Classical Techniques

Abstract

The purpose of this chapter is to provide an introduction to three classical search techniques, branch and bound, dynamic programming and network flow programming, all of which have a well established record in the solution of both classical and practical problems. All three have their origins in, or prior to, the 1950s and were the result of a surge in interest in the use of mathematical techniques for the solution of practical problems. The timing was in part due to developments in Operations Research in World War II, but was also spurred on by increasing competition in the industrial sector and the promise of readily accessible computing power in the foreseeable future. A fourth technique belonging to this class, that of Integer Programming, is covered in Chapter 3. Given their age, it is not surprising that they no longer generate the same level of excitement as the more modern approaches covered elsewhere in this volume, and as a result they are frequently overlooked. This effect is reinforced as many texts such as this omit them—presumably because they have already been covered by a range of sources aimed at a wide variety of different abilities and backgrounds. In this volume we provide an introduction to these well-established classics alongside their more modern counterparts. Although they have shortcomings, many of which the more recent approaches were designed to address, they still have a role to play both as stand-alone techniques and as important ingredients in hybridized solution methods.