There were multiple issues weighing heavily on the mind Wally, a VP at Sports Obermeyer, in November of 1992. Sports Obermeyer, a successful manufacturer of ski apparel was having trouble planning the manufacturing levels of its various skiwear items for 1993-94 based on whatever scant information it had on the end customers’ likes and dislikes. Waiting to make these decisions till after the Las Vegas trade show, the one event which would give reliable retailer feedback, would prove very costly given the extremely long lead times of it’s suppliers in Hong Kong and China. In the past, Sports Obermeyer had relied on a group of company managers, called the “buying committee” to make a consensus forecast on the demand of for each of the company’s various products but it’s track was not particularly impressive. In the 1991-92 season, for e.g, some women’s parka styles outsold the original forecast by 200%, while sales of other styles amounted to less than 15% of the forecasted amount [Ref 1] [Exhibit 1]. Going forward the company needed a more reliable way to forecast demand before seeing orders, reduce lead times and decide on the production levels of it’s suppliers in Hong Kong and China.
Is 20000 units the correct amount to anticipate making in total? Why or why not?
20000 may not be the correct amount to anticipate as more analysis will have to be done to determine the optimal quantity of each style of parka, based on the overage and underage costs associated with each style of parka. Also, given that the actual standard deviation was historically twice the forecasted standard deviation injects a lot of risk of incurring overage and underage costs when going with just the average. More analysis is done in answering the following question.
Using the sample data given in Exhibit 10, make a recommendation for how many units of each style Wally Obermeyer should order during the initial phase of production. Assume that all ten styles in the sample problem are made in Hong Kong and that Obermeyer’s initial production commitment must be 10000 units. (Ignore price differences among styles in your initial analysis).
We first calculate the cost of underage and cost of overage for the various styles:
Cost of underage = profit lost because of lost sales.
Cost of overage = loss incurred by selling at sub manufacturing prices.
We know that the estimated profit on each parka that Obermeyer sold = 24% We know that the estimated loss on each parka that Obermeyer sold at discount = 8%
Therefore, Cost of underage = 0.24
Cost of overage = 0.08
The critical ratio Cu/(Cu+Co) = 0.24/0.32 = 0.75.
Hence Obermeyer should stock up enough items to satisfy all the seasonal demand with probability 0.75. The optimal Q* is the 75th percentile of the demand distribution of each style of parka, which is:
Q* = (std-dev)*(Z-value) + mean
Z value = 0.67449. From this the optimal Q* for each style is given in the following table (highlighted in bold)
StyleForecast AverageForecast St. DevUnit PriceCuCoCu/(Cu+Co)Z-valueoptimal prod level Seduced401711137317.525.840.750.674494767.707092
If we were to sum the optimal quantities of all the styles, it would come to about 26360 units, the half of which is way more than 10000, a constraint which the company must adhere to in the first phase. To find the optimal quantities we’ll need to find out a way of maximizing...