# James Long, the owner of Longs Inc., is a distributor

James Long, the owner of Longs Inc., is a distributor of one size fit all T-shirts. T-shirts are purchased from the manufacturer in Asia before the beginning of the season and are stocked and sold to resellers. At the end of the season, unsold T-shirts are all sold to the local discount stores at a deep discount. Consider the following situation regarding a T-shirt, which comes in two popular colors, red and green.

 T-shirt (color) Average demand Std. dev. of demand Unit Selling Price (\$) Unit Purchasing Cost (\$) Unit Holding Cost (for the entire season) Unit Salvage Price (\$) Red 10,000 3000 15 10 0.5 8 Green 15,000 4000 15 10 0.5 8

Assuming that demand for T-shirts are Normal,

a) Find the optimal quantities to be ordered for each T-shirt color and the overall average total cost for the season associated with this operation.

Instead of ordering the T-shirts with colors to the Asian Manufacturer and then stocking them at the warehouse, James is considering ordering white T-shirts to the manufacturer and then complete the dying of the T-shirts locally, as needed. This way, only white T-shirts will be stocked as dying can be completed expeditiously in no time. Each white T-shirt will cost \$6. Unsold white T-shirts will be salvaged at the end of the season at \$4.5. In addition, the unit holding cost of stocking white a T-shirt for the season is \$0.3. Finally, the dying cost will be \$1 per T-shirt.

b) Which supply chain concept(s) discussed in class is (are) being considered here?

c) Assuming that the demand for Red and Green T-shirts are independent, calculate the optimal order quantity for the white T-shirts, the average total cost for the season associated with this operation. Based on your analysis, should James take this action?

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