Research Korner: Evaluation of Rational Expressions

Question 1   Situation:               Based on the above data: a. What trends, if any are evident? Figure 1             From figure 1, we can see that there is a cyclical movement.  Based on the given data, cyclical trend is apparent.  Actually, there is a swing of values or there is a swing from prosperity, recession, depression, recovery and back again to prosperity. This trend varies in time, length and intensity.   b. Calculate the forecasts for the last six months (July to December inclusive) using the following methods: Ø      three-period moving average To obtain three-period moving average, in the table below, the first three numbers are added, the first three number is then replaced by the next number in the column of figures and the process continued until the entire series has been included.  Each total is then divided by 3.   Bottles of 100 sold Three-period Moving Average January 80   February 95   March 87   April 82 87.33 May 97 88 June 94 88.67 July 89 91 August 82 93.33 September 87 88.33 October 72 89.33 November 94 80.33 December 89 77.67   From the table, the forecasted values for the last six months are:   July 91 August 93.33 September 88.33 October 89.33 November 80.33 December 77.67   Ø      exponential smoothing forecast using an α value of 0.1 (assume the forecast for June was 87 bottles) Exponential smoothing is a forecasting method that is easy to use and efficiently handled by computers.  It is also a type of moving average technique but it involves very little record-keeping of the past data.  The basic exponential smoothing formula can be use for our given data is:             Using this formula, the forecast for the last six months are: July 87 + 0.1 (89 - 87) 87.2 August 87.2 + 0.1 (82 - 87.2) 86.68 September 86.68 + 0.1 (87 - 87.2) 86.7 October 86.7 + 0.1 (72 - 86.7) 85.23 November 85.23 + 0.1 (94 - 85.23) 86.107 December 86.107 + 0.1 (80 - 86.107) 86.396             c. For the last six months (July to December inclusive), calculate the root mean square deviation, mean absolute deviation, and bias for both three-period moving average forecast and the exponential smoothing forecast.       For three-period moving average forecast we have:   Forecasted values(x) July 91 91-86.665 4.335 18.79222 August 93.33 93.33-86.665 6.665 44.42222 September 88.33 88.33-86.665 1.665 2.772225 October 89.33 89.33-86.665 2.665 7.102225 November 80.33 80.33-86.665 6.335 40.13223 December 77.67 77.67-86.665 8.995 80.91003     =30.66 =194.1312   root-mean-square deviation = = M.A.D =   For exponential smoothing forecast we have:   Forecasted values(x) July 87.2 87.2-86.3855 0.8145 0.66341 August 86.68 86.68-86.3855 0.2945 0.08673 September 86.7 86.7-86.3855 0.3145 0.09891 October 85.23 85.23-86.3855 1.1555 1.33518 November 86.107 86.107-86.3855 0.2785 0.077562 December 86.396 86.396-86.3855 0.0105 0.00011     =2.868 =2.262   root-mean-square deviation = = M.A.D =   d. What is the three-period moving average forecast for the forthcoming January?             Using the table in b i.e. July 91 August 93.33 September 88.33 October 89.33 November 80.33 December 77.67               The computed three-period moving average forecast for the forthcoming January is 85.   e. What is the exponential smoothing forecast the forthcoming January using an α value of 0.1?             From the data in b we have, January= 86.396 + 0.1 (80 – 86.396) = 85.76   f. In your opinion, are these forecasts reasonable? Why? Without doing any calculations, describe how you would determine which technique is better, and speculate on which of these forecasts you would expect to be better?               Yes, these forecasts are reasonable since the resulting forecasted values of the two techniques are close to each other (e.g for January we have 85 and 85.75). Without doing any calculations, we can determine which technique is better by simply observing the trend of data and since the data behaves in cyclical manner, thus it is suggested to use the exponential smoothing. In addition exponential method is easy to handle and it only involves very little record-keeping of past data.   g. Comment on the other forecasting that might be useful in this situation? What would they entail?             With respect to the behavior of data, the other forecasting technique that is useful in this situation is the least square method. This technique fits a trend line to a series of historical data points and then projects the line into the future from medium to long-range forecasts.  If we decide to develop a linear trend line by a precise statistical method, the least square method may be applied. This approach minimizes the sum of the squares of the vertical differences from the line to each of the actual observations.   h. What is your sales forecasts for the forthcoming January? How many bottles would you buy?             Using the method of least square from the given data, the computed model is : Y= 88.24 – X (0.139), where x could be 1, 2, 3 up to 12 (note: 1=January, 2=February and so on). Thus, for the forthcoming January we have, Y= 88.24 – X (0.139) Y= 88.24 – 1 (0.139) Y= 88.10             For this reason I will buy 88 bottles. Question 2 a. Explain the elements of the “system approach”, and describe how it differs from other methods.             System approach is an approach that allows different participants to conduct forecasting analysis. Unlike other method, it is a systematic approach of analysis. For example the Delphi process.  There are three different types of participants in the Delphi process: (1) decision maker (2) personnel, and (3) respondents. The decision makers consist of a group of experts that will be making the actual forecasts. To be manageable, this group usually consists of five to ten members.  The personnel assist the decision makers.  It is in-charge of the preparation, distribution, collection, and summarization of questionnaires and survey results.  The respondents are group of people whose judgment are sought after and valued.  The actual forecasting procedure consists of the following steps: <li class="MsoNormal" style="text-align: justify; line-height: 200%"> Select the decision maker, staff and respondents group.</li> <li class="MsoNormal" style="text-align: justify; line-height: 200%"> Develop and administer questionnaire #1.</li> <li class="MsoNormal" style="text-align: justify; line-height: 200%"> Analyze questionnaire #1</li> <li class="MsoNormal" style="text-align: justify; line-height: 200%"> Develop and administer questionnaire #2.</li> <li class="MsoNormal" style="text-align: justify; line-height: 200%"> Analyze questionnaire #2</li> <li class="MsoNormal" style="text-align: justify; line-height: 200%"> Do final analysis and present results.</li> <li class="MsoNormal" style="text-align: justify; line-height: 200%"> Develop the forecast.</li>     b. Why is the system approach not always used? System approach is not always used because it is not usually applicable for quick analysis. Although the result of it is reliable compared to other forecasting method but then there is still a need to consider the constraints such as time, personnel, etc.   Question 3. The textbook describes several types of process: project, job shop, batch, continuous, and process.  Explain the factors that influence process choice.   Project- A project is a temporary endeavor undertaken to create a unique product or service. Thus, the end result sought may be distinct from the mission from the organization which undertakes it because the project specifically has a deadline and the endeavor is temporary.   It can also comprise an ambitious plan to define and constrain a future by limiting it to set goals and parameters. The planning, execution and monitoring of major projects sometimes involves setting up a special temporary organization, consisting of a project team and one or more work teams. A project usually needs resources.   job shop- Job shops are typically small manufacturing operations that handle specialized manufacturing processes such as small customer orders or small batch jobs. Job shops typically move on to different jobs (possibly with different customers) when each job is completed. By nature of this type of manufacturing operation, job shops are usually specialized in skill and processes.   Batch- A batch is a group of similar items produced, processed or gathered together and treated as a single unit. Basically, batch is use as ype of production called batch production. Batch production is a method used to produce or process any product in groups that can be called batches, as opposed to a continuous production process. For example baked goods such as cakes are typically produced in batches, while oil refineries (including biodiesel ones) often use continuous processes.   Continuous production- is a method used to produce or process any product without interruption. There is no discrete rate at which goods are produced, as opposed to a batch production process, or a one-time production. Examples of continuous production are those used to make pens, paper, cars and computers.   This process is followed in most of the Float Glass Industries where glass of different thickness is processed in a continuous manner. Once the molten glass flows out of the furnace (usually rectangular in shape), machines work on the glass from either sides and either compress or expand the glass. By controlling the speed of rotation of those machines and varying them in numbers, we can get a glass ribbon of varying width and thickness.   Process-in business, process is a recipe for achieving a commercial result. Each business process has inputs, method and outputs. The inputs are a pre-requisite that must be in place before the method can be put into practice. When the method is applied to the inputs, then certain outputs will be created.   A business process is a collection of related structural activities that produce something of value to the organization, its stake holders or its customers. It is, for example, the process through which an organization realizes its services to its customers.   A business process can be part of a larger, encompassing process and can include other business processes that have to be included in its method. In that context a business process can be viewed at various levels of granularity. The linkage of business process with value generation leads some practitioners to view business processes as the workflows which realize an organization's use cases.

FORECASTING

Question 1 Situatio n: Based on the above data: a. What trends, if any are evident? Figure 1 Fr...