1Introductory Problems

Logistic problems are all around us. We only need to observe a little and to have some imagination to find them. In this chapter we propose three problems that perfectly illustrate the potential touch of madness of an operations researcher. These examples enable us to approach the issues that may crop up in the industrial world gradually, which will be described more formally in the following chapters. They are drawn from exam papers assigned to undergraduate students that have taken classes in a subject called “optimization problems and procedures”. They are kept in their original form on purpose. The questions asked will be answered over the course of this book. A detailed answer key for the exercises, including comments, is supplied in the last chapter of this book. Beginners in combinatorial optimization can play the following little game: could you recognize the correlation between each practical problem and its theoretical equivalent?

1.1. The “swing states” problem

In the United States of America, during the presidential elections, there are certain states called “swing states”, which are liable to swing from the Democratic Party towards the Republican or vice versa. It is these states that both parties pay most attention to, especially when the results day is drawing near. Table 1.1 shows the list of these states and the figures of their Electoral College.

The advisers of one of two candidates (you are free to choose either side) ask you to help ...

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