Forecasting THE FIRST STEP FOR DEMAND PLANNING Investigación de Operaciones Intro Vs. ¿Why do I need to forecast demand? Investigación de Operaciones Intro – In Pull processes: Plan for inventory levels and capacity – In Push processes: Plan for Production & wharehousing, logistics In supply chains, forecasting is essential for the estimation of future demand It is the first step of a supply chain manager in order to plan & scale all other activities Investigación de Operaciones Forecasting basics Beware of how you use the forecast!!! Case 1: Sales for next semester are expected to be between 100 and 1900 units monthly Case 2: Sales for next semester are expected to be between 900 and 1100 units monthly Average expected monthly sales: 1000 However…. Supply chain policies should be very different Investigación de Operaciones Forecasting basics Better short term than long term Case 1: Ice cream shop forecasting for next week Case 2: Ice cream shop forecasting for next month or semester In general, short-term forecasts are more precise than long term forecasts, because they use more accurate information Investigación de Operaciones Forecasting basics Always easier to aggregate demand (SKU families, geography, etc.) Case 1: Annual Coca-Cola sales in Uruguay vs Daily Coca-Cola Light sales in Montevideo Case 2: Students entering the University in Uruguay in 2022 vs number of students entering at FIUM in 2022 Investigación de Operaciones Forecasting basics There is no best system to forecast Usually, the further up in the value chain, the more distorted the information Most planners/managers usually prefer a range of acceptable values rather than a single value. Investigación de Operaciones Factors affecting the demand • Historic demand • Product lead time • Marketing campaigns or promotions • Economic and political issues • Other competitors Observed Demand = Systematic component + random component (noise) Investigación de Operaciones Beware: You have to be skeptical with a forecast that has no error with respect to the historical demand!!! Basic steps 1. Understand the purpose of the forecast 2. Understand the relative importance of forecasting demand in the supply chains and integrate it into planning 3. Understand and identify the different segments, products, customers 4. Establish the main factors influencing demand 5. Select the most proper technique for forecasting and run the forecast 6. Select and calculate error and performance metrics Investigación de Operaciones Different methods Judgmental (Qualitative) Causal Subjective, based on human judgements. Products with little or no historical information. Correlation with certain specific factors. Look for that correlation and estimate demand from regressions Time series Simulation Historical demand to predict future demand. Simple methods that serve for stable products or as a basis for other methods. Seeks to mimic consumer behavior to predict future scenarios Investigación de Operaciones Time series definition • Series of observations over time of some quantity of interest, measured at constant intervals of time (X1, X2, X3,…) Daily Monthly Bi-annually Annually Investigación de Operaciones Possible components of Time-series Constant Level (L) Seasonality (S) Trend (T) All together Important: Remember that all observed demand will always have random error Investigación de Operaciones Basic Notation Origin: t: when I do the forecast Time horizon k: for which period I am forecasting Ft,t+k is the forecast at period t for period t+k: Ft,t+k = E [Xt+k | Xt, Xt-1, Xt-2,….,X1] Example: If t=10, k=4 , then F10,14 is the forecast for t=14 conducted at the end of period t=10 (using data point until X10): F10,14 = E [X14 | X10, X9, … ,X1] 4 0 Investigación de Operaciones 2 4 6 8 10 12 14 16 FORECASTING METHODS FOR A CONSTANT-LEVEL MODEL • The simplest model to make a forecast using time-series is to assume only a constant-level model • Four alternative forecastig methods: Last-Value Forecast Averaging Forecast Moving-Average Forecast Exponential Smoothing Forecast Investigación de Operaciones Last Value Forecast (Naïve method) Model: Xt = Lt + εt Our model is trying to estimate the Level (L) at time t. By interpreting t as the current time, the last-value forecasting procedure uses the value of the time series observed at time t (xt) as the forecast at time t+1. Therefore, Ft+1 = xt It is worth considering when the underlying assumption about the constant-level model is “shaky” and the process is changing so rapidly that anything before time t is almost irrelevant or misleading Investigación de Operaciones Averaging Forecast Model: Xt = Lt + εt Our model is trying to estimate the Level (L) at time t. This method uses all the data points in the time series and simply averages these points. Thus, the forecast of what the next data point will turn out to be is: Ft+1 = 𝑡 𝑥𝑖 𝑖=1 𝑡 This estimate is an excellent one if the process is entirely stable Investigación de Operaciones Moving Average Forecast Model: Xt = Lt + εt Our model is trying to estimate the Level (L) at time t. This method averages the data for only the last n periods as the forecast for the next period: Ft+1 = 𝑥𝑖 𝑡 𝑖=𝑡−𝑛+1 𝑛 The moving-average estimator combines the advantages of the last value and averaging estimators in that it uses only recent history, and it uses multiple observations Investigación de Operaciones Exponential Smoothing Forecast This forecasting method is just a weighted sum of the last observation xt and the preceding forecast Ft for the period just ended. Ft+1= αxt + (1-α)Ft where α(0 ≤ α ≤ 1) is called the smoothing constant Because of this recursive relationship between Ft+1 and Ft, alternatively Ft+1 can be expressed as Ft+1= αxt + α(1-α)xt-1 + α(1-α)2xt-2 + α(1-α)3xt-3 + … + α(1-α)nxt-n Another alternative form for the exponential smoothing technique is given by: Ft+1= Ft + α(xt – Ft) Investigación de Operaciones Exponential smoothing ¿What happens for different values of α? If α=0 then: Ft+1= Ft the forecast turns into the averaging forecast method (using all historical data) If α=1 then: Ft+1= xt the forecast turns into de Last value method (only considering last data point available) If 0<α<1 then: Ft+1= αxt + α(1-α)xt-1 + α(1-α)2xt-2 + … + α(1-α)nxt-n the forecast turns into a smoothing average, considering all data points, but gives less weigth to older information Investigación de Operaciones Comparing the four constant level forecasting methods Consider Ft+1= ΣwiDi with D being the actual demand points Di D0 Último valor Promedio total histórica Promedio Móvil (N períodos) Suavizado exponencial wi wi wi wi 0 1/t 0 D1 0 1/t 0 D2 0 1/t 0 D3 0 1/t 0 … 0 1/t 0 si i<t-N; 1/N si i≥t-N α(1-α) Dt-i Dt-2 0 1/t 1/N α(1-α)2Dt-2 Dt-1 0 1/t 1/N α(1-α)Dt-1 Dt 1 1/t 1/N α Investigación de Operaciones i INCORPORATING SEASONAL EFFECTS It is fairly common for a time series to have a seasonal pattern with higher values at certain times of the year than others. In other words, the level changes according to the “season” in which we are. Repetitive pattern appearing every certain periodic cycles, e.g., seasonal months in the year, seasonal days in the week, hours in the day, etc. Investigación de Operaciones Example of seasonal effects Investigación de Operaciones Example of seasonal effects First, we need to adjust data point to remove the effect of seasonal patterns. To remove the seasonal effects from the time series shown in Fig. 27.3, each of these average daily call volumes needs to be divided by the corresponding seasonal factor given in Table 27.2. Investigación de Operaciones The General Procedure to forecast using seasonal factors 1. Compute seasonal factors S 2. Adjust each value in the time series using the seasonal factors 3. Select a time series forecasting method 4. Apply this method to the seasonally adjusted time series to obtain a forecast of the next seasonally adjusted value (or values) 5. Multiply this forecast by the corresponding seasonal factor to obtain a forecast of the next actual value (without seasonal adjustment). Investigación de Operaciones Forecast error Every demand value has an error component. A good forecast should capture only the systematic part of the demand (and not the error) The error should be considered within the forecast error, and it is important to measure it to: o See that the selected method correctly predicts the demand pattern o Take it into account when calculating risks and contingency plans E=F-D The error should be calculated with a term at least equal to the lead time we will have to be able to solve any problem Investigación de Operaciones Accuracy and Bias Investigación de Operaciones Forecast error metrics Investigación de Operaciones Exercise (constant level) “La Rinconada” Port The operational manager of the port terminal of Puerto La Rinconada wants to try different methods to update the forecasts of grain discharge from ships. You are requested to examine the moving average (N=3), Last value, and simple exponential smoothing with alpha 0.10 and alpha 0.50. Graph and compare using MAD. Select the most appropriate method. Investigación de Operaciones Month Past sales (tons) September October November December January February March April May 180 168 159 175 190 205 180 182 ? Incorporating Linear Trend into Forecasting models Suppose that the generating process of the observed time series can be represented by a linear trend superimposed with random fluctuations General Model: Xi = A + B*i + ε i Our Forecast should try to estimate A and B as best as possible Investigación de Operaciones Incorporating Linear Trend into Forecasting models Modelo Holt’s (double smoothing): We define Tt+1 as the exponential smoothing estimate of the trend factor B at time t+1, given the observed values, X1= x1, X2= x2, . . . , Xt= xt. Given Tt+1, the forecast of the value of the time series at time t+1 (Ft+1) is obtained simply by adding Tt+1 to the formula for Ft+1 seen for simple exponential smoothing: Ft+1= xt + (1- )Ft + Tt+1 Then, we could use the following formula in order to update the forecasted trend: Tt+1= (α(xt-xt-1) + (1- α)(Ft – Ft-1)) + (1- )Tt 0<α<1 0<β<1 This method requires two initial estimates: • x0= initial estimate of the expected value of the time series (A) if the conditions just prior to beginning forecasting were to remain unchanged without any trend • T1 =initial estimate of the trend of the time series (B) just prior to beginning forecasting Investigación de Operaciones Example (double smoothing) A manufacturer of music players notes that their demand has been increasing in the last 6 months. It has the following data. You want to forecast your future demand for period 7 using double exponential smoothing with alpha = 0.1 and beta = 0.2. Investigación de Operaciones Month Units sold (miles) 1 8415 2 8732 3 9014 4 9808 5 10413 6 11961 Exercise (double smoothing) Factory “Blue ducks" The factory manager for blue ducks wants to forecast the demand for his main product which is blue duck shaped pop machines. The manager suspects that the latest data reflects a positive trend in the data. You want to test Holt's method using alpha 0.2 and beta 0.4 . Investigación de Operaciones Month Demand (units sold) 1 2 3 4 5 6 7 8 9 10 12 17 20 19 24 21 31 28 36 ?
