# Twilight Network Flow

Part of a professor’s job is to come up with new exam questions each year. That may be a time-consuming (and sometimes tedious) task. You want the question to be just right: not too easy, not too difficult, and capable of testing whether or not the students understood a given concept. This year, I figured I might as well have some fun while doing it. Inspired by Laura McLay’s insightful (and very popular) post on vampire populations, I decided to create a Twilight-themed network flow question:

Alice is in charge of planning Edward and Bella’s wedding and she ordered 2000 roses to be delivered to three locations as shown in the network below. The Cullen’s house (node 2) needs 1000 roses, Charlie’s house (node 4) needs 800 roses, and Billy’s house (node 7) is supposed to get 200 roses (just to tease Jacob). The numbers next to the arcs of the network represent shipping costs per rose (in cents); they’re proportional to the distance between each node. The roses are coming from two local growers in Forks (nodes 1 and 3). Each of them can supply 1000 roses. Arrows with two heads indicate that shipments can be made in both directions.

Write down the supply and/or demand values next to each node and write a linear programming model to determine the shipment plan that minimizes the total cost of delivering all the roses (include all the necessary constraints). (Note: Alice already knows whether you’re going to get the right answer.)

The second half of the fun is to see if any students react to it. In fact, I got a couple of interesting written comments: “How dare you incorporate Twilight into Management Science?”, and a Harry Potter enthusiast wrote “Team Harry!”, while at the same time substituting the names of Hermione, Harry, Ginny and Malfoy for Alice, Edward, Bella, and Jacob.