integer programming for locating ambulances

Last week I visited Oberlin College to deliver the Fuzzy Vance Lecture in Mathematics (see post here). In addition, I gave two lectures to Bob Bosch’s undergraduate optimization course. I will post my materials for both of my lectures on my blog. The first lecture was related to my evening talk and focused on ambulance location models and modeling integer programs.

The purpose of the lecture was to work on modeling in integer programming. We focused on coverage models and worked through two of the three models that successively lift simplifying assumptions (in a 75 minute lecture). The “Integer Programming Bag of Tricks” on slide 18 contains a series of constraints for modeling conditional constraints (courtesy of Jeff Linderoth and Jim Luedtke). We use these tricks to assign at least L calls for service (demand) to stations–but only stations that are “open”–in the modeling exercise. Slides are below.

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