Today, as I entered my department’s Xerox/coffee room to make myself some tea, I noticed a big pile of old books and a note from one of my colleagues saying they were up for grabs. As I browsed through the titles, one of them caught my attention:
And here’s the text that appears on the flaps of the outer paper cover:
The publication date is 1966. And here’s an interesting quote:
“The best-known European book on linear programming. Considered one of the most complete studies of the field ever written,…”
I must confess I didn’t know about this book, but I decided to keep it for its (potential) historical value. A little Googling led me to discover that Adi Ben-Israel wrote a half-page SIAM Review about this book in 1967 (volume 9, no. 3, p. 608). Here are some highlights:
“This book is, in my opinion, among the best in the class of general reference and self-instruction L.P. texts presently available, and as such is most valuable to practitioners and students of L.P.”
Later on Adi also says that the book has “Many well-chosen, worked out examples.” That sounds pretty good! I haven’t had time to browse through it yet, but if anyone knows about this book, I’d love to hear your thoughts.
Penny is organizing a party at her apartment, but she is on a tight budget. Having a working knowledge of all of the important things in the universe, Sheldon knows everything about linear programming and offered to help her. He postulates that it’s ideal to have two kinds of mixed nuts: a plain party mix, and a luxury mix (for those with a distinct taste like himself). Based on the expected number of guests, Howard quickly calculates that they’ll need a total of at least 10 pounds of snacks, but no more than 6 pounds of each kind of mix. On his white board, Sheldon has already come up with the following table:
Raj wants to dip the hazelnuts into liquor, but that’s not in the budget, so he gives up. Leonard reminds everyone that, because of their allergies, it’s important to keep the average allergenicity level per pound in both mixes to no more than 3. Write an optimization model to help Penny prepare the two kinds of snacks at minimum cost. But be careful: Sheldon will check it later for correctness!
This post is part of my series “Having Fun with Exam Questions”. Previous questions dealt with Farmville, vampires, and (potentially) Valentine’s day.
I just finished my presentation to business undergraduate students and, from what I could tell by looking at them, I think it was successful. Of course the real test will be whether someone stops by my office saying “I love OR! Can I work with you?”. I want to thank our vice dean for this opportunity and I am looking forward to doing it again next year.
I closed the presentation with a little “quiz” based on a very nice paper by Brown, Klein, Rosenthal and Washburn entitled Steaming on Convex Hulls. Here’s how it goes (you can open the image on a new window to make it larger):
An aircraft carrier can run with 2 or 4 engines online. The graph below shows gallons of gasoline used per hour versus possible speeds for each engine configuration. How would you run the ship to cover 100 miles in 4 hours?
According to the article, the Navy spends over 1 billion dollars a year on surface combatants alone. An officer who became a ship commander after graduating from the academy was smart enough to solve the above problem the right way. His ship was saving so much fuel that it had to be inspected under the suspicion that it was violating safety regulations. But we all know it wasn’t. It was just a case of using analytical techniques to make better decisions.
CAUTION: Spoiler Alert!
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.
This had been in the back burner for a long while. Each time I taught my O.R. class (either undergrad or MBA), I kept thinking that the students would like to be able to see the Excel setup of an LP model over and over again. Many of them are not proficient in Excel, and my class is their first contact with things like absolute cell references and SUMPRODUCT. I watched a number of YouTube videos on the topic, but I wasn’t happy with any of them. Besides, I wanted the video to be about the same example that I use in the classroom. So I decided to bite the bullet and go for it. I think the outcome was decent: not great, but not terrible either. My wife said I sound a little stilted. I agree. I was only willing to do it once, no second takes, which means I was a little nervous :-)
Before I give you the link to the videos, I need to bring your attention to two disclaimers:
Disclaimer 1: I used the demo version of iShowU to record my screen action. That means you’ll see a green watermark on top of the video. I know it’s ugly, but I didn’t want to pay $29.95 for it. At least not until I get some feedback to convince me that I’ll be doing more of these videos.
Disclaimer 2: I shamelessly use the same example that they (used to?) use at the Tepper School in my classes: the “famous” farmer problem (sorry Javier :-). I was the head TA for that class a number of times and I literally sat through it at least 3 or 4 times.
Here they are:
Linear Programming: The Farmer Problem, Part I (9:07 min)
Linear Programming: The Farmer Problem, Part II (8:57 min)
I hope these videos turn out to be useful to my students and to anyone who wants to learn about linear programming and Excel Solver. I’m thinking about doing more videos on the diet problem, transportation, sensitivity analysis, etc. Let’s see how things go.