University bookstore - Research Paper Example

Term Paper Bookstore Computer Purchase Program Table of Contents Introduction 02 University Bookstore Computer Sale Data 03 Table 1: Sales University Bookstore Computer Purchase 03 Program Diagram 1: Trend line 04 Choosing the Appropriate Forecast Model 05 Table 2: Sales Data Percentage Change over Time 05 Linear Equation to Forecast 06 Diagram 3: Linear Equation 06 Conclusion 07 Table 4: Deviations (Accuracy) 07 Sources 09 Introduction The university bookstore has been in operations for the past fourteen years, the presence of the book store has been of significance for the university as well as the students due to the fact that it has been providing academic material as well as computer supplier. Due to the fact that the computer supplies are in more sdemand during he intake season usually during the fall season or the proceeding summers. The demand arising due to the usual intake of students as well as the accumulating demand over the previous intake, causes the operations of the bookstore are affected unusually. Arising primarily from the scenario that the orders for he computer comes through out the summers aside from that of that of the sophomores or the newly admitted, the competitive advantage maintained by he book store has been due to the bottom-line prices charged by he sore. Hence, considering the fact that the book sore is charging such low prices, as the profit base and keeping in view that if the store orders to many supplies, the cash reserves become very low, besides that storage concerns have to be accounted for as well. The quantity demanded by the students for the computers also determines the number of employees to be hired for the installation to take place. Moreover, the university itself has been emphasizing the fact ha t the store should provide high quality services for the assumed quality students being admitted in he institute This report attempts to analyze the data provided by the store in order to forecast in an accurate manner the quantity that would be required of the bookstore in the proceeding fall. Hence the key issues to be resolved include 1. To be able to identify the quantity demand for the next fall semester 2. To develop an appropriate forecast model for the book store, indicate its accuracy and identify other models It would be most appropriate to mention that the forecasting models despite the comparison of relative accuracies remain models to forecast. Hence, their accuracies remain subject to the actual outcome of the event they forecast. As a consequence, whether it is through the means of Linear Equation, Seasonal Indexes or Smoothing Techniques such as Averages, they remain subject to the risk involved from the aspect of actual outcome. University Bookstore Computer Sale Data Table 1: The Sales for University Bookstore Student Computer Purchase Program Year 1 Computer Sold 518 2 651 3 708 4 921 5 775 6 810 7 856 8 792 9 877 10 693 11 841 12 1009 13 902 14 1103 The above data has been provided in the form of a diagram on the next page, since the raw data in itself would prove to be discerning. A graphic representation is a more appropriate alternative to examine the trends in the quantity of the computers sold. The diagram presents the scenario that there occurs a phase of progression which is usually ends with a year of regression in the sale of computers and the progression then occurs again. This pattern is noticeable in the overall demand and sale scenario. The fact that a continuous increase occurs in the computers sold for the first four years, followed by a sudden drop in the fifth year, an increase in the demand of the computers in the next two years, sixth and seventh respectively. In the eighth year there is again a sudden drop in the computers being demanded from the university bookstore computer program. A sudden surge and a respective drop concur in the ninth and the tenth year respectively. An increase takes place in the eleventh and twelfth year respectively, a sudden drop occurs in the thirteenth year, followed by an increase in the fourteenth year. The following trend line would be able to define the trend more specifically, the actual demand scenarios could be effectively monitored through the graph so as to be able to identify whether a certain increase or decrease is associated with seasonal or cyclic fluctuations. Diagram 1: Trend line The fact that the there has been a considerable increase in the sale of computers over the initial period of four years, the rate of increase of the computers sold progressed at approximately 19.45% in comparison to the base year. It faced a decline in the fifth year of 15.85%, after that gradual recovery over the next two years of approximately 10.45%, when there is a decrease of 7.47%, an unusual upturn of 9.92% in the ninth year. As the diagram predicts there is drop in the sales in year tenth of approximately 20.98%, there is a constant increase in sales from year eleven and twelve, accumulating to 45.45% progress. There is a slight decrease in the preceding year thirteen, of approximately 10.604%, in year fourteen an upturn of 22.38%. The fact that the demand of computers is at its highest in the twelfth year with a thousand and nine units being demanded is not associated with a certain aspect of the University activity which may be classified as seasonal or cyclic. The same holds true for the lowest point on the graph which indicates that the lowest demand for the computers had been during the first year, which seems reasonable since the case mentions that although the in take of students has been steady he demand for the computers has been on an increase. The lowest point however in the true sense would be year tenth with a demand of six hundred and ninety three computers; this would be so because since then the trend of an increase in the demand of computers has been established. Choosing the Appropriate Forecasting Technique: The options to be considered in selecting the appropriate technique included Smoothing Techniques Seasonal Indexes Linear Equations: The case presented by University Book Store Computer Purchase Program, has to take into account the fact that there are no seasonal changes observed, the fluctuations in the quantity demanded on annual basis is due to random allocations. As presented below: Table 2: Sales Data Percentage Change over Time Year Percentage Increase/Decrease 1 2 25.68 3 8.76 4 30.08 5 -15.85 6 4.52 7 5.68 8 -7.48 9 10.73 10 -20.98 11 21.36 12 19.98 13 -10.60 14 22.28 It is ascertained from the percentages demonstrated above that the percentage changes have been occurring on a random basis and as the data demonstrates there is a long term trend with random fluctuations. In order to be able to accurately calculate the next fall semester's demand of the computers, it would be appropriate to apply the trend line to be able to forecast quantity. Linear Equation to Forecast Diagram 3: Linear Equation In statistics, regression analysis examines the relation of a dependent variable (response variable) to specified independent variables (predictors). The mathematical model of their relationship is the regression equation. The dependent variable is modeled as a random variable because of uncertainty as to its value, given values of the independent variables. Uses of regression include prediction (including forecasting of time-series data. Regression analysis, Retrieved May27, 2007, from http://en.wikipedia.org/wiki/Regression_analysis The regression line which is also referred to as the least squares method, takes into account the path across the trend line which is the closest to the trend points, in itself. The regression method or the linear equation method is well suited for incorporating the random fluctuations in the data provided. The linear equation provided: y=26.905x+616.49 The equation above represents the straight line, which crosses through the points; the 26.905 figure represents the gradient for the line, while the 616.49 is the y-intercept. The regression analysis enables a correlation between the two variables being evaluated, hence in this scenario it is worthwhile noticing that replacing x with the value of the year would present, the forecasted demand of computers for the respective year. The forecasted demand would always represent the demand that should occur considering the trend of the time period of fourteen years. The fact that the gradient of the linear equation is positive, reflects that there is a positive correlation between time and quantity demanded, that is as time increased the quantity demanded also increased over the fourteen year period. Conclusion: The task of this report had been to resolve the following issues: 1. To be able to identify the quantity demand for the next fall semester y=26.905x+616.49 y=26.905(15) +616.49 y= 1021 Computers The linear regression forecasting model would indicate that the computers that would be demanded in the fifteenth year based on the past demand data of fourteen years would be a thousand and twenty one computers. As described below in the table as well in the preceding paragraphs, it is essential for the management to take the accuracy into account, the deviations described below are for the purpose of aligning their past experience with the proposed figure. 2. To develop an appropriate forecast model for the book store, indicate its accuracy and identify other models Table 4: Deviations (Accuracy) Year Actual Data Linear Equation Deviation (Qty) Deviation Percent 1 518 643.395 -125.395 2 651 670.3 -19.3 -2.96467 3 708 697.205 10.795 1.524718 4 921 724.11 196.89 21.37785 5 775 751.015 23.985 3.094839 6 810 777.92 32.08 3.960494 7 856 804.825 51.175 5.978388 8 792 831.73 -39.73 -5.01641 9 877 858.635 18.365 2.094071 10 693 885.54 -192.54 -27.7835 11 841 912.445 -71.445 -8.49524 12 1009 939.35 69.65 6.902874 13 902 966.255 -64.255 -7.12361 14 1103 993.16 109.84 9.958296 11456 11455.89 The table presents the possible deviation percentages that may possible occur using the approach. It is noticeable that the maximum deviations occur in Year 4 and Year 10. This is due to the unexpected drops in these years in demand of the computers; this may be observed in the diagram portraying the sales trends in the respective years. Besides, that of immediate concern to the University Bookstore is the figures relating to the recent past, in which there have been relatively lesser deviations. It would be more feasible for the board of directors to consider the actual expectations of the next period's demand after examining the figure proposed by the linear equation and the extent of accuracy posed by this forecast model. If the management thinks that the demand would be more than the forecasts model could indicate based on certain aspects, then it would be appropriate for the management to examine the deviations which have taken place, in the past fourteen years, it would assist in determining an accurate value. As the case is described at the moment, the conditions are favorable and the demand for computers are expected to be on an increase, however factors such as: The average number of computer ordered by the freshman, The average number of computer ordered by sophomores, The number of students enrolled this year, The number of students enrolled last year, The number of students enrolled last year, who did order the computer through the bookstore, Such considerations would provide two domains to be analyzed Computers Ordered By Freshman: When the bookstore is aware of the students who have ordered computers, the bookstore could gather data which would allow better forecasting of the demand placed by the next intake of the students. It would also allow the book store to identify those freshmen who have-not ordered a computer as yet, and be prepared in the following summer to cater to their demands. It would be even better for the bookstore to approach the freshman who has not ordered their computers, to ask them before hand whether they had plans for ordering the computers. Computers Ordered By Sophomores and others: The computers ordered by the sophomores depend to a large extent on those who did not order them in the firs year of their university life. The quantity demanded by the sophomores and the others would also present a significant source of data to be tapped in order to present accurate forecasts. . Sources: http://home.ubalt.edu/ntsbarsh/Business-stat/otherapplets/ForecaSmo.htm http://en.wikipedia.org/wiki/Linear_regression http://en.wikipedia.org/wiki/Special:Searchsearch=moving+averages http://en.wikipedia.org/wiki/Exponential_smoothing#The_weighted_moving_average http://en.wikipedia.org/wiki/Exponential_smoothing#The_simple_moving_average Read More