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## MNG221 - Management Science

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**MNG221 - Management Science**Forecasting**Lecture Outline**• Forecasting basics • Moving average • Exponential smoothing • Linear trend line • Forecast accuracy**Forecasting**Forecasting Basics**Forecasting Basics**• A Forecast– is a prediction of something that is likely to occur in the future. • A variety of forecasting methods exist, and their applicabilityis dependent on the: • time frame of the forecast (i.e., how far in the future we are forecasting),**Forecasting Basics**• A variety of forecasting methods exist, and their applicabilityis dependent on the: • the existence of patterns in the forecast (i.e., seasonal trends, peak periods), and • the number of variables to which the forecast is related.**Forecasting**Forecasting Components**Forecasting Components**• Time Frames of Forecast: • Short Range - encompass the immediate future and are concerned with the daily operations rarely goes beyond a couple months into the future.**Forecasting Components**• Time Frames of Forecast: • Medium Range - encompasses anywhere from 1 or 2 months to 1 year. • More closely related to a yearly production plan and will reflect such items as peaks and valleys in demand**Forecasting Components**• Time Frames of Forecast: • Long Range - encompasses a period longer than 1 or 2 years. • It is Related to management's attempt to plan new products for changing markets, build new facilities, or secure long-term financing.**Forecasting Components**• Forecasts can exhibit patterns or trend: • A trend is a long-term movement of the item being forecast • Random variations are movements that are not predictable and follow no pattern (and thus are virtually unpredictable).**Forecasting Components**Forecasts can exhibit patterns or trend: • A cycle is an undulating movement in demand, up and down, that repeats itself over a lengthy time span (i.e., more than 1 year). • A seasonal pattern is an oscillating movement in demand that occurs periodically (in the short run) and is repetitive. • Seasonality is often weather related.**Forecasting Components: Forecast Patterns**Forms of forecast movement: (a) trend, (b) cycle, (c) seasonal pattern, and (d) trend with seasonal pattern**Forecasting**Forecasting Methods**Forecasting Methods**The forecasting component determines to a certain extent the type of forecasting method that can or should be used. • Time Series - is a category of statistical techniques that uses historical data to predict future behavior.**Forecasting Methods**• Regression (or causal) methods - attempt to develop a mathematical relationship (in the form of a regression model) between the item being forecast and factors that cause it to behave the way it does.**Forecasting Methods**• Qualitative methods - use management judgment, expertise, and opinion to make forecasts. • Often called "the jury of executive opinion," • They are the most common type of forecasting method for the long-term strategic planning process.**Forecasting Methods**Time Series Analysis**Time Series Methods**• Time series methods tend to be most useful for short-range forecasting, (although they can be used for longer-range forecasting) and relate to only one factor time.**Time Series Methods**• Two types of time series methods: • The Moving Average • Simple Moving Average • Weighted Moving Average • Exponential Smoothing.**Time Series – Moving Average**Moving Averages • The moving average method uses several values during the recent past to develop a forecast. • The moving average method is good for stable demand with no pronounced behavioral patterns.**Time Series – Moving Average**Moving Averages • Moving averages are computed for specific periods, such as 3 months or 5 months, depending on how much the forecaster desires to smooth the data.**Time Series – Moving Average**Simple Moving Averages • Moving average forecast may be computed for specified time period as follows: where n = number of periods in the moving average D = data in period i**Time Series – Moving Average**Simple Moving Averages - Delivery Orders for 10-month period**Time Series – Moving Average**Simple Moving Averages Example • The moving average from the demand for orders for the last 3 months in the sequence:**Time Series – Moving Average**Simple Moving Averages Example • The 5-month moving average is computed from the last 5 months of demand data, as follows:**Time Series – Moving AverageSimple 3- and 5- month Moving**Average**Time Series – Moving AverageSimple 3- and 5- month Moving**Average Longer-period moving averages react more slowly to recent demand changes than do shorter-period moving averages.**Time Series – Moving Average**Weighted Moving Average • The major disadvantage of the Simple Moving Averagemethod is that it does not react well to variations that occur for a reason, such as trends and seasonal effects (although this method does reflect trends to a moderate extent).**Time Series – Moving Average**Weighted Moving Average • The Simple Moving Average method can be adjusted to reflect more closely more recent fluctuations in the data and seasonal effects. • This adjusted method is referred to as a Weighted Moving Average method.**Time Series – Moving Average**• Weighted Moving Average - isa time series forecasting method in which the most recent data are weighted. • It may be computed for specified time period using the following:**Time Series – Moving Average**• Weighted Moving Average - Where: Wi= the weight for period i, is between 0% and 100% ∑Wi =1.00 Di= data in period i**Time Series – Moving AverageWeighted Moving Average**For example, if the Instant Paper Clip Supply Company wants to compute a 3-month weighted moving average with a weight of 50% for the October data, a weight of 33% for the September data, and a weight of 17% for August, it is computed as.**Time Series – Exponential Smoothing**• The Exponential Smoothing forecast method is an averaging method that weights the most recent past data more strongly than more distant past data. • There are two forms of exponential smoothing: • Simple Exponential Smoothing • Adjusted Exponential Smoothing (adjusted for trends, seasonal patterns, etc.)**Time Series – Exponential Smoothing**Simple Exponential Smoothing • The simple exponential smoothing forecast is computed by using the formula:**Time Series – Exponential Smoothing**Simple Exponential Smoothing where Ft+1 = the forecast for the next period Dt = the actual demand for the present period Ft = the previously determined forecast for the present periods α= a weighting factor referred to as the smoothing constant**Time Series – Exponential Smoothing**Simple Exponential Smoothing • The smoothing constant, α, is betw. 0 & 1. • It reflects the weight given to the most recent demand data. • For example, if α= .20, • Ft+1 = .20Dt + .80Ft • This means that our forecast for the next period is based on 20% of recent demand (Dt) and 80% of past demand.**Time Series – Exponential Smoothing**Simple Exponential Smoothing • The higher α is (the closer α is to one), the more sensitive the forecast will be to changes in recent demand. • Alternatively, the closer αis to zero, the greater will be the dampening or smoothing effect.**Time Series – Exponential Smoothing**Simple Exponential Smoothing • The most commonly used values of αare in the range from .01 to .50. • However, the determination of αis usually judgmental and subjective and will often be based on trial-and-error experimentation.**Time Series – Exponential Smoothing**• A company - PM Computer Serviceshas accumulated demand data in table for its computers for the past 12 months. • It wants to compute exponential smoothing forecasts, using smoothing constants (α) equal to 0.30 and 0.50. Simple Exponential Smoothing Example**Time Series – Exponential Smoothing**Simple Exponential Smoothing Example • To develop the series of forecasts for the data i, start with period 1 (January) and compute the forecast for period 2 (February) by using α= 0.30. • The formula for exponential smoothing also requires a forecast for period 1, which we do not have, so we will use the demand for period 1 as both demand and the forecast for period 1.**Time Series – Exponential Smoothing**Simple Exponential Smoothing Example • Thus the forecast for February is: • F2 = αD1+ (1 - α)F1 • = (.30)(37) + (.70)(37) = 37 units**Time Series – Exponential Smoothing**Simple Exponential Smoothing Example • The forecast for period 3 is computed similarly: F3= α D2+ (1 - α)F2 = (.30)(40) + (.70)(37) = 37.9 units • The final forecast is for period 13, January, and is the forecast of interest to PM Computer Services: F13= α D12+ (1 - α)F12 = (.30)(54) + (.70)(50.84) = 51.79 units**Time Series – Exponential Smoothing**Simple Exponential Smoothing Example**Time Series – Exponential Smoothing**Simple Exponential Smoothing Example • In general, when demand is relatively stable, without any trend, using a small value for αis more appropriate to simply smooth out the forecast. • Alternatively, when actual demand displays an increasing (or decreasing) trend, as is the case, a larger value of αis generally better.**Time Series – Exponential Smoothing**Adjusted Exponential Smoothing • The adjusted exponential smoothing forecast consists of the exponential smoothing forecast with a trend adjustment factor added to it. • The formula for the adjusted forecast is: AFt+1= Ft+1 + Tt+1 where T = an exponentially smoothed trend factor**Time Series – Exponential Smoothing**Adjusted Exponential Smoothing • The trend factor is computed much the same as the exponentially smoothed forecast. • It is, in effect, a forecast model for trend: Tt+1 = β(Ft+1- Ft) + (1 - β)Tt where Tt = the last period trend factor β = a smoothing constant for trend**Time Series – Exponential Smoothing**Adjusted Exponential Smoothing • Like α, βis a value between 0 and 1. • It reflects the weight given to the most recent trend data. • Also like α, β is often determined subjectively, based on the judgment of the forecaster.**Time Series – Exponential Smoothing**Adjusted Exponential Smoothing • A highβ reflects trend changes more thanalowβ. • It is not uncommon for β to equal αin this method. • The closer βis to one, the stronger a trend is reflected.**Time Series – Exponential Smoothing**Adjusted Exponential Smoothing Example • PM Computer Services now wants to develop an adjusted exponentially smoothed forecast, using the same 12 months of demand. • The adjusted forecast for February, AF2, is the same as the exponentially smoothed forecast because the trend computing factor will be zero (i.e., F1 and F2 are the same and T2 = 0).