Operations and Supply Chain Management CHASE | SHANKAR | JACOBS

FORECASTING Chapter Eighteen McGraw-Hill/Irwin Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved.

Learning Objectives LO18–1: Understand how forecasting is essential to supply chain planning LO18–2: Evaluate demand using quantitative forecasting models LO18–3: Apply qualitative techniques to forecast demand LO18–4: Apply collaborative techniques to forecast demand

The Role of Forecasting Forecasting is a vital function and affects every significant management decision. Finance and accounting use forecasts as the basis for budgeting and cost control. Marketing relies on forecasts to make key decisions such as new product planning and personnel compensation. Production uses forecasts to select suppliers; determine capacity requirements; and drive decisions about purchasing, staffing, and inventory. Different roles require different forecasting approaches. Decisions about overall directions require strategic forecasts. Tactical forecasts are used to guide day-to-day decisions.

Forecasting and Decoupling Point Decoupling point: Point at which inventory is stored, which allows SC to operate independently. The choice of the decoupling point in a SC is strategic. Forecasting helps determine the level of inventory needed at the decoupling points. The decision will be affected by the error produced in the forecast and the type of product (easily inventoried or easily perishable).

Types of Forecasting There are four basic types of forecasts. Qualitative Time series analysis (primary focus of this chapter) Causal relationships Simulation Time series analysis is based on the idea that data relating to past demand can be used to predict future demand.

Average demand for a period of time Components of Demand Average demand for a period of time Trend Seasonal element Cyclical elements Random variation Autocorrelation Excel: Components of Demand For the Excel template visit www.mhhe.com/sie-chase14e

Trends Identification of trend lines is a common starting point when developing a forecast. Common trend types include linear, S-curve, asymptotic, and exponential.

Time Series Analysis Using the past to predict the future Used mainly for tactical decisions Short term – forecasting less than 3 months Used to develop a strategy that will be implemented over the next 6 to 18 months (e.g., meeting demand) Medium term – forecasting 3 months to 2 years Useful for detecting general trends and identifying major turning points Long term – forecasting greater than 2 years

Model Selection Choosing an appropriate forecasting model depends upon Time horizon to be forecast Data availability Accuracy required Size of forecasting budget Availability of qualified personnel

Forecasting Method Selection Guide Amount of Historical Data Data Pattern Forecast Horizon Simple moving average 6 to 12 months; weekly data are often used Stationary (i.e., no trend or seasonality) Short Weighted moving average and simple exponential smoothing 5 to 10 observations needed to start Stationary Exponential smoothing with trend Stationary and trend Linear regression 10 to 20 observations Stationary, trend, and seasonality Short to medium

Simple Moving Average Forecast is the average of a fixed number of past periods. Useful when demand is not growing or declining rapidly and no seasonality is present. Removes some of the random fluctuation from the data. Selecting the period length is important. Longer periods provide more smoothing. Shorter periods react to trends more quickly.

Simple Moving Average Formula  

Simple Moving Average – Example

Weighted Moving Average The simple moving average formula implies equal weighting for all periods. A weighted moving average allows unequal weighting of prior time periods. The sum of the weights must be equal to one. Often, more recent periods are given higher weights than periods farther in the past. 𝐹𝑡=𝑤1𝐴𝑡−1+𝑤2𝐴𝑡−2+ …+𝑤𝑛𝐴𝑡−𝑛

Selecting Weights Experience and/or trial-and-error are the simplest approaches. The recent past is often the best indicator of the future, so weights are generally higher for more recent data. If the data are seasonal, weights should reflect this appropriately.

Exponential Smoothing A weighted average method that includes all past data in the forecasting calculation More recent results weighted more heavily The most used of all forecasting techniques An integral part of computerized forecasting

Exponential Smoothing Well accepted for six reasons Exponential models are surprisingly accurate Formulating an exponential model is relatively easy The user can understand how the model works Little computation is required to use the model Computer storage requirements are small Tests for accuracy are easy to compute

Exponential Smoothing Model

Exponential Smoothing Example Week Demand Forecast 1 820 2 775 3 680 811 4 655 785 5 750 759 6 802 757 7 798 766 8 689 772 9 756 10 760          

Exponential Smoothing – Effect of Trends The presence of a trend in the data causes the exponential smoothing forecast to always lag behind the actual data This can be corrected by adding a trend adjustment The trend smoothing constant is delta (δ)  

Example – Exponential Smoothing with Trend Adjustment Calculate the new forecast, assuming the following: The previous forecast including trend (FITt-1) is 110 and the previous estimate of the trend (Tt-1) is 10 α = 0.2 and δ = 0.3 Actual demand for period t-1 is 115 Ft = Ft-1 + α(At-1 – FITt-1) = 110 + 0.2(115-110) = 111.0 Tt = Tt-1 + δ(Ft-1 – FITt-1) = 10 + 0.3(111-110) = 10.3 FITt = Ft + Tt = 111.0 + 10.3 = 121.3

Choosing Alpha and Delta Relatively small values for α and δ are common Usually in the range 0.1 to 0.3 α depends upon how much random variation is present δ depends upon how steady the trend is Measurement of forecast error can be used to select values of α and δ to minimize overall forecast error

Linear Regression Analysis Regression is used to identify the functional relationship between two or more correlated variables, usually from observed data. One variable (the dependent variable) is predicted for given values of the other variable (the independent variable). Linear regression is a special case that assumes the relationship between the variables can be explained with a straight line.   Y = a + bt

Example 18.2 – Least Squares Method The least squares method determines the parameters a and b such that the sum of the squared errors is minimized – “least squares” Quarter Sales 1 600 7 2,600 2 1,550 8 2,900 3 1,500 9 3,800 4 10 4,500 5 2,400 11 4,000 6 3,100 12 4,900  

Example 18.2 – Calculations   1 600 360,000 801.3 2 1,550 3,100 4 2,402,500 1,160.9 3 1,500 4,500 9 2,250,000 1,520.5 6,000 16 1,880.1 5 2,400 12,000 25 5,760,000 2,239.7 6 18,600 36 9,610,000 2,599.4 7 2,600 18,200 49 6,760,000 2,959.0 8 2,900 23,200 64 8,410,000 3,318.6 3,800 34,200 81 14,440,000 3,678.2 10 45,000 100 20,250,000 4,037.8 11 4,000 44,000 121 16,000,000 4,397.4 12 4,900 58,800 144 24,010,000 4,757.1 Sum 78 33,350 268,200 650 112,502,500           The forecast is extended to periods 13-16        

Regression with Excel Microsoft Excel includes data analysis tools, which can perform least squares regression on a data set.

Time Series Decomposition Chronologically ordered data are referred to as a time series. A time series may contain one or many elements. Trend, seasonal, cyclical, autocorrelation, and random Identifying these elements and separating the time series data into these components is known as decomposition.

Seasonal Variation Seasonal variation may be either additive or multiplicative (shown here with a changing trend).

Determining Seasonal Factors : Simple Proportions Example 18.3 The seasonal factor (or index) is the ratio of the amount sold during each season divided by the average for all seasons. Season Past Sales Average Sales for Each Season Seasonal Factor Spring 200 1000 4 = 250 200 250 = 0.8 Summer 350 1000 4 = 250 350 250 = 1.4 Fall 300 300 250 = 1.2 Winter 150 150 250 = 0.6 Total 1000

Example 18.3 (Continued) Expected Demand for Next Year Average Sales for Each Season (1,100y4) Seasonal Factor Next Year’s Forecast Spring 275 X 0.8 = 220 Summer 1.4 385 Fall 1.2 330 Winter 0.6 165 1100

Decomposition Using Least Squares Regression Decompose the time series into its components Find seasonal component Deseasonalize the demand Find trend component Forecast future values of each component Project trend component into the future Multiply trend component by seasonal component

Decomposition – Steps 1 and 2 Using the data for periods 1-12, apply time series analysis (decomposition, linear regression, trend estimate & seasonal indices) to forecast for periods 13-16

Decomposition – Steps 3 and 4 Develop a least squares regression line for the deseasonalized data. Project the regression line through the period of the forecast. Regression Results: Y = 555.0 + 342.2t Forecast for periods 13-16

Decompostion – Step 5 Create the final forecast by adjusting the regression line by the seasonal factor. Period Quarter Y from Regression Seasonal Factor Forecast (F x Seasonal Factor 13 I 5,003.5 0.82 4,102.87 14 II 5,345.7 1.10 5,880.27 15 III 5,687.9 0.97 5,517.26 16 IV 6,030.1 1.12 6,753.71

Forecast Errors Forecast error is the difference between the forecast value and what actually occurred. All forecasts contain some level of error. Sources of error Bias – when a consistent mistake is made Random – errors that are not explained by the model being used Measures of error Mean absolute deviation (MAD) Mean absolute percent error (MAPE) Tracking signal

Forecast Error Measurements Ideally, MAD will be zero (no forecasting error). Larger values of MAD indicate a less accurate model. MAPE scales the forecast error to the magnitude of demand.   Tracking signal indicates whether forecast errors are accumulating over time (either positive or negative errors).    

Computing Forecast Error

Causal Relationship Forecasting Causal relationship forecasting uses independent variables other than time to predict future demand. This independent variable must be a leading indicator. Many apparently causal relationships are actually just correlated events – care must be taken when selecting causal variables.

Multiple Regression Techniques Often, more than one independent variable may be a valid predictor of future demand. In this case, the forecast analyst may utilize multiple regression. Analogous to linear regression analysis, but with multiple independent variables. Multiple regression supported by statistical software packages.

Qualitative Forecasting Techniques Generally used to take advantage of expert knowledge. Useful when judgment is required, when products are new, or if the firm has little experience in a new market. Examples Market research Panel consensus Historical analogy Delphi method

Collaborative Planning, Forecasting, and Replenishment (CPFR) A web-based process used to coordinate the efforts of a supply chain. Demand forecasting Production and purchasing Inventory replenishment Integrates all members of a supply chain – manufacturers, distributors, and retailers. Depends upon the exchange of internal information to provide a more reliable view of demand.

CPFR Steps Creation of a front-end partnership agreement Joint business planning Development of demand forecasts Sharing forecasts Inventory replenishment

Principles Forecasting is a fundamental step in any planning process. Forecast effort should be proportional to the magnitude of decisions being made. Web-based systems (CPFR) are growing in importance and effectiveness. All forecasts have errors – understanding and minimizing this error is the key to effective forecasting processes.