Quantitative Forecasting Methods (Non-Naive) Time Series Associative Models Models Méthodes chronologiques – Projeter dans le futur les expériences passées, avec ou sans ajustements. Méthodes causales – Développement d’une équation mathématique qui permet aux gestionnaires de prévoir le volume des ventes en fonction d’autres variables. Exemples: - Prix du baril de pétrole - Prévisions météorologiques - En terme de dollars publicitaires dépensés - Demande pour un produit complémentaire (ex: clavier pour ordinateur) - Indices économiques Moving Exponential Trend Multiple Average Smoothing Projection Regression

Time Series Assume that what has occurred in the past will continue to occur in the future Relate the forecast to only one factor  TIME Include naive forecast simple average moving average exponential smoothing linear trend analysis

Moving Averages Naive forecast Simple moving average Demand of the current period is used as next period’s forecast Simple moving average stable demand with no pronounced behavioral patterns Weighted moving average weights are assigned to most recent data

Naive forecast ORDERS MONTH PER MONTH - 120 90 100 75 110 50 130 Nov - Jan 120 Feb 90 Mar 100 Apr 75 May 110 June 50 July 75 Aug 130 Sept 110 Oct 90

n = number of periods in the moving average Simple Moving Average n i = 1  Di MAn = n where n = number of periods in the moving average Di = demand in period i

3-month Simple Moving Average ORDERS MONTH PER MONTH MOVING AVERAGE Jan 120 Feb 90 Mar 100 Apr 75 May 110 June 50 July 75 Aug 130 Sept 110 Oct 90 Nov - – 103.3 88.3 95.0 78.3 85.0 105.0 110.0 MA3 = 3 i = 1  Di = 90 + 110 + 130 = 110 orders for Nov Concentrates on most recent data. The more dynamic the environment, the smaller n is used. If we use n=2 (110+90) / 2 = 100 If we use n=4 (90+110+130+75) /4 = 101,3 The n is established through trial and error. Note: April’s forecast was way too high but the low sales corrected May’s forecast.

Weighted Moving Average WMAn = i = 1  Wi Di where Wi = the weight for period i, between 0 and 100 percent  Wi = 1.00 Adjusts moving average method to more closely reflect data fluctuations Copyright 2006 John Wiley & Sons, Inc.

Weighted Moving Average Example MONTH WEIGHT DATA August 17% 130 September 33% 110 October 50% 90 WMA3 = 3 i = 1  Wi Di = (0.50)(90) + (0.33)(110) + (0.17)(130) = 103.4 orders November Forecast Traditionally, Nov looks more like Oct than Aug. Weight is also established by trial and error. Copyright 2006 John Wiley & Sons, Inc.

Potential Problems With Moving Average Increasing n smooths the forecast but makes it less sensitive to changes Do not forecast trends well Require extensive historical data

Exponential Smoothing Form of weighted moving average Weights decline exponentially Most recent data weighted most Requires smoothing constant () Ranges from 0 to 1 Subjectively chosen Involves little record keeping of past data

Exponential Smoothing New forecast = last period’s forecast + a (last period’s actual demand – last period’s forecast) Ft = Ft – 1 + a(At – 1 - Ft – 1) where Ft = new forecast Ft – 1 = previous forecast a = smoothing (or weighting) constant (0  a  1)

Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant a = .20

Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant a = .20 New forecast = 142 + .2(153 – 142)

Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant a = .20 New forecast = 142 + .2(153 – 142) = 142 + 2.2 = 144.2 ≈ 144 cars

Common Measures of Error Mean Absolute Deviation (MAD) MAD = ∑ |actual - forecast| n Mean Squared Error (MSE) MSE = ∑ (forecast errors)2 n

Trend analysis Many trends are possible: Linear Exponential Logarithmic S-growth curve

Linear Trend Analysis