Lta qrb501 wk6
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This document discusses Quantum Cars' inventory management system and historical inventory data. It provides statistical analysis of Quantum's monthly inventory figures from 2006 to 2009, including measures of central tendency, dispersion, frequency distributions and normal curves. It also examines relationships between inventory levels and number of dealerships. Forecasting predicts 2020 inventory based on this analysis.
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- 2. About the Company JIT Inventory System Inventory Data Inventory Forecasting Statistical Data Mean, Mode and Median Range and Standard Deviation Frequency Distribution Normal Distribution
- 3. manufacturer of affordable luxury cars started in the 1920s filed a Chapter 11 bankruptcy in 2009 shut down production during bankruptcy court hearings planned to close 20% of its dealership
- 4. Just-In-Time (JIT) Inventory System Quantum Solutions™ Back-up Inventory System
- 5. Year 1 Year 2 Year 3 Year 4 Month 2006 2007 2008 2009 1 18,000 45,100 59,800 35,500 2 19,800 46,530 30,740 51,250 3 15,700 22,100 47,800 34,400 4 53,600 41,350 73,890 68,000 5 83,200 46,000 60,200 68,100 6 72,900 41,800 55,200 61,100 7 55,200 39,800 32,180 62,300 8 57,350 64,100 38,600 66,500 9 15,400 47,600 25,020 31,400 10 27,700 43,050 51,300 36,500 11 21,400 39,300 31,790 16,800 Click to open 12 17,100 10,300 31,100 18,900 Quantum Cars Historical Quantum Cars 4-year Inventory Data.xlsx
- 6. Unadjusted Adjusted Year 1 Year 2 Year 3 Year 4 Year 5 Month Month Index Index 2006 2007 2008 2009 Forecast 1 1.102656232 1.109183964 1 18,000 45,100 59,800 35,500 46973 2 1.019051129 1.025083918 2 19,800 46,530 30,740 51,250 43411 3 0.794836249 0.799541684 3 15,700 22,100 47,800 34,400 33860 4 1.38607416 1.394279728 4 53,600 41,350 73,890 68,000 59046 5 1.319562701 1.327374521 5 83,200 46,000 60,200 68,100 56213 6 1.19862318 1.205719037 6 72,900 41,800 55,200 61,100 51061 7 1.035870513 1.042002874 7 55,200 39,800 32,180 62,300 44128 8 1.274911183 1.282458666 8 57,350 64,100 38,600 66,500 54311 9 0.691337883 0.695430608 9 15,400 47,600 25,020 31,400 29451 10 0.939362047 0.944923077 10 27,700 43,050 51,300 36,500 40017 11 0.706272705 0.710453844 11 21,400 39,300 31,790 16,800 30087 12 0.460820022 0.463548079 12 17,100 10,300 31,100 18,900 19631 Average: 0.994114834 1 Total: 11.929378 12 Average 38,113 40,586 44,802 45,896 42,349 Inventory and Seasonal Indices
- 7. Dealership Impact on Inventory Number Forecasted Monthly M 50,000 Year of Monthly o y = 11.37x + 9966. Average 45,000 R² = 0.983 Dealers Average n t 40,000 h l 35,000 1 2,493 38,113 38,322 y 30,000 2 2,687 40,586 40,528 I n 25,000 3 3,008 44,802 44,179 v e 20,000 4 3,200 45,896 46,363 n t 15,000 5 2,560 42,349 39,084 o r y 10,000 5,000 Click to open 0 Quantum 0 500 1,000 1,500 2,000 2,500 3,000 3,500 Cars Historical Number of Dealers Data.xlsx Dealership Impact on Inventory
- 8. Measures of Central Tendency 4-Year Measures of Central Tendency and Dispersion and Dispersion 10 Mean 42,348.96 9 Mode 55,200.00 Median 41,575.00 8 Range 72,900.00 F 7 Median (41,575.00) Variance 329,688,384.33 r e 6 Standard Deviation 18,157.32 q Mean (42,348.96) u 5 e Mode (55,200.00) n 4 c Click to open y 3 Standard Deviation Quantum (18,157.32) Cars 2 Range (72,900.00) Historical 1 Data.xlsx 0 Inventory in untis Mean, Mode, Median, Range & Standard Deviation
- 9. Month Year 1 - 2006 Year 2 - 2007 Year 3 - 2008 Year 4 - 2009 1 18,000 45,100 59,800 35,500 2 19,800 46,530 30,740 51,250 3 15,700 22,100 47,800 34,400 4 53,600 41,350 73,890 68,000 5 83,200 46,000 60,200 68,100 6 72,900 41,800 55,200 61,100 7 55,200 39,800 32,180 62,300 8 57,350 64,100 38,600 66,500 9 15,400 47,600 25,020 31,400 10 27,700 43,050 51,300 36,500 11 21,400 39,300 31,790 16,800 12 17,100 10,300 31,100 18,900 Mean 38112.50 40585.83 44801.67 45895.83 Mode #N/A #N/A #N/A #N/A Median 24550.00 42425.00 43200.00 43875.00 Range 67800.00 53800.00 48870.00 51300.00 Variance 561022552.08 163041457.64 217615380.56 337421857.64 StdDev 23685.91 12768.77 14751.79 18369.05 Yearly Statistical Data
- 10. Yearly Mean & Median Comparison 50,000 I 45,000 n v e n 40,000 t o r y 35,000 Mean Median 30,000 25,000 20,000 Year 1 Year 2 Year 3 Year 4 2006 2007 2008 2009
- 11. Yearly Mean, Range & StDev Comparison 70,000 60,000 I n 50,000 Mean v e n 40,000 t o r y 30,000 Range 20,000 10,000 Year 1 Year 2 Year 3 Year 4 2006 2007 2008 2009
- 12. Year 1 Year 2 Year 3 Year 4 Standard Month Mean Median Mode Range 2006 2007 2008 2009 Deviation 1 18,000 45,100 59,800 35,500 39,600 40,300 #N/A 41,800 17,528 2 19,800 46,530 30,740 51,250 37,080 38,635 #N/A 31,450 14,479 3 15,700 22,100 47,800 34,400 30,000 28,250 #N/A 32,100 14,179 4 53,600 41,350 73,890 68,000 59,210 60,800 #N/A 32,540 14,643 5 83,200 46,000 60,200 68,100 64,375 64,150 #N/A 37,200 15,528 6 72,900 41,800 55,200 61,100 57,750 58,150 #N/A 31,100 12,931 7 55,200 39,800 32,180 62,300 47,370 47,500 #N/A 30,120 13,811 8 57,350 64,100 38,600 66,500 56,638 60,725 #N/A 27,900 12,634 9 15,400 47,600 25,020 31,400 29,855 28,210 #N/A 32,200 13,535 10 27,700 43,050 51,300 36,500 39,638 39,775 #N/A 23,600 10,000 11 21,400 39,300 31,790 16,800 27,323 26,595 #N/A 22,500 10,152 12 17,100 10,300 31,100 18,900 19,350 18,000 #N/A 20,800 8,665 Monthly Statistical Data
- 13. Monthly Mean & Median Comparison 70,000 60,000 50,000 I n v 40,000 e n t Mean o 30,000 Median r y 20,000 10,000 0 1 2 3 4 5 6 7 8 9 10 11 12 Month
- 14. Monthly Mean, Range & StDev Comparison 90,000 80,000 70,000 I 60,000 n v 50,000 e n Mean 40,000 t Range o r 30,000 y 20,000 10,000 0 1 2 3 4 5 6 7 8 9 10 11 12 Month
- 15. Inventory Histogram (Frequency Distribution) Bin Frequency Limits 9 F 8 15,000 1 r e 7 q 25,000 9 u 6 e 35,000 8 n 5 c 4 45,000 8 y 3 55,000 8 2 65,000 8 1 0 75,000 5 85,000 1 Quantum Cars Inventory Frequency Distribution
- 16. Inventory Normal Distribution Click to open Quantum 0.000025 Cars P Historical r Data.xlsx o 0.00002 b a b i 0.000015 l i t y 0.00001 D e 0.000005 n s i t 0 y -20000 0 20000 40000 60000 80000 100000 120000 -3σ -2σ -1σ μ 1σ 2σ 3σ Inventory in Units
Editor's Notes
- Quantum Cars began producing automobiles in the 1920s and since then has been successful in making affordable, luxury cars. As with the US economy, business has fluctuated since then. Unfortunately, Quantum Cars was forced into Chapter 11 bankruptcy in 2009 after struggling to repay debts. Many analysts predict a loss in jobs and tax revenue because of this bankruptcy, but the company is dealing with a more immediate issue – too much inventory. Quantum Cars’ inventory history has been always high in numbers, and this is compounding the company’s problems.The Quantum manufacturing plant produced far too many automobiles and the dealerships lacked time and resources to move the products. Quantum Cars shut down production of automobiles during the bankruptcy court hearings and also plans to close approximately 2,000 Quantum dealerships, 20% of its dealerships. Herein lays the problem. The dealerships that close must do away with their inventory, so these extra cars (inventory) are either sold to customers at low prices, resulting in a loss, or sold to existing dealerships. Consumer buying was somewhat sluggish in 2009, so selling extra cars to existing dealerships instigated excess inventory and further caused those dealers to worry about selling even more cars.
- Out with the old, in with the new…Quantum Solutions Inventory Systemfollows the back-up system technologyHelps avoid a disruption in customer serviceDoes not address the age of the inventory being storedInventory requires careful attention The JIT inventory system is a costly system developed by the Japanese auto industry to eliminate waste while controlling inventory production and amounts of products stocked. The JIT inventory system demands a long term commitment with a complete understanding of what the company’s plans and objectives are. It is designed to seamlessly match supply and demand and result in an inventory level of zero. The JIT system will not repair existing errors or flaws already existent in the company brought about by the current inventory system; thus, corrections must be completed prior to switching to the JIT system. Because Quantum Cars is currently experiencing problems with inventory, an analysis-based suggestion will be made before the JIT system will be set strategically into place.
- Even though Quantum Cars began manufacturing automobile in the 1920s, the problems with inventory began in 2006 and carried on through 2009. The company kept an accurate account for the number of units manufactured during those years.For each year the amount of inventory manufactured every each month varied. The current inventory problem illustrates that there were no accurate projections for seasonal indices or uncontrollable variables such as competition and difficult economic circumstances, so some of these units were either over or underestimated.
- In 2009, Quantum Cars lost 20% of its dealers, but instead of decreasing its inventory, the company decided to manufacture according to inventory trends. Like many other businesses, Quantum Cars experiences movement in sales, depending on the month and season. By calculating the seasonal ratio, the manager of the company will be able to identify trends, which in turn will help forecast units sold in upcoming years of business. To further the investigation of trends in units manufactured, the company’s analyst finds an index for the data. This index will determine changes in the percent of units sold each quarter. Once Quantum Cars forecasts units sold in the fifth year, the uncertainty of sales for each month of that year will decrease. This, in turn, will give the manufacturer, as well as the dealerships, a better understanding of how much inventory to produce and keep in stock.
- Quantum Cars failed to see the problem when less than 50% of their dealers returned sales greater than 1.5%. This was an opportunity for Quantum Cars to expand its dealership support to include teaching financial skills and planning for the growth in sales of commercial vehicles. Quantum Cars should have considered competition of dealers in their bearing on their inventory before manufacturing more cars. Thus, instead of manufacturing 42,349 automobiles, the company should have gone down to 39,084 automobiles. Dealerships with manufacturer’s support will overcome the issues of excess inventory and be able to support the company for a longer period of time.
- Determining the statistical data for Quantum Cars requires extensive analysis. Fortunately, the raw data collected from this manufacturer from 2006 to 2009 assist substantially in calculating this supporting, statistical data. The graph shows that the mean is being dragged to the direction of the skew. Considering the data set for four years, we find that the inventory is skewed to the right, making the median the best representative of the data’s central location. However, the difference between the median and mode is negligible and thus the mean could be a reliable representative of the data set’s central location.The graph also shows the data set’s range and standard deviation. The range is the simplest way to measure how the data is spread within the population. This is also known as dispersion. Thus, the range could tell us how much variation is there in the inventory data. A computed range of 72,900 tells us that it is far greater than the mode or the median and that it is a weak measure of dispersion especially that it only depends on two extreme observations.The table shows a computed value of 18,157.32 for standard deviation. This value represents the approximate measurement of the average distance between the data points and its mean. There is no direct relationship between the range and the standard deviation as the former only depends on two values while the latter depends on all values in the data set. Both range and standard deviation measure variation but while the range measures the total amount of disparity, the standard deviation measures the average disparity among values in the data set.
- To make sure that proper evaluation of raw data is made, the company analyst decided to generate statistical data yearly and monthly for four years. In doing so, the analyst is able to explore all possibilities when it comes to using statistical data for the company’s benefit.
- The mean for each year is simply an average of units manufactured each month of the corresponding year. The median is the center point between the lowest number of units and the highest number of units manufactured during each respective year. If numbers are repeated in the data set, then a mode represents the number that is repeated the most.
- The frequency distribution histogram provides the Quantum Cars’ management an illustrated look at the data gathered in regard to the company’s inventory manufactured from 2006 to 2009. As seen in the above table, the first step to this illustration is to make a table describing how frequent a piece of data falls into each class observed. The frequency distribution shows that the data is clustered tightly around the mean and that the mean could then be a good basis of future inventory. The frequency distribution is very useful for displaying data in a way that would help Quantum Cars see how frequently certain values in the inventory occur. The company can then use this frequency to assess the probability that the overabundance of inventory could have sprung from the fact that the company is producing within the range of 15,001 to 65,000 and that going below these figures might help them solve their inventory problem.
- The Normal Distribution is a bell-shaped curve that displays the mean and standard deviation of the data (Normal Distribution Tutorial, n.d). The normal distribution for Quantum Cars’ 4-year Inventory is illustrated in this chart. The mean is displayed as the peak of the bell curve and the standard deviation is represented by the dark blue lines in this figure. As the standard deviation grows wider, the percentage of observed data that lies between those numbers gets larger. In this case, 68% of the data lies between 23,999 and 60,698 units; 95% of the data lies between 5,650 and 79,047 units; and 97% of the data lies between -12,699 and 97,397 units.The normal distribution can be very useful for Quantum Cars for further statistical analysis of its inventory because the mean and the variance tends to be normally distributed as the number of values in the inventory grows. In this assumption, inventory issues that may arise in the future can be easily analyzed and solved under a normally distributed data set. Also, it is highly advisable to analyze the values that are clustered around the central measures as with the mean being in the center of a normal distribution because the farther the value is from the mean, the less likely it would occur. This means that in a normally distributed graph, it would be easier for Quantum Cars to see which inventory data matters and must then be given more attention in future data analysis endeavors.