MS 401 - Production and Service Systems Operations Forecasting Murat Kaya FENS, Sabanci University

Predicting the Future “My concern is with the future since I plan to spend the rest of my life there” C. F. Kettering Hertz: How many cars will be rented during March 2008? Apple: How many iPod Nano 8GB will be sold in 2008? Why is it important to know the answers to these questions?

If Forecasting Fails Cisco could not forecast the demand for networking equipment correctly result: lost $2.5 billion due to unsold products Volvo – Green car example (mid 1990s) excessive amount of green color cars in the middle of the year to sell these cars, marketing offered special promotions and discounts

Forecasts Forecast: An estimate of the future level of some variable Characteristics of Forecasts They are usually wrong the planning systems that use forecasts should be robust A good forecast is more than a single number include some measure of anticipated error Aggregate forecasts are more accurate The longer the forecast horizon, the less accurate the forecast will be Forecasts should not be used to the exclusion of known information some information may not be present in the past history

Time Series Methods Time series: A collection of observations of some economic or physical phenomenon drawn at discrete points in time The idea: Information can be inferred from the pattern of past observations and can be used to forecast the future value of the series Patterns in time series trend: tendency of a time series to exhibit a stable pattern of growth or decline seasonality: having a pattern that repeats in fixed intervals cycles: similar to seasonality, but the length and the magnitude of the cycle may vary randomness: when there is no recognizable pattern to the data

Time Series Patterns Copyright © 2001 by The McGraw-Hill Companies, Inc

Evaluating Forecasts

Random versus Biased Forecast Errors Copyright © 2001 by The McGraw-Hill Companies, Inc

Forecasting Stationary Time Series Stationary time series: Each observation can be represented by a constant plus a random fluctuation Two methods moving averages (MA) exponential smoothing (ES)

Moving Averages (MA) A moving average of order N is the arithmetic average of the most recent N observations When calculating the forecast for the following period (period t+1), we do not need to recalculate the N-period average because Example 2.2

Moving Average Lags Behind the Trend

Exponential Smoothing (ES) The current forecast is the weighted average of the current observation of demand and the last forecast High α: forecast reacts better, however it is less stable

Weights in Exponential Smoothing Copyright © 2001 by The McGraw-Hill Companies, Inc

Exponential Smoothing with Different α Values Copyright © 2001 by The McGraw-Hill Companies, Inc

The forecasts are quite stable due to low α Example 2.3 from Nahmias Observed number of failures: 200, 250, 175, 186, 225, 285, 305 190 Assume F1 was 200 (we need a starting value) Using α=0.1 The forecasts are quite stable due to low α

In-Class Exercise Handy, Inc. produces a calculator that experienced the following monthly sales history for the first four months of the year: Jan:23.3; Feb: 72.3; March: 30.3; April: 15.5 If the forecast for January was 25, determine the one-step-ahead forecasts for February, March, April and May using exponential smoothing with α=0.15 Repeat the calculations using α=0.40 Compute the MSEs for the forecasts in parts (a) and (b)

Solution - 1 Ft = Dt-1 + (1-)Ft-1

Solution - 2

Similarities Between Moving Averages and Exponential Smoothing Stationary demand assumption can also handle shifts in demand (will adjust) Single parameter: N, α small N or large α results in greater weight on current data more responsive forecasts Not effective in catching trends both lag behind trends

Differences Between Moving Averages and Exponential Smoothing ES assigns weight to all past data points MA uses only the latest N ES requires only the latest data point MA requires to save N past data points

Forecasting Time Series with Trend Two methods regression analysis (we will not cover) fits a straight line to a set of data double exponential smoothing (Holt’s method) simultaneous smoothing on the series and the trend

Double Exponential Smoothing Using Holt’s Method Intercept Slope Initialization issue: The best way is to use some initial period data to estimate the initial intercept (S0) and slope (G0)

Example 2.5 from Nahmias Observed number of failures: 200, 250, 175, 186, 225, 285, 305, 190 Assume S0 = 200, G0 = 10. Use α=0.1, β=0.1 t Ft-1,t (forecasted) Dt (actual) St (intercept) Gt (slope) --- 200.0 10.0 1 210.0 200 209.0 9.9 2 218.9 250 222.0 10.2 3 232.2 175 226.5 9.6 4 236.1 186 … 5 240.3 225 6 247.7 285 Multi-step ahead forecast: F2,5=S2+(3)G2=222+(3)(10.2)=252.6

Forecasting Seasonal Series A seasonal series is a series that has a pattern repeating every N periods (length of the season) Note that this is different than using “season” to refer to a time of the year To model seasonality, use seasonal factors: ct represents the average amount that the demand in the tth period of the season is above or below the overall average We will study the Winter’s method triple exponential smoothing

Winter’s Method: Seasonal Series with Increasing Trend Copyright © 2001 by The McGraw-Hill Companies, Inc

Winter’s Method Assume a model of the form Trend Seasonal factors

Winter’s Method: Initialization Procedure Check Nahmias, page 85 for details Use at least two seasons of data (2N data) Calculate the sample means for the two seasons V1, V2 Calculate the initial slope estimate G0 Calculate the initial intercept estimate S0 Calculate the initial seasonal factors find the average of each seasonal factor normalize the seasonal factors (so that they sum up to 1)

Example 2.8 from Nahmias The data set: 10, 20, 26, 17, 12, 23, 30, 22 Initialize Suppose that at time t=1, we observe D1=16. Update the equations using α=0.2, β=0.1, γ=0.1 Suppose that we observe one full year of demand given by D1=16, D2=33, D3=34, D4=26. Update the equations again Season 1 Season 2

Seasonal Demand, No Trend Copyright © 2001 by The McGraw-Hill Companies, Inc

Affecting the Demand “The best way to forecast the future is to create it” Peter Drucker “Forecasting the demand” versus “demand planning”, or “demand management” Firms can “affect” their demand through their actions promotions sales effort Encourages the retailers / wholesalers to “forward buy” What are the effects of past promotions in the health of forecasting data?

Some Practical Issues Sales data versus demand data how can a firm capture “lost sales” ? Forecasting demand for a new product is difficult will it generate demand, or will it steal demand from existing products? Forecasting assumes that history represents future. What if there are some external changes? a new competitor Slow-moving items are hard to forecast sparse data