Analytics Exercise $20-1($Algo$)$

Steve majored in accounting and likes to pump the numbers. He has done a great job of keeping the books and selling the company to some small venture capital people in the area. Last year, he was successful in getting them to invest $$2,000,000$ in the company $($a onetime investment$).$ There were some significant strings attached to this investment in that it stipulated that only $$100,000$ per year could go toward paying the salary of the two principals. The rest had to be spent on the website, advertising, and inventory. In addition, the venture capital company gets $26$ percent of the company profits, before taxes, during the first four years of operation, assuming the company makes a profit.

Your first job is to focus on the firm$$s inventory. The company is centered on selling the premium sweaters to college football fans through a website. Your analysis is important since a significant portion of the company$$s assets is the inventory that it carries.

The business is cyclic, and sales are concentrated during the period leading up to the college football season, which runs between late August and the end of each year. For the upcoming season, the firm wants to sell sweaters to only a few of the largest schools in the Midwest region of the United States. In particular, they are targeting The Ohio State University $($OSU$),$ the University of Michigan $($UM$),$ Michigan State University $($MSU$),$ Purdu University $($PU$),$ and Indiana University $($IU$).$ These five schools have major football programs and a loyal fan base.

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 supplier has a $20-$week lead 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$-$large, $50$ percent large, $20$ percent medium, and $10$ percent small based on their historical data.

Once an order is received, 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 $2,230$ OSU, $1,820$ UM$,$ and $950$ PU sweaters. Of the $5,000$ sweaters, $347$ 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 collected some data relevant to the decision. Exhibit $20\mathrm{.}12$ 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 $$55\mathrm{.}83.$ This price is valid for any quantity that we order above $5,000$ sweaters. This order can be a mix of sweaters for each of the five 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.

COST INFORMATION FOR THE BIG TEN SWEATERS

China supplier cost

Material

$

$26\mathrm{.}00$

Labor

$11\mathrm{.}50$

Overhead

$1\mathrm{.}25$

Transportation within China

$1\mathrm{.}00$

Supplier profit

$8\mathrm{.}90$

Agent's fee

$2\mathrm{.}68$

Freight $($ocean carrier$)$

$1\mathrm{.}50$

Duty, insurance, etc.

$3\mathrm{.}00$

Total supplier cost

$

$55\mathrm{.}83$

Domestic subcontractor cost

Monogram material

$

$3\mathrm{.}50$

Labor

$7\mathrm{.}00$

Total subcontractor cost

$

$10\mathrm{.}50$

Total $($per sweater$)$

$

$66\mathrm{.}33$

FORECAST DATA FOR THE BIG TEN SWEATERS

AVERAGE FOOTBALL GAME ATTENDANCE

LAST YEAR$$S

ACTUAL SALES

$($FULL PRICE$)$

RHONDA$$S

FORECAST FOR

NEXT YEAR

STEVE$$S

FORECAST FOR

NEXT YEAR

MARKET RESEARCH FORECAST FOR

NEXT YEAR

AVERAGE

FORECAST

STANDARD

DEVIATION

Ohio State

$105,261$

$2,230$

$2,470$

$2,230$

$2,730$

$2,477$

$250$

Michigan

$108,933$

$1,523$

$1,760$

$1,560$

$1,940$

$1,753$

$190$

Purdu

$50,457$

$900$

$1,060$

$920$

$1,110$

$1,030$

$98$

Michigan State

$74,741$

$-$

$1,700$

$1,560$

$1,590$

$1,617$

$74$

Indiana

$41,833$

$-$

$560$

$560$

$420$

$513$

$81$

Penn State

$107,008$

Wisconsin

$80,109$

Iowa

$70,214$

Illinois

$59,545$

Minnesota

$50,805$

Northwestern

$24,190$

Nebraska

$85,071$

Total

$4,653*$

$7,550$

$6,830$

$7,790$

$7,390$

$347**$

$*347$ sweaters were sold through eBay for $$49$ each $($the customer pays shipping on all orders$).$

$**$Calculated assuming the demand at each school is independent $=\backslash$Sigma i$=1$N$\backslash$sigma $2$i$\backslash$Sigma