Case Study 1: Specialty Toys |
Group 10 |
Amy GarlitzAlison MalzahnRudy RodelasAngad SinghAbigail Webber |
The data of the sales of the Weather Teddy presented in the Specialty Toys case has a normal probability distribution. The company has a 95% probability of demand for the Weather Teddy being between 10,000 and 30,000 units. Therefore, 95% of the data is within two standard deviations of the mean. The standard deviation is 5,000, or the data deviates from the mean by 5,000 units. The graph below presents this probability distribution for the sales demand of the new product based on the sales forecast.
The managers of Specialty Toys had identified ...view middle of the document...
5% probability that the sales will be less than or equal to the quantity ordered and only a 5.5% chance that the company will run out of stock. Of the four order quantities suggested, these probabilities are the highest for ensuring sales are less than or equal to inventory and the lowest for the possibility of running out of stock.
Sales Estimate of 10,000
Sales Estimate of 20,000
Sales Estimate of 30,000
Note: Gross margin information is included in the charts above for reference in Question #5 below.
The above charts calculate the profit and loss for each sales estimate based on the suggested order quantities. If the company wants to order based on the worst case scenario for sales, the company should order 15,000 units. The company will earn a profit of $25,000 with an order quantity of 15,000, but will generate losses with the higher order quantities. If the company believes the most likely sales volume is 20,000, and wants to order inventory accordingly, it should order 18,000 units (the suggested order quantity that is closest to 20,000). At this order quantity, the company will generate the highest profit with this order volume. However, the potential sales will exceed the amount ordered and the company will lose out on 2,000 sales. Even with the inclusion of the lost profit on 2,000 sales, the order quantity of 18,000 will still have higher profits than the next order quantity of 24,000 units. With an order quantity of 24,000 units and sales of 20,000 units, the post-holiday sales of the excess inventory drive down the company’s overall profit from $144K (profit at 18,000 units) to $116K (profit at 24,000 units) . For a sales estimate of 30,000, the company should order 28,000 units. Under all four suggested order quantities, the company will have lost profits since the order quantities are less than the sales figures. Even including the lost profit, a suggested order quantity of 28,000 will maximize the company’s actual profits and minimize its lost profits.
In determining the specific order quantity where a 70% chance of meeting probability and a 30% chance of stocking out exist, we must solve for x in the z-score formula. Since the distribution of Weather Teddy is assumed to be a normal distribution, we can use the z-score formula and solve for x. We can find the needed numbers in the case and use figures determined by previous questions (µ=20,000 and σ=5,000). Also, in order to find the z-score, we can use the standard normal probability table to find the value that corresponds to a 70% probability. Since this percentage is not listed under the table, we can use the probability of .6985, which is the closest figure to 70% (this gives a z-score of .52). Finally, we get a formula as follows: x=20,000 * (.52*5,000). In this situation, the x figure is determined to be 22,600. In other words, if the company orders 22,600 units, there is a 70% chance they will not stock out.