Going with the flow (25 pts)

Wilhelm Dryer is one of the great immigration stories. Escaping the Nazis as a child, he came home after the war and is the number one seller supplier of beauty salons. He sells hair sculpting systems he calls the Herr Dryer.

He can produce 1.2 million hair dryers in Madrid and he finds that shipping by train is the most efficient way to ship his parts (i.e., dryers) out. However, he cannot ship directly due to capacity restrictions.

In terms of capacity of the routes, from Madrid he can potentially ship the following number of parts (or dryers):

500,000 to Porto

900,000 to Geneva

700,000 to Rome

In addition to the 900,000 parts, Geneva is a major hub and can receive 750,000 parts from Porto and 650,000 parts from Rome.

From Geneva, 400,000 parts can be shipped to Amsterdam and 600,000 parts directly to Berlin.

Porto can ship 500,000 parts to Amsterdam and 750,000 to Geneva.

Amsterdam can send 500,000 parts to Berlin.

a. Draw the network diagram of capacities. If I cannot read it, there is no credit. 5 pts

b. Using one of the techniques shown in class, what is the maximum number of parts that can be shipped out of Madrid? Show the flows through every node. Trial and error will result in zero points. 10 pts

c. Which nodes are deficit, excess and balanced? Are any of these nodes dead (i.e., no flow through it); if so, which arc(s)? 5 pts

d. Any dryer that does not go out with a 1.2 million part shipment is a $1/dryer loss for Herr Dryer. Amsterdam claims that it can raise its 500,000 output to 800,000 for an added fee of $0.25/part running through this segment. Is it worth it? Why? 5 pts

Europe Europe