Math 30210 - Introduction to Operations Research

Fall 2014

Instructor: David Galvin


NOTE: all course policies announced here are subject to change before the first day of semester! The date for the in-class midterm exam is tentative, and subject to change beyond the first day of semester (though plenty of notice will be given if it changes).

About the course

Operations Research (OR) is the application of mathematical ideas to decision making. In a typical decision-making problem tackled by OR, one has some (usually limited) resources, some ways of deploying those resources, and some objective, and one asks how the resources should be deployed in order to reach the objective, or get as close to it as possible. For example, the resources might be a fleet of trucks, and the objective might be to send a collection of packages to some addresses across the state, at low cost (this is an OR problem that UPS has to solve everyday); the resources might be classrooms on campus, and the objective might be to schedule a semester's worth of classes with as few time-conflicts as possible for students and professors (this is a problem ND has to solve twice a year); or the resource might be time, and the objective might be to spend it in a fulfilling way (this is a problem one spends a lifetime solving).

Fundamental to OR is programming, in which there is a finite collection of variables, collectively subject to some constraints, and a function of those variables (the objective function) that one wishes to maximize or minimize, without violating any of the constraints. When the constraints and objective are all linear functions of the variables (as is the case in many important examples), one has a linear programming problem. We will devote much of the semester to the study of linear programming, for which a beautiful mathematical theory has been developed over the last half century; unlike many mathematical theories, it is one which is applied the world over on a daily basis.

Towards the end of the semester, we will apply the theory of linear programming to the study of games, specifically to those games in which two people compete to capture as much as possible of a finite resource.

The rough plan is to cover Chapters 1 through 4, 7 and 9 of the textbook.

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Basic information

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Late assignments

All homework must be done by the due date to receive credit, and all quizzes and exams must be taken at the assigned times.

I will not consider requests for homework extensions, or make-up quizzes and/or exams, except in the case of legitimate, university-sanctioned conflicts. It is your responsibility to let me know the full details of these conflicts before they cause you to miss an assignment! Excepting university-sanctioned conflicts, it is your responsibility to be in class for all scheduled lectures.

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Homework assignments are posted here, in a single file that will be updated throughout the semester. For homework solutions, see the end of this section.

The weekly homework is an important part of the course; it gives you a chance to think more deeply about the material, and to go from seeing (in lectures) to doing. It's also your opportunity to show me that you are engaging with the course topics.

Homework is an essential part of your learning in this course, so please take it very seriously. It is extremely important that you keep up with the homework, as if you do not, you may quickly fall behind in class and find yourself at a disadvantage during exams.

You should treat the homework as a learning opportunity, rather than something you need to get out of the way. Reread, revise, and polish your solutions until they are correct, concise, efficient, and elegant. This will really deepen your understanding of the material. I encourage you to talk with your colleagues about homework problems, but your final write-up must be your own work.

Homework solutions should be complete (and in particular presented in complete sentences), with all significant steps justified.

Homework solutions:

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Quizzes will be posted here, in a single file that will be updated throughout the semester.

Quiz solutions:

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Final exam: In 117 Hayes-Healy, Tuesday, December 16, 4.15-6.15pm. Here is the information that you need to know:

Midterm exam: In class on Wednesday, October 15. Here is the information that you need to know:

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Supplementary material

Here is where I will post any supplementary material for the course, such as slides that I go over in class.

In-class slides

Example of greed not being good:

Worksheet on Solver:

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Honor code: You have all taken the Honor Code pledge, to not participate in or tolerate academic dishonesty. For this course, that means that although you may (and should) discuss assignments with your colleagues, you must write the final version of each of your assignments on your own; if you use any external sources to assist you (such as other textbooks, computer programmes, etc.), you should cite them clearly; your work on the mid-semester exam and the final exam should be your own; and you will adhere to all announced exam policies.

Class conduct: The lecture room should be a place where you should feel free to engage in lively discussion about the course topic; don't be shy! But non course related interruptions should be kept to a minimum. In particular, you should turn off or switch to silent all phones, etc., before the start of class. If for some good reason you need to have your phone on during class, please mention it to me in advance.

A general comment: Like many other endeavors (such as driving a car or mastering a piece of software), mathematics is something that you learn by doing. Attending class and reading the appropriate sections of the textbook is very important, but isn't enough to do well. After each lecture you should work through every example and proof from your class notes. Don't be perturbed if you have to re-read and re-do some topics many times before you begin to feel that you are mastering them. That is just how mathematical learning goes. It's a slow process, but a worthwhile one.

If after struggling with a topic you still feel like you are making no headway, don't give up! Leave it aside for a while to let your unconscious brain work on it. Then go back to it, and talk it over with you colleagues, and come talk to me. It's what I'm here for!

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