Optimization methods: An applications-oriented primer

Effectively sharing resources requires solving complex decision problems. This requires constructing a mathematical model of the underlying system, and then applying appropriate mathematical methods to find an optimal solution of the model, which is ultimately translated into actual decisions. The development of mathematical tools for solving optimization problems dates back to Newton and Leibniz, but it has tremendously accelerated since the advent of digital computers. Today, optimization is an inter-disciplinary subject, lying at the interface between management science, computer science, mathematics and engineering. This chapter offers an introduction to the main theoretical and software tools that are nowadays available to practitioners to solve the kind of optimization problems that are more likely to be encountered in the context of this book. Using, as a case study, a simplified version of the bike sharing problem, we guide the reader through the discussion of modelling and algorithmic issues, concentrating on methods for solving optimization problems to proven optimality.