Specialty Toys Inc Case Study - Quantitative Methods and solution

Question: Describe about the Quantitative Methods of Specialty Toys Inc? Answer: Introduction According to Armstrong and Hilton (2011) companies should adopt the maintenance of economic order quantity so that the companies can manage the inventory and maximize the profit through continuous review of the system. The report deals with the ascertainment of the economic order quantity of Weather Teddy which is a new range of product introduced by the Specialty Inc. Normal probability distribution of the sales forecast The Normal distribution curve Carlberg (2011) commented that normal distribution curve which is also known as the bell curve refers to the shape created when a line is plotted using the data points for an item that meets the criteria of normal distribution. The centre of the curve is the highest point containing the greatest value. The centre point is referred as the mean of the curve. The bell curve decreases on the either side of the centre thereby outlining the standard deviations of the curve. The standard deviation determines the height and the width of the bell. Calculation of the mean and standard deviation Mean = 20000 (Expected demand) So P (10k X 30k) = 0.95 By symmetry P (20k X 30k) = 0.475 P (0 Z 10k/ ) = 0.475 From normal tables, Z value corresponding to this 0.475 is 1.96 So 10000/ = 1.96 Or, 1.96 = 10000/ Or, Standard deviation is 10000/1.96 = 5102. 04 or approximated to 5102 In the above calculation it can be said that 95% of the normal distribution falls between 10000 and 30000 hence 47.5% falls between 20000 and 30000. From the normal distribution table the value of 47.5% can be determined as 1.96 (Standard deviation). Hence the required standard deviation is around 5102. The mean for the purpose of calculation is assumed to be the 20000 units which is the expected demand for the companys sell. Normal distribution curve Computation of probability of stock out for order quantities Stock out may be defined as the situation where the current market demand cannot be fulfilled by the company from the current inventory (Diday, 2013). The issue of stock out is a grave issue for the consumers. Since the stock out will hamper the demand of the customers. A stock out is when virtual inventory has been depleted and is no longer available from either the supplier or the retailer. The majority of the cases of stock out are seen in cases of retail companies. In the case of Specialty Inc the management depending upon the various suggested quantities tried to calculate the stock out probabilities for each quantity. The variation in the order quantities shows that being a retail company Specialty Inc has formulated the various ranges of order quantity so that the stock out risks can be managed. The profitability of stock out with an order of K units is P(X K) P (X K) = P (Z (K 20000) / 5102 Here Z is the standard normal The order quantities suggested by the management of Specialty Inc are namely 15000, 18000, 24000 and 28,000 Order ( K) (K 20000) / 5102 P ( X K) 15000 -0.98001 0.83 18000 -0.392 0.65 24000 0.784006 0.21 28000 1.568012 0.05 Computation of projected profits The projected profits are calculated based on the three different scenarios adopted by the management of the company (Sprinthall, 2012). The management of the company adopted the worst case scenario, the most likely scenario and the best scenario and with the help of the ordering quantities calculated the profit that the company will experience in each case. In the calculation of the same the company took into account two types of profit rates firstly the initial profit rate of $ 8 and secondly the surplus profit rate of $11 for the excess of the ordering quantity (Hardle and Simar, 2012). Projected profits for order quantity of 15000 The initially cost price is $ 16 and the initial selling price is $ 24 and after holiday the company will sell the surplus at $ 5 selling price. Profit initially = (24-16) = $ 8 Profit later = (16- 5) = $ 11 Worst case scenario (10000) Most likely case scenario (20000) Best case scenario (30000) (8*10000) - (11*5000) = 25000 (8 * 15000) = 120000 (8 * 15000) = 120000 Projected profits for order quantity of 18000 The initially cost price is $ 16 and the initial selling price is $ 24 and after holiday the company will sell the surplus at $ 5 selling price. Profit initially = (24-16) = $ 8 Profit later = (16- 5) = $ 11 Worst case scenario (10000) Most likely case scenario (20000) Best case scenario (30000) (8*10000) - (11*8000) = -8000 (8 * 18000) = 144000 (8 * 18000) = 144000 Projected profits for order quantity of 24000 The initially cost price is $ 16 and the initial selling price is $ 24 and after holiday the company will sell the surplus at $ 5 selling price. Profit initially = (24-16) = $ 8 Profit later = (16- 5) = $ 11 Worst case scenario (10000) Most likely case scenario (20000) Best case scenario (30000) (8*10000) - (11*14000) = -74000 (8 * 20000) ( 11 * 4000) = 116000 (8 * 24000) = 192000 Projected profits for order quantity of 28000 The initially cost price is $ 16 and the initial selling price is $ 24 and after holiday the company will sell the surplus at $ 5 selling price. Profit initially = (24-16) = $ 8 Profit later = (16- 5) = $ 11 Worst case scenario (10000) Most likely case scenario (20000) Best case scenario (30000) (8*10000) - (11*18000) = -118000 (8 * 20000) ( 11 * 8000) = 72000 (8 * 28000) = 224000 Computation of ordering quantities As per the management the ordering quantity which will meet 70% demand and has a probability of 30% stock out can be found as follows: P(X K) = 0.70 P (Z (K 20000) / 5102) = 0.70 Or, (K 20000) / 5102 = 0.5244 (As per the corresponding value of Z in normal distribution table) K = (20000 + 5102) * 0.5244 = 20000+2675 = 22675 (Economic order quantity) Objected profit under three diverse sales scenario Worst case scenario (10000) Most likely case scenario (20000) Best case scenario (30000) (8*10000) - (11*12675) = -59425 (8 * 20000) ( 11 * 2675) = 130575 (8 * 22675) = 181400 Recommendation The order quantity that the company should maintain should range between 20000 and 25000. The management had determined that with a order quantity of around 22675 the profitability of the company increases to 70% and the probability of stock out reduces to 30%. Moreover the most likely scenario considered by the company management is 20000. Hence keeping the order quantity between the range of 20000 and 25000 will neither put the company at risk of stock out nor keep excess amount of stock for the company. Moreover the company will also be able to maintain a steady amount of profit in this range of stock. The probability of stock out for the company under the option of most likely range of ordering quantity is also low that is .21 or 21%.Weather Teddy is a new addition to the existing product line of the toy company. Although the product is designed in an innovative manner in order to cater to the needs of the children in an informative as well as innovative manner. However since the product is a toy hence it is not possible to measure the demand graph of the product and it is not possible to judge the amount of ordering quantity in order to balance the situations of stock out. If the company adopts the best possible scenario and orders products ranging between 26000 and 30000 then if the product flops in the market then the company may get stuck with the high levels of inventory in the warehouse along with high levels of cost of production and inability to recover the variable costs. In that situation the company would have to sell the goods at reduced prices. Hence it is advisable to maintain a lower level of ordering quantity initially and after judging the demand level the company can effectively increase the amount of ordering quantity. Conclusion The report shows the overall findings in terms of profitability, mean, standard deviation, probability of stock out and also the ordering quantity and the expected profit at the different given scenarios. From the analysis it can be ascertained that the company should maintain a best possible scenario and should ideally make quantity orders ranging between 20000 and 25000 so that the company doesnt suffer any situation of stock out or any situation of over stocking of the goods. Hence from the report it can be ascertained that stock out is not a favorable situation for the company and hence it should be avoided. References list Armstrong, R. and Hilton, A. (2011).Statistical analysis in microbiology. Hoboken, NJ: Wiley-Blackwell Pub. Carlberg, C. (2011).Statistical analysis. Indianapolis, Ind.: Que. Clarke, B. (2013). Special Issue on Statistical Learning.Statistical Analy Data Mining, 6(4), pp.271-272. Diday, E. (2013). Principal component analysis for bar charts and metabins tables.Statistical Analy Data Mining, p.n/a-n/a. Hardle, W. and Simar, L. (2012).Applied multivariate statistical analysis. Berlin: Springer. Kobayashi, H., Mark, B. and Turin, W. (2012).Probability, random processes, and statistical analysis. Cambridge: Cambridge University Press. Noorossana, R., Saghaei, A. and Amiri, A. (2011).Statistical analysis of profile monitoring. Hoboken, N.J.: Wiley. Sprinthall, R. (2012).Basic statistical analysis. Boston: Pearson Allyn Bacon.