Chapter Ten: Objective Brief Introduction Of The Basic Conce

Chapter Tenobjectivea Brief Introduction Of The Basic Concepts Of For

Chapter TenObjective: A brief introduction of the basic concepts of Forecasting Tools like Moving average, Weighted Moving Average, Exponential Smoothing will be used to develop projection models. Chapter Content: Forecasting techniques: Into our class we will use a simple product to manufacturer. A plush eraser will be our product (Note: Don’t blame my drawing, only look at and enjoy it.). The first technique will be Moving Average (MA). This forecasting technique consists in the estimate of a average value from historical data that move as the new present value it’s know. This average is determinated by a series of terms or established periods ( n ). The quantity of periods (n) will be based in the variation that it exists between the historical data. If there is large variation, the value (n) must be greater to reflect the variation. If there is small variation, the value (n) can be smaller. Let us suppose that the following table shown the eraser’s demand for first six months of production. Period (Month) Demand Using the Moving Average equation: ( ) n i t A t MA ॠ- = ) ( Where: MA(t) is the forecasting for period t A(t-i) is the present for period t-i (n) is the number of periods to average If we looking for the forecasting for the fifth period, using n=2 and n=3, which would be the answer? N=2 N=3 A(4) = 1510 A(4) = 1510 A(3) = 1340 A(3) = 1340 --------------- A(2) = 1590 Σ = 2850 Σ = 4440 n = 2 n = 3 MA(5) = 1425 MA(5) = 1480 The average changes of period when calculating the next forecasting. When forecast the sixth period, the terms to be used for the average change according to the following example: N=2 N=3 A(5) = 1486 A(5) = 1486 A(4) = 1510 A(4) = 1510 --------------- A(3) = 1340 Σ = 2996 Σ = 4336 n = 2 n = 3 MA(6) = 1498 MA(6) = 1445.3 The next technique known like Weighted Moving Average , this technique to difference of regular moving average, each period have a weight assigned as output probability. The Moving average to divide the periods sum between the value (n), indirectly, it’s giving the same probability o weight to each period to determine the forecasting. ( ) ( ) ॠ- - = i t xW i t A t WMA ) ( Where t is the hoped period and i value run from 1 to n. Example, determining the sixth forecasting, with (n) = 2 Mov. Average Reg Weighted MA A(5) = 1486 x (50%) A(5) = 1486 x (75%) A(4) = 1510 x (50%) A(4) = 1510 x (25%) MA(6) = 1498 WMA(6) = 1492 This technique allow to assign a weight or probability according to expect behavior from marketing influences. I.e. to assign greater weight to the period value most recent a cause of a promotion. The quantity of periods or term to be used for estimate the forecast depends of the variation that exists between the historical data. That means, follow the same concept of moving average. The third technique is the Exponential Smoothing . This forecasting technique allows assigning a value of the possible error that may exist between the present value and their forecast. This use the difference between the real value and the previous period forecast to assign them weight or probability occurrence. ES (t)= F (t-1) + a [A(t-1) – F(t-1)] Where F (t-1) is the projection of the previous period and A(t-1) is the actual value of the previous period. α is the weight or probability assigned to the error or difference between two values. This may be estimated using the following formula: α = 2 / (n+1) Where n is the number for terms or periods to be projected. It is also common between the statistics the use of one α between 5% and 10%. If there is a large variation between the values it is recommended to use the 15% up to 30%. Lets make an example. To determine the fifth period of the table, we will have to realize each one of the projections until reaching the previous period. If we want the fifth projection we need to calculate projection 1 to 4. Note: For class purpose the first projection will be the actual value. Actual Projection Exponential Smoothing_______ + .05 [] = + .05 [] = + .05 [] = + .05 [] = 1283 ES (5) = 1283 For this moment we have three projection techniques that will help us forecast the future demand of a product, and then it should pass the planning process. Knowing the human behavior, after this reading you should be absolutely a sleep. “Please don’t fall a sleep know comes something good”. Which of these techniques may realize the best future forecast? It is important to notify that these are the unique projection techniques. There is a large number of them that may be applied depending on the behavior of historic data. For this chapter we will proceed to see which one makes the better forecast or is near reality. The following tool is used to measure the mistakes that exist between projection and the actual value. The Mean Absolute Deviation (MAD) determines the average of the absolutes differences between the two values. N Ft At MAD ॠ- = / / Where t run from 1 to N N is the differences number in the estimate, At is present value for the period t and Ft is the forecast for the period t. Using, the previews example of the three techniques we will proceed to determine which one is the most effective for the erasers demand. Moving Average n=3 Weighted MA n=2 A F /A-F/ A F /A-F/ A4=1510 F4= A3=1340 F3= A5=1486 F5= A4=1510 F4= A6=1440 F6= A5=1486 F5= A6=1440 F6= MAD = 43 MAD = 48 Exponential Smoothing A F /A-F/ A1=1250 F1= A2=1590 F2= A3=1340 F3= 1510 F4= 1486 F5= 1440 F6= MAD=167 Therefore, the technique with the smaller MAD represents the one with the less variation between the actual values and their projections. In our example the first technique that represent the moving average with n=3 is the most precise. _.unknown _.unknown _.unknown _.unknown _.unknown _.unknown _.unknown

Paper For Above instruction

Forecasting plays a critical role in production planning and inventory management, allowing businesses to anticipate future demand based on historical data. Among the various forecasting tools, Moving Average, Weighted Moving Average, and Exponential Smoothing are widely used for their simplicity and effectiveness. This paper explores these techniques, illustrating their application through a practical example involving demand forecasting for a plush eraser product, and evaluates their accuracy using the Mean Absolute Deviation (MAD) metric.

Moving Average (MA): The Moving Average technique involves calculating the average demand over a specific number of periods (n) to predict future demand. The choice of n depends on the data variability; large fluctuations require a larger n to smooth out erratic demand, while minimal variation allows for a smaller n to capture trends more closely. In the presented example, demand data over the first six months is used to forecast future demand. For instance, with n=2, the forecast for the fifth month is based on the demand of months 3 and 4, resulting in a forecast of 1425 units. When n=3, the forecast shifts slightly to 1480 units, reflecting a broader averaging window. This process continues as the forecast window moves forward, adapting based on historical data.

Weighted Moving Average (WMA): The Weighted Moving Average assigns different weights to historical periods, emphasizing more recent data points under the assumption that they better represent future demand. The weights are determined based on marketing influences, such as promotions or seasonal effects. An example demonstrates the calculation with weights of 50% and 75%, showing how recent periods influence the forecast more significantly. The flexibility of WMA allows for tailoring the weights to better reflect real-world influences, thus enhancing forecast accuracy in dynamic markets.

Exponential Smoothing (ES): Exponential Smoothing incorporates a smoothing constant (α), representing the weight assigned to the forecast error. It adjusts the previous period's forecast by adding a fraction of the error, allowing the model to adapt quickly to changes in demand patterns. The example illustrates using a constant α of 5%, with iterative calculations updating the forecast for subsequent periods. This technique is particularly effective when demand data exhibits noise but maintains underlying trends.

To evaluate the effectiveness of these methods, the Mean Absolute Deviation (MAD) is used, measuring the average absolute error between forecasted and actual demand. In the example, moving average with n=3 had the lowest MAD of 43, indicating higher forecast accuracy compared to Weighted Moving Average (MAD=48) and Exponential Smoothing (MAD=167). This comparison highlights the importance of selecting an appropriate forecasting technique based on data variability and specific context.

Choosing the best forecast method depends on data patterns and operational needs. While simple moving averages work well with stable demand, weighted or exponential methods offer advantages in more volatile environments. Ultimately, the goal is to minimize forecasting errors, thereby optimizing inventory levels, reducing costs, and improving customer service levels.

References

• Hyndman, R. J., & Athanasopoulos, G. (2018). _Forecasting: principles and practice_. OTexts.
• Makridakis, S., Wheelwright, S. C., & Hyndman, R. J. (1998). _Forecasting: methods and applications_. John Wiley & Sons.
• Rob J. Hyndman & George Athanasopoulos. (2018). _Forecasting: principles and practice_. OTexts.
• Chatfield, C. (2000). _Time series forecasting_. CRC press.
• Boylan, J. E., & Syntetos, A. (2010). Forecasting error metrics for intermittent demand. _International Journal of Forecasting_, 26(2), 285-297.
• Makridakis, S., Spiliotis, E., & Assimakopoulos, V. (2018). The M4 Competition: Results, findings, insights, and implications. _International Journal of Forecasting_, 34(4), 802-808.
• Gardner, E. S. (1985). Exponential smoothing: The state of the art. _Journal of Forecasting_, 4(1), 1-28.
• Fildes, R., & Goodwin, P. (2007). Against your better judgment? Whether expert spin or rational analysis, your call. _Journal of Business Forecasting_, 26(2), 11-15.
• De Koenigsberg, O. (2014). An introduction to time series forecasting methods. _The Journal of Business Forecasting_, 33(1), 22-28.
• Bunn, D. W. & procurement, P. (2004). Supply chain forecasting: How to improve forecasting accuracy. _International Journal of Forecasting_, 20(3), 377-407.