Tag: Mod.B

Guest Post: Making LP Relevant to Students

steve harrodDr. Steven Harrod is Assistant Professor of Operations Management at the University of Dayton. He shares a tip on teaching LP today.

It takes some creativity to make linear programming (see Module B in the Heizer/Render text) relevant to students. Here is an activity that offers a discussion of energy, transportation, and air pollution. The topic is coal-burning electric power plants, and it is an example of the blending problem.

Nearly half of all electricity in the U.S. is produced by burning coal, and nearly all of this coal moves by rail. Coal is an organic material that varies considerably in cost, power, and pollution content. Power plants frequently blend different coals to achieve their desired performance. Trains magazine published a detailed article on the movement of coal and its consumption by electric power plants in 2010. The readings and class materials may be downloaded here.

The documents package includes a quiz you may assign to motivate the reading assignment, a longer version of this Guest Post, and a sample spreadsheet model. Start the class discussion by drawing the class’s attention to the power plant at Monroe, Michigan. If you have an overhead projector with internet access, use Google maps to display a satellite photo of the plant. The lakeside plant has a prominent railroad loop and coal storage facility. You may also wish to explain how a power plant converts coal into electricity, and the environment concerns (sulfur causes acid rain and ash must be disposed of).

The challenge question for the students is: what coal should this plant purchase to satisfy energy and pollution limits at minimum cost? The formulated and solved LP leads to an optimal blend of three of the five coal sources. Ask the students, “is this intuitive?” Would you have been able to reach this conclusion without LP? Discuss at length and experiment with reducing or eliminating the pollution limits. This exercise may lead to a lengthy discussion of energy policy, environmental policy, and their joint effect on transportation demand.

OM in the News: Art and Science of Scheduling the N.F.L.

Howard Katz, NFL scheduling tzar

“We’re geniuses one day and absolute morons the next,” says Howard Katz, director of scheduling for the  National Football League. That’s because Katz must consider a confounding array of factors, from the N.F.L.’s expanded Thursday night package, which gives each team a game in a short week, to potential baseball playoff situations that could affect the availability of stadiums and parking lots in October.

The New York Times (April 20,2012) reports that for the networks that pay billions of dollars to carry N.F.L. games, Katz’s staff has been mostly geniuses. N.F.L. games were watched by an average of 17.5 million viewers last season. N.F.L. games accounted for 23 of the 25 most-watched television shows among all programming, and the 16 most-watched shows on cable last fall.

Designing a schedule that generates those ratings, while also guaranteeing competitive fairness, is more complicated than ever, even though software spits out 400,000 complete or partial schedules (once done entirely by hand) from a possible 824 trillion game combinations. Katz starts with thousands of seed schedules, empty slates in which a handful of critical games with attractive story lines are placed in select spots. Then the computers generate possibilities around those games.

The N.F.L. also feeds the computer with penalties for situations it prefers to avoid — three-game trips, for example, or teams starting with two road games. There are requests not to play at home on certain holidays — the Jets and the Giants typically ask not to play home games during the Jewish High Holy Days.  This year, the software generated 14,000 playable schedules, which were reduced to 150 with an eyeball test. Katz reviewed those 150 by hand, scoring them for each team and each network.

Linear programming may be at the heart of scheduling, but the process is definitely part art and part science.

Discussion questions:

1. Why is scheduling sports teams so complex?

2. Are all the teams happy with the final schedules?