This book grew out a number of distribution and logistics graduate courses we have taught over the last ten years. In the first few years, the emphasis was on very basic models such as the traveling salesman problem, and on the seminal papers of Haimovich and Rinnooy Kan (1985), which analyzed a simple vehicle routing problem, and Roundy (1985), which introduced power-of-two policies and proved that they are effective for the one warehouse multi-retailer distribution system. At that time, few results existed for more complex, realistic distribution problems, stochastic inventory problems or the integration of these issues.
In the last few years however, there has been renewed interest in the area of logistics among both industry and academia. A number of forces have contributed to this shift. First, industry has realized the magnitude of savings that can be achieved by better planning and management of complex logistics systems. Indeed, a striking example is Wal-Mart's success story which is partly attributed to implementing a new logistics strategy, called cross-docking. Second, advances in information and communication technologies together with sophisticated decision support systems now make it possible to design, implement and control logistics strategies that reduce system-wide costs and improve service level. These decision support systems, with their increasingly user-friendly interfaces, are fundamentally changing the management of logistics systems.
These developments have motivated the academic community to aggressively pursue answers to logistics research questions. Indeed, in the last five years considerable progress has been made in the analysis and solution of logistics problems.
This progress was achieved, in many cases, using an approach whose purpose is to ascertain characteristics of the problem or of an algorithm that are {\it independent of the specific problem data}. That is, the approach determines characteristics of the solution or the solution method that are intrinsic to the problem and not the data. This approach includes the so-called worst-case and average-case analyses which, as illustrated in the book, help not only to understand characteristics of the problem or solution methodology, but also provide specific guarantees of effectiveness. In many case, the insights obtained from these analyses can then be used to develop practical and effective algorithms for specific complex logistics problems. Our objective in writing this book is to describe these tools and developments.
Of course, the work presented in this book is not necessarily an exhaustive account of the current state of the art in logistics. The field is too vast to be properly covered here. In addition, the practitioner may view some of the models discussed as simplistic and the analysis presented as complex. Indeed, this is the dilemma one is faced with when analyzing very complex, multi-faceted, real-world problems. By focusing on simple yet rich models that contain important aspects of the real-world problem, we hope to glean important aspects of the problem that might be overlooked by a more detail-oriented approach.
The book is written for graduate students, researchers and practitioners interested in the mathematics of logistics management. We assume the reader is familiar with the basics of linear programming and probability theory and, in a number of sections, complexity theory and graph theory, although in many cases these can be skipped without loss of continuity. The book provides: