QRB/501 – Quantitative Reasoning for Business
University of Phoenix

Inventory Proposal This proposal is for a solution for an inventory problem within an organization. The details of the organization’s business operations are established and the problem identified so a potential solution may be formulated and proposed. The expected benefits to the organization are also examined as the motivation for implementation. Additionally, an inventory index is used to compare and contrast historical trends leading to the inventory problem and supporting evidence is presented through a histogram and slope-intercept calculations. Organization Vertical Entertainment (VE) is a fireworks wholesaler headquartered in Austin, Texas.
VE has been in business since 2005 and provides fireworks products through business-to-business and business-to-consumer channels. The organization’s key segments are the small-box retailers and fireworks display companies. The small-box retailers account for increased volume during the summer months (e.g. 4th of July) whereas the fireworks display companies purchase goods year-round. In recent years VE has expanded to direct sales via the company website. Inventory Problem VE purchases all firework inventories directly from China and they arrive in roughly 12 weeks. Product backorder usually result in lost sales because most events are time specific. The main inventory issue for VE is reducing stale inventory. Although stale inventory affects several key areas, the main focus is the effect on the company’s cash flow. Purchasing too much inventory and relaxed return policies results in 5% of VE product inventory to be stale.

Expected Benefits The goal of this proposal is to reduce stale inventory from 5% to 3% of the total inventory. This reduction will provide VE with much needed cash flow, increase the profit margin, and reduce seasonal temporary warehousing needs. Use of Indices as Vehicle for Solution
Indices are used to analyze changes in data overtime and to predict what causes the fluctuations. Companies use this information to estimate periods of increased sales and inventory needs more accurately. The University of Phoenix Summer Historical Inventory Data provided does not describe what the data is measuring or what the indices expect to forecast. When analyzing data any period may be used; however the only way the data is meaningful is to fully understand what the historic data is trying to predict or analyze.
For example, the Consumer Price Index (CPI) predicts the price of goods in relation to years past and measures inflation. In 2008 the CPI rose .1% and in 2009 the CPI rose 2.7%. 1982 is the base year used in calculating the indices for 2008 and 2009 (Thredgold, Jeff, 2010). This change shows a 2.6% increase in the price of goods in one year indicating the inflation rate. Information provided by the University of Phoenix does not state the units of measurement (e.g. inventory units or dollar amounts) necessary to analyze changes in the indices over time for the purpose of accurately forecasting future inventory.
For forecasting purposes some assumptions must be made. The first assumption is that the data provided is total inventory value in dollars. The second assumption is relative supply cost of inventory does not change from Year 1 to Year 5. Given these assumptions the data can be converted to indices and a forecast for Year 5 can be made from the University of Phoenix Summer Historical Data listed in Table 1 (University of Phoenix, 2010).
Table 1. Summer Historical Inventory Data. Inventory Data | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Month 1 | 18,000 | 45,100 | 59,800 | 35,500 | 31,536 | Month 2 | 19,800 | 46,530 | 30,740 | 51,250 | 46,754 | Month 3 | 15,700 | 22,100 | 47,800 | 34,400 | 32,419 | Month 4 | 53,600 | 41,350 | 73,890 | 68,000 | 39,577 | Month 5 | 83,200 | 46,000 | 60,200 | 68,100 | 45,040 | Month 6 | 72,900 | 41,800 | 55,200 | 61,100 | 41,454 | Month 7 | 55,200 | 39,800 | 32,180 | 62,300 | 39,613 | Month 8 | 57,350 | 64,100 | 38,600 | 66,500 | 46,856 | Month 9 | 15,400 | 47,600 | 25,020 | 31,400 | 33,385 | Month 10 | 27,700 | 43,050 | 51,300 | 36,500 | 37,759 | Month 11 | 21,400 | 39,300 | 31,790 | 16,800 | 15,355 | Month 12 | 17,100 | 10,300 | 31,100 | 18,900 | 18,000 |

Table 2. Vertical Entertainment Inventory Index. Inventory Index | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Total | Average | Month 1 | 100 | 251 | 332 | 197 | 175 | 1055 | 211 | Month 2 | 110 | 259 | 171 | 285 | 260 | 1085 | 217 | Month 3 | 87 | 123 | 266 | 191 | 180 | 847 | 169.4 | Month 4 | 298 | 230 | 411 | 378 | 220 | 1537 | 307.4 | Month 5 | 462 | 256 | 334 | 378 | 250 | 1680 | 336 | Month 6 | 405 | 232 | 307 | 339 | 230 | 1513 | 302.6 | Month 7 | 307 | 221 | 179 | 346 | 220 | 1273 | 254.6 | Month 8 | 319 | 356 | 214 | 369 | 260 | 1518 | 303.6 | Month 9 | 86 | 264 | 139 | 174 | 185 | 848 | 169.6 | Month 10 | 154 | 239 | 285 | 203 | 210 | 1091 | 218.2 | Month 11 | 119 | 218 | 177 | 93 | 85 | 692 | 138.4 | Month 12 | 95 | 57 | 173 | 105 | 100 | 530 | 106 |

The index in Table 2 uses the Inventory Data from Year 1, Month 1 as the base to create each index value for Year 1 through Year 4. These indices are then plotted annually and by quarters in Tables 3.1 – 3.5 and the slope-intercept is used to establish the trend for forecasting Year 5 as shown in Table 2. The five years are then totaled by month and averaged to show the months of highest and lowest volume, May and December respectively. Isolating the months of highest and lowest volume allow the organization to plan ahead when purchasing future inventory, predict the month of greatest excess inventory, and thus potentially reduce excess stale inventory.
Table 3.1. Annual Indices with Negative Slope.

Table 3.2. First Quarter Indices with Positive Slope.

Table 3.3. Second Quarter Indices with Negative Slope.

Table 3.4. Third Quarter Indicies with Negative Slope

Table 3.5. Fourth Quarter Indicies with No Slope

Forecasting Future Inventory Cost Finally, the organization can use the future indices to forcast the future cost of inventory each month based on the earlier assumption, relative supply cost of inventory does not change from year one to year five, by using the formula: Dollars at time A = Dollars at time O * (Index at time A/Index at time O) for each month as represented in year five of Table 1 (Sevilla & Somers, 2007, p. 136). Additional information is obtained from the histogram in Table 4.2 created by the frequency of indices as represented in Table 4.1. This graph shows the mean to be 226 and the standard deviation to be 94. The histogram also shows that the data is skewed rather than a normal distribution indicating months of lower inventory scattered throughout the year (Sevill & Somers, 2007, p. 293).

Table 4. Frequency Range of Indices for Summer Historical Inventory Data. Table 4.2. Histogram of Indices for Summer Historical Inventory Data. In conclusion, stale inventory is reduced by analyzing historical inventory data and forecasting future need. The inventory data converted into an index shows the respective change in inventory from month to month and year to year. This index is then plotted and represented in the form of a histogram to show times of increased and decreased inventory volume. Finally, forecasting future cost of inventory allows the organization to predict times of excess inventory and more accurately order product reducing the amount of stale inventory.

References
Sevilla, A. A. & Somers, K. 2007. Quantitative Reasoning. Tools For Taday’s Informed Citizen. Published by Key College Publishing, an imprint of Key Curriculum Press.
Thredgold, J. (2010, March ). Springtime Update The American Economy-Still Fighting Headwinds. Enterprise/Salt Lake City, 39(41), 12.
University of Phoenix. 2010. University of Phoenix Material: Summer Historical Inventory Data. Retrieved February 20, 2012 from the UOP database.