps. 173.18 + .10(175 - 173.18) = 173.36

Exponential Smoothing Graph Month Sales 140 150 160 170 180 190 6 7 8 9 10 11 Actual Forecast This slide illustrates graphically the results of the example forecast.

Exponential Smoothing Methods Increasing α makes forecast: More sensitive to changes. More sensitive to recent data. α controls emphasis on recent data. Do not forecast trend well. Trend adjusted exponential smoothing - p. 90-93 These points should have been brought out in the example, but can be summarized here.

Exponential Smoothing Graph Time Demand Actual This slide illustrates graphically the results of the example forecast.

Exponential Smoothing Graph Time Demand Actual Large α Small α This slide illustrates graphically the results of the example forecast.

Forecast Effects of Smoothing Constant  Ft =  At - 1 + (1- )At - 2 + (1- )2At - 3 + ... Weights Prior Period  2 periods ago (1 - ) 3 periods ago (1 - )2 = = 0.10 = 0.90 This slide illustrates the decrease in magnitude of the smoothing constant. In the Power Point presentation, the several previous slides show the steps leading to this slide. 10% 9% 8.1% 90% 9% 0.9%

Choosing  - Comparing Forecasts A good method has a small error. Choose  to produce a small error. Error = Demand - Forecast Error > 0 if forecast is too low Error < 0 if forecast is too high MAD = Mean Absolute Deviation: Average of absolute values of errors. MSE = Mean Squared Error: Average of squared errors. MAPE = Mean Absolute Percentage Error: Average of absolute value of percentage errors. This slide indicates one method of selecting .

Forecast Error Equations Mean Absolute Deviation (MAD) Mean Squared Error (MSE) This slide illustrates the equations for two measures of forecast error. Students might be asked if there is an occasion when one method might be preferred over the other.

Forecast Error Equations Mean Absolute Percentage Error (MAPE) This slide illustrates the equations for two measures of forecast error. Students might be asked if there is an occasion when one method might be preferred over the other.

Forecast Error Example Actual F1 F2 F1 error F2 error 20 19 1 18 2 10 15 -5 13 -3 24 22 2 21 3 20 21 -1 18 2 MAD F1 = 9/4 = 2.25 F2 = 10/4 = 2.5 MSE F1 = 31/4 = 7.75 F2 = 26/4 = 6.5 MAPE F1 = 0.171 = 17.1% F2 = 0.156 = 15.6% This slide indicates one method of selecting .

Which Forecast is Best? MAD F1 = 9/4 = 2.25 F2 = 10/4 = 2.5 MSE F1 = 31/4 = 7.75 F2 = 26/4 = 6.5 MAPE F1 = 0.171 = 17.1% F2 = 0.156 = 15.6% This slide indicates one method of selecting .