The firm has considered the idea of making the sweaters in their own factory, but for now they purchase them from a supplier in China. The prices are great, but service is a problem since the suppller has a 20 -week tead time for each order and the minimum order size is 5,000 sweaters. The order can consist of a mix of the different logos, such as 2,000 for OSU, 1,500 for UM, 750 for MSU, 500 for PU, and 250 for IU. Within each logo sub lot, sizes are allocated based on percentages and the supplier suggests 20 percent X-Iarge, 50 percent large, 20 percent medium, and 10 percent small based on their historical data. Once an order is recelved, a local subcontractor applies the monograms and ships the sweaters to the customer. They store the inventory of sweaters for the company in a small warehouse area located at the subcontractor. This is the company's second year of operation, Last year they only sold sweaters for three of the schools, OSU, UM, and PU. They ordered the minimum 5,000 sweaters and sold all of them, but the experience was painful since they had too many UM sweaters and not enough for OSU fans. Last year they ordered 2,340 OSU, 1,750 UM, and 910 PU sweaters. Of the 5,000 sweaters, 311 had to be sold at a steep discount on eBay after the season. They were hoping not to do this again. For the next year, you have coliected some data relevant to the decision. Exhibit 20.12 shows cost information for the product when purchased from the supplier in China. Here we see that the cost for each sweater, delivered to the warehouse of our monogramming subcontractor, is $63.28. This price is valid for any quantity that we order above 5,000 sweaters. This order can be a mix of 5 weaters for each of the flve schools we are targeting. The supplier needs 20 weeks to process the order, so the order needs to be placed around April 1 for the upcoming football season. advertising outets but has decided to wat at least another year to try something different. Forecasting demand is a major problem for the company. You have asked Rhonda and Steve to predict what they think sales might be next year, You have also asked the market research firm to apply their forecasting tools. Data on these forecasts are given in Exhibit 20.13. To generate some statistics you have averaged the forecasts and calculated the standard deviation for each school and in total. Based on advice from the market research firm, you have decided to use the aggregate demand forecast and standard deviation for the aggregate demand. The aggregate demand was calculated by adding the average forecast for each itom. The aggregate standard deviation was calculated by squaring the standard deviation for each item (this is the variance), summing the variance for each item, and then taking the square root of this sum. This assumes that the demand for each school is independent, meaning that the demand for Ohio State is totally unrelated to the demand at Michigan and the other schools. You will allocate your aggregate order to the individual schools based on their expected percentage of total demand. You discussed your analysis with Rhonda and Steve and they are OK with your analysis. They would like to see what the order quantities would be if each school was considered individually. How many sweaters should be ordered this year? Compute your answer for each individual school using two methods: (1) based on overall aggregate demand which is then opportioned to each individual school based on its average forecast, (2) based directly on average forecast for each individual school. Use the single-period inventory model approach as the basis for each method. (Round your answers to the nearest whole number.) Exhibit 20.13 311 sweaters were sold through eBay for $46 each (the customer pay5 shipping on all orders). "Calculated assuming the demand at each school is independent \( =\longdiv { \sum _ { i = 1 } ^ { N } o _ { 1 } ^ { 2 } } \) Out monogramming subcontractor gets $16.50 for each sweater Shipping cost is paid by the customer when the order is placed. In addition to the cost data, you also have some demand information, as shown in Exhibit 2013. The exact sales numbers for last year are given. The exhibit indicates the retall or "full price" sales for the swoaters that were sold for $128 each. Sweaters that we had at the end of the season were sold through eBoy for $46 each and were not monogrammed. Keep in mind that the retail sales numbers do not accurately reflect actual demand since they stocked out of the OSU swesters toward the end of the season. As for advertising the sweaters for next season, Rhonda is committed to using the same approach used last year, The firm placed ads in the football program sold at each game. These worked very well for reoching those attending the games, but she realized there might be ways to advertise that would open sales to more alumn. She has hired a market research firm to help identify other advertising outlets but has decided to wait ot least another yoar to try something different