Forecasting

Forecasting February 26, 2007

Laws of Forecasting • Three Laws of Forecasting • Forecasts are always wrong! • Detailed forecasts are worse than aggregate forecasts! • The further into the future, the less reliable the forecast will be!

Forecasting • Starting point of all Production Planning systems • Qualitative Forecasting techniques • Quantitative Forecasting techniques • Choice of technique varies with the Product Life Cycle

Product Development Stage • Should we enter into this business? What segments? • What are the alternative growth opportunities for product X? • How have established products similar to X fared? • How should we allocate R&D efforts and funds? • Where will be the market 5 years, 10 years from now?

Preliminaries • What is the purpose of forecast? How is it to be used? • Accuracy and power required by the techniques • Requirements for entering a business vs. next year’s budget • Impact of promotions and other marketing devices • Techniques vary with cost, scope and accuracy • Forecaster should fix the level of tolerance of accuracy • Helps in managing the trade-offs • Accurate forecast reduces inventory (cost of inventory vs. cost of forecasting)

Qualitative Forecasting • Relies on expertise of people • Data is scarce • Usually used for technological forecasts (long term forecasts) • Delphi Method, Market Research, Panel Consensus

Quantitative Forecasting • Time Series models • Predict a future parameter as a function of past values of that parameter (e.g., historical demand) • Systematic variation is captured (seasonality, trend) • Cyclic patterns • Growth (decline) rates of the trends • Assume future is like past (hence useful for short term forecasts) • Managers need to look at the turning points in future that change the past trends

Time Series Forecasting • Time period i = 1,2,…..t (most recent data) • A(i): Actual observations • f(t+λ): Forecasts for t + λ, λ = 1,2,……, • F(t): smoothed estimate (current position of the process under consideration) • T(t): smoothed trend A(i), i =1,2,…t Time Series Model f(t+λ), λ =1,2,3,…,

Time Series Forecasting • Moving-Average Model • Exponential Smoothing Model • Exponential Smoothing with a Linear Trend Model • Winter’s Method (adds seasonal multipliers to the exponential smoothing with linear trend model)

Quantitative Forecasting • Causal models • Most sophisticated • Predict a future parameter (e.g., demand for a product) as a function of other parameters (e.g., interest rates, marketing strategy).

Causal Forecasting • Opening a fast food restaurant • Demand forecast? • Predictable parameters • Population in the vicinity • Competition • Use statistics (e.g., regression) to estimate the parameters • Y = b0 + b1x1 + b2X2

Components of an Observation Observed demand (O) = Systematic component (S) + Random component (R) Level (current deseasonalized demand) Trend (growth or decline in demand) Seasonality (predictable seasonal fluctuation) • Systematic component: Expected value of demand • Random component: The part of the forecast that deviates from the systematic component • Forecast error: difference between forecast and actual demand

Time Series Forecasting Forecast demand for the next four quarters.

Time Series Forecasting

Basic Approach toDemand Forecasting • Understand the objectives of forecasting • Integrate demand planning and forecasting • Identify major factors that influence the demand forecast • Understand and identify customer segments • Determine the appropriate forecasting technique • Establish performance and error measures for the forecast

Quantity Time Patterns of Demand (a) Horizontal: Data cluster about a horizontal line.

Quantity Time Patterns of Demand (b) Trend: Data consistently increase or decrease.

Year 1 Quantity Year 2 | | | | | | | | | | | | J F M A M J J A S O N D Months Patterns of Demand (c) Seasonal: Data consistently show peaks and valleys.

Quantity | | | | | | 1 2 3 4 5 6 Years Patterns of Demand (c) Cyclical: Data reveal gradual increases and decreases over extended periods.

DEMAND FORECAST APPLICATIONS Demand Forecast Applications Time Horizon Medium Term Long Term Short Term (3 months– (more than Application (0–3 months) 2 years) 2 years) Forecast quantity Individual products or services Decision area Inventory management Final assembly scheduling Workforce scheduling Master production scheduling Forecasting Time series technique Causal Judgment Total sales Groups or families of products or services Staff planning Production planning Master production scheduling Purchasing Distribution Causal Judgment Total sales Facility location Capacity planning Process management Causal Judgment

Deviation, or error Regression equation: Y = a + bX Y Estimate of Y from regression equation { Actual value of Y Dependent variable Value of X used to estimate Y X Independent variable Causal MethodsLinear Regression

Sales Advertising Month (000 units) (000 $) 1 264 2.5 2 116 1.3 3 165 1.4 4 101 1.0 5 209 2.0 Causal MethodsLinear Regression a = – 8.136 b = 109.229X r = 0.98 r2 = 0.96

300 — 250 — 200 — 150 — 100 — 50 Sales Advertising Month (000 units) (000 $) 1 264 2.5 2 116 1.3 3 165 1.4 4 101 1.0 5 209 2.0 a = – 8.136 b = 109.229X r = 0.98 r2 = 0.96 syx = 15.61 Sales (thousands of units) | | | | 1.0 1.5 2.0 2.5 Advertising (thousands of dollars) Causal MethodsLinear Regression

300 — 250 — 200 — 150 — 100 — 50 Sales Advertising Month (000 units) (000 $) 1 264 2.5 2 116 1.3 3 165 1.4 4 101 1.0 5 209 2.0 a = – 8.136 b = 109.229X r = 0.98 r2 = 0.96 syx = 15.61 Sales (thousands of units) Y = – 8.136 + 109.229X | | | | 1.0 1.5 2.0 2.5 Advertising (thousands of dollars) Causal MethodsLinear Regression

300 — 250 — 200 — 150 — 100 — 50 Sales Advertising Month (000 units) (000 $) 1 264 2.5 2 116 1.3 3 165 1.4 4 101 1.0 5 209 2.0 a = – 8.136 b = 109.229X r = 0.98 r2 = 0.96 syx = 15.61 Sales (thousands of units) Y = – 8.136 + 109.229X | | | | 1.0 1.5 2.0 2.5 Forecast for Month 6 X = $1750, Y = – 8.136 + 109.229(1.75) Advertising (thousands of dollars) Causal MethodsLinear Regression

300 — 250 — 200 — 150 — 100 — 50 Sales Advertising Month (000 units) (000 $) 1 264 2.5 2 116 1.3 3 165 1.4 4 101 1.0 5 209 2.0 a = – 8.136 b = 109.229X r = 0.98 r2 = 0.96 syx = 15.61 Sales (thousands of units) Y = – 8.136 + 109.229X | | | | 1.0 1.5 2.0 2.5 Forecast for Month 6 X = $1750, Y = 183.015, or 183,015 units Advertising (thousands of dollars) Causal MethodsLinear Regression

300 — 250 — 200 — 150 — 100 — 50 Sales Advertising Month (000 units) (000 $) 1 264 2.5 2 116 1.3 3 165 1.4 4 101 1.0 5 209 2.0 a = – 8.136 b = 109.229X r = 0.98 r2 = 0.96 syx = 15.61 Sales (thousands of units) Y = – 8.136 + 109.229X | | | | 1.0 1.5 2.0 2.5 Advertising (thousands of dollars) Causal MethodsLinear Regression

300 — 250 — 200 — 150 — 100 — 50 Sales Advertising Month (000 units) (000 $) 1 264 2.5 2 116 1.3 3 165 1.4 4 101 1.0 5 209 2.0 a = – 8.136 b = 109.229X r = 0.98 r2 = 0.96 syx = 15.61 Sales (thousands of units) Y = – 8.136 + 109.229X | | | | 1.0 1.5 2.0 2.5 If current stock = 62,500 units, Production = 183,015 – 62,500 = 120,015 units Advertising (thousands of dollars) Causal MethodsLinear Regression

450 — 430 — 410 — 390 — 370 — Patient arrivals Actual patient arrivals | | | | | | 0 5 10 15 20 25 30 Week Time-Series MethodsSimple Moving Averages

450 — 430 — 410 — 390 — 370 — Patient Week Arrivals 1 400 2 380 3 411 Patient arrivals Actual patient arrivals Actual patient arrivals | | | | | | 0 5 10 15 20 25 30 Week Time-Series MethodsSimple Moving Averages

450 — 430 — 410 — 390 — 370 — Patient Week Arrivals 1 400 2 380 3 411 Patient arrivals 411 + 380 + 400 3 F4 = Actual patient arrivals | | | | | | 0 5 10 15 20 25 30 Week Time-Series MethodsSimple Moving Averages

450 — 430 — 410 — 390 — 370 — Patient Week Arrivals 1 400 2 380 3 411 Patient arrivals F4 = 397.0 Actual patient arrivals | | | | | | 0 5 10 15 20 25 30 Week Time-Series MethodsSimple Moving Averages

450 — 430 — 410 — 390 — 370 — Patient Week Arrivals 2 380 3 411 4 415 Patient arrivals 415 + 411 + 380 3 F5 = Actual patient arrivals | | | | | | 0 5 10 15 20 25 30 Week Time-Series MethodsSimple Moving Averages

450 — 430 — 410 — 390 — 370 — Patient Week Arrivals 2 380 3 411 4 415 Patient arrivals F5 = 402.0 Actual patient arrivals | | | | | | 0 5 10 15 20 25 30 Week Time-Series MethodsSimple Moving Averages

450 — 430 — 410 — 390 — 370 — 6-week MA forecast 3-week MA forecast Patient arrivals Actual patient arrivals | | | | | | 0 5 10 15 20 25 30 Week Time-Series MethodsSimple Moving Averages

450 — 430 — 410 — 390 — 370 — Exponential Smoothing  = 0.10 Ft +1 = Ft +  (Dt – Ft ) | | | | | | 0 5 10 15 20 25 30 Week Time-Series MethodsExponential Smoothing Patient arrivals

450 — 430 — 410 — 390 — 370 — Exponential Smoothing  = 0.10 F3 = (400 + 380)/2 D3 = 411 F4 = 0.10(411) + 0.90(390) | | | | | | 0 5 10 15 20 25 30 Week Time-Series MethodsExponential Smoothing Ft +1 = Ft +  (Dt – Ft ) Patient arrivals

450 — 430 — 410 — 390 — 370 — Exponential Smoothing  = 0.10 Ft +1 = Ft +  (Dt – Ft ) Patient arrivals F3 = (400 + 380)/2 D3 = 411 F4 = 392.1 | | | | | | 0 5 10 15 20 25 30 Week Time-Series MethodsExponential Smoothing

450 — 430 — 410 — 390 — 370 — Exponential Smoothing  = 0.10 Ft +1 = Ft +  (Dt – Ft ) Patient arrivals F4 = 392.1 D4 = 415 F4 = 392.1 F5 = 394.4 | | | | | | 0 5 10 15 20 25 30 Week Time-Series MethodsExponential Smoothing

450 — 430 — 410 — 390 — 370 — Patient arrivals | | | | | | 0 5 10 15 20 25 30 Week Time-Series MethodsExponential Smoothing

450 — 430 — 410 — 390 — 370 — Patient arrivals Exponential smoothing  = 0.10 | | | | | | 0 5 10 15 20 25 30 Week Time-Series MethodsExponential Smoothing

450 — 430 — 410 — 390 — 370 — 6-week MA forecast 3-week MA forecast Patient arrivals Exponential smoothing  = 0.10 | | | | | | 0 5 10 15 20 25 30 Week Time-Series MethodsExponential Smoothing

80 — 70 — 60 — 50 — 40 — 30 — Patient arrivals Actual blood test requests | | | | | | | | | | | | | | | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Week Time-Series MethodsTrend-Adjusted Exponential Smoothing

80 — 70 — 60 — 50 — 40 — 30 — Medanalysis, Inc. Demand for blood analysis At = Dt + (1 – )(At-1+ Tt-1) Tt = (At – At-1) + (1 – )Tt-1 Patient arrivals | | | | | | | | | | | | | | | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Week Time-Series MethodsTrend-Adjusted Exponential Smoothing

80 — 70 — 60 — 50 — 40 — 30 — Medanalysis, Inc. Demand for blood analysis At = Dt + (1 – )(At-1+ Tt-1) Tt = (At – At-1) + (1 – )Tt-1 Patient arrivals A0 = 28 patients T0 = 3 patients  = 0.20  = 0.20 A1 = 0.2(27) + 0.80(28 + 3) T1 = 0.2(30.2 - 28) + 0.80(3) | | | | | | | | | | | | | | | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Week Time-Series MethodsTrend-Adjusted Exponential Smoothing

80 — 70 — 60 — 50 — 40 — 30 — Medanalysis, Inc. Demand for blood analysis At = Dt + (1 – )(At-1+ Tt-1) Tt = (At – At-1) + (1 – )Tt-1 Patient arrivals A0 = 28 patients T0 = 3 patients  = 0.20  = 0.20 A1 = 30.2 T1 = 2.8 Forecast2 = 30.2 + 2.8 = 33 | | | | | | | | | | | | | | | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Week Time-Series MethodsTrend-Adjusted Exponential Smoothing

Forecasting

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