Mathematical Background

The methodology suggested in this book is based on three mathematical tools — optimal control, combinatorics and mathematical programming — which are traditionally related to separate areas of research and application. The methodology involves, first, investigating a continuous-time problem with the aid of the maximum principle and then reducing it to a discrete combinatorial or mathematical programming problem solvable in polynomial time. The following sections present selected combinatorics, the maximum principle and a constructive approach for integrating both mathematical tools.