Sports of All Sorts produces, distributes, and sells high-quality skateboards. Its supply chain consists of three factories (located in Detroit, Los Angeles, and Austin) that produce skateboards. The Detroit and Los Angeles facilities can produce 350 skateboards per week, but the Austin plant is larger and can produce up to 700 skateboards per week. Skateboards must be shipped from the factories to one of four distribution centers, or DCs (located in Iowa, Maryland, Idaho, and Arkansas). Each distribution center can process (repackage, mark for sale, and ship) at most 500 skateboards per week. Skateboards are then shipped from the distribution centers to retailers. Sports of All Sorts supplies three major U. S. retailers: Just Sports, Sports âN Stuff, and The Sports Dude. The weekly demands are 200 skateboards at Just Sports, 500 skateboards at Sports âN Stuff, and 650 skateboards at The Sports Dude. The following tables display the per-unit costs for shipping skateboards between the factories and DCs and for shipping between the DCs and the retailers.

Shipping Costs ( $ per skateboard)

Factorys/DC's Iowa maryland idaho arkansas

Detroit $25 25 35 40

L. A 35 45 35 42

Austin 40 40 42.50 32.50

Retailers?DC's

Just sports 30 20 35 27.50

sports n stuff 27.50 32.50 40 25

the sports dude 30 40 32.50 42.50

a. Draw the network representation for this problem.
b. Build a model to minimize the transportation cost of a logistics system that will de-

liver skateboards from the factories to the distribution centers and from the distribu- tion centers to the retailers. What is the optimal production strategy and shipping pattern for Sports of All Sorts? What is the minimum attainable transportation cost?

c. Sports of All Sorts is considering expansion of the Iowa DC capacity to 800 units per week. The annual amortized cost of expansion is $40,000. Should the company ex- pand the Iowa DC capacity so that it can process 800 skateboards per week? (Assume 50 operating weeks per year.)