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Network and discrete location models, algorithms and applications
Localion Science, Vol. 4, No. l/2, pp. 117-119, 1996 Published by Elsevier Science Ltd Printed in Great Britain 0966-8349196 $15.00+0.00
Pergamon
BOOK REVIEW
FRANK PLASTRIA Network and Discrete Location Models, Algorithms and Applications Mark S. Daskin. Wiley-Interscience Series in Discrete Mathematics Wiley & Sons, 1995. 498 pp. + 1 diskette. ISBN 0-471-01897-X.
and Optimization
John
Textbooks on location theory and models are rare objects. The few existing ones emphasize continuous location models at the detriment of discrete and, perhaps in a lesser way, network models. A book dedicated to these latter therefore looks like a welcome addition to the literature. The goals of the present book, as stated in the preface, are fivefold: introduce a number of classical facility location models on which more realistic models are based; develop modeling skills; introduce a number of key methodologies commonly used in the field, such as linear programming, graph-theoretic algorithms, heuristic methods, Lagrangean relaxation, branch and bound, dual ascent algorithms and Bender’s decomposition; introduce selected applications through the text and the exercises; finally provide software for solving moderate size instances of the basic location models. In the introductory chapter a number of key questions addressed by facility location models are discussed with some examples, leading to a broad classification. The second chapter, announced as a review of linear programming, defines LP’s, their dual and the relationships between these, then moves to the transportation problem, the shortest path problem and the minimum cost network flow problem. For each of these the classical algorithms are explained, based on duality notions, but a general purpose LP technique is lacking. The third and last introductory chapter then gives a very short overview of complexity analysis of algorithms and problems. The actual location theory starts in chapter four with covering models where the aim is to choose a cheapest set of sites such that all or many demand points lie within reach of at least one of them. First the minimum cost set covering problem is directly formulated as a discrete optimization problem, although the examples look at networks with locations restricted to vertices. Focusing on the equal cost version, a branch and bound technique is introduced. Then the maximal covering problem is studied. This allows discussion of several important heuristic approaches such as greedy methods and Lagrangean relaxation. This latter is clearly a much more technically involved method, and one may wonder if the introductory material in chapter 2 was sufficient to really follow here without more background. Chapter 5 then moves to center problems on networks in which the distance necessary for covering is minimized. After indicating that p-center problems are NP-complete in general, direct polynomial methods aie described for the 1 and 2 center versions on tree-networks. For the general vertex restricted problem, a binary search is described, based on set covering 117
118
Book
Review
as subproblems. In the absolute case where any point along any network-edge may be chosen it is shown how to reduce this feasible set and how the previous binary search technique may be extended. Median problems typically attempt to minimize global transport costs, and form the subject matter of chapter 6. The main model here is the p-median, which may always be considered to be vertex-restricted, but thereby in general still remains NP-hard. On a tree, however, it becomes polynomial, and the simplest l-median case is explained in detail. The general case is attacked by way of several heuristic techniques: greedy construction, neighborhood search improvement and Lagrangean relaxation based methods. This chapter ends with an in depth comparison of the results obtained by these various methods on a sample problem. In chapter 7 lixed costs are considered in addition to the transport costs, leading to fixed charge facility location problems, perhaps better known as the simple and the capacitated plant location problem. For the uncapacitated version, similar heuristic methods are described as before, now also including the dual-based approach. For the capacitated version, several different techniques are outlined. Langrangean relaxation of the capacity constraints leads to uncapacitated versions as subproblems, while relaxing the demand constraints leads to subproblems which decompose into easy knapsack problems; Bender’s decomposition is proposed as a third solution method. All the basic models having been introduced, chapter 8 now takes a quick look at several extensions in which these basic models lie at the heart. This comprises several classes of models like bi- or multi-objective models, location of hierarchical facility systems of various structures, other types of interactions like inter-facility flows/proximity, multiple product systems, integration of location and routing aspects for distribution modeling, hub location and undesirable facility location. In each case some formulations as mixed integer linear programming are worked out, but no direct information is given on special purpose solution strategies. This may hardly be considered as a disadvantage, the aim of this chapter being mainly to show the modeling versatility of integer programming by example, thereby introducing some of the standard tricks of the trade. The final chapter (chapter 9) is aimed at the starting practitioner. It puts the material developed in the book in its proper perspective within the whole decision process, and cautions against unreflected use of ready-made models. To quote “The problems faced by an enterprise may have little to do with the locations of the organization’s facilities. We must avoid falling into the trap of viewing every problem as a nail simply because all we have in our toolbox is a hammer”. The book ends with an 80 page reference manual for the use of the software accompanying the book as a 3.5” diskette. This software consists of three main parts: SITATION, MODDIST and MENU-OKF, all executables under MS-DOS. The first allows solution of maximum covering location problems, p-median problems and uncapacitated fixed charge location problems, by way of any of the heuristic methods described in this book. Branch and bound for a guaranteed exact optimal solution of these problems is not included, but this should not be a great drawback thanks to the availability of many general purpose mixed integer linear programming packages. The second is a utility to build networks, generate distance data and modify them selectively. The third is a network flow exact solution method based on the out-of-kilter method. The book is well structured for self-teaching and the accompanying software, although somewhat restricted in scope, makes the book directly useful in simple practical situations.
Book Review
119
Most models and methods are introduced and described with ample details, and each chapter ends with several exercises. As such it is well suited for students and practitioners who quickly want to become acquainted with the basic models and the standard techniques. However, some of the presented material is clearly of much higher technical level and less prepared readers will probably have a hard time with these parts. Conversely do not expect too much technical details and formal proofs. Mathematically oriented readers will probably remain somewhat frustrated and will have to turn elsewhere to find the hard theory behind it all. And the book is not very helpful in this respect; it offers only few references to further literature and these are quite restricted: in the final reference list only some 150 titles appear, which is clearly far below the thousands of papers published in the field. Non-native North Americans may also feel somewhat left-out, since all examples are clearly US oriented, and the nice graphical output of the software is restricted to northern America.
Pergamon
BOOK REVIEW
FRANK PLASTRIA Network and Discrete Location Models, Algorithms and Applications Mark S. Daskin. Wiley-Interscience Series in Discrete Mathematics Wiley & Sons, 1995. 498 pp. + 1 diskette. ISBN 0-471-01897-X.
and Optimization
John
Textbooks on location theory and models are rare objects. The few existing ones emphasize continuous location models at the detriment of discrete and, perhaps in a lesser way, network models. A book dedicated to these latter therefore looks like a welcome addition to the literature. The goals of the present book, as stated in the preface, are fivefold: introduce a number of classical facility location models on which more realistic models are based; develop modeling skills; introduce a number of key methodologies commonly used in the field, such as linear programming, graph-theoretic algorithms, heuristic methods, Lagrangean relaxation, branch and bound, dual ascent algorithms and Bender’s decomposition; introduce selected applications through the text and the exercises; finally provide software for solving moderate size instances of the basic location models. In the introductory chapter a number of key questions addressed by facility location models are discussed with some examples, leading to a broad classification. The second chapter, announced as a review of linear programming, defines LP’s, their dual and the relationships between these, then moves to the transportation problem, the shortest path problem and the minimum cost network flow problem. For each of these the classical algorithms are explained, based on duality notions, but a general purpose LP technique is lacking. The third and last introductory chapter then gives a very short overview of complexity analysis of algorithms and problems. The actual location theory starts in chapter four with covering models where the aim is to choose a cheapest set of sites such that all or many demand points lie within reach of at least one of them. First the minimum cost set covering problem is directly formulated as a discrete optimization problem, although the examples look at networks with locations restricted to vertices. Focusing on the equal cost version, a branch and bound technique is introduced. Then the maximal covering problem is studied. This allows discussion of several important heuristic approaches such as greedy methods and Lagrangean relaxation. This latter is clearly a much more technically involved method, and one may wonder if the introductory material in chapter 2 was sufficient to really follow here without more background. Chapter 5 then moves to center problems on networks in which the distance necessary for covering is minimized. After indicating that p-center problems are NP-complete in general, direct polynomial methods aie described for the 1 and 2 center versions on tree-networks. For the general vertex restricted problem, a binary search is described, based on set covering 117
118
Book
Review
as subproblems. In the absolute case where any point along any network-edge may be chosen it is shown how to reduce this feasible set and how the previous binary search technique may be extended. Median problems typically attempt to minimize global transport costs, and form the subject matter of chapter 6. The main model here is the p-median, which may always be considered to be vertex-restricted, but thereby in general still remains NP-hard. On a tree, however, it becomes polynomial, and the simplest l-median case is explained in detail. The general case is attacked by way of several heuristic techniques: greedy construction, neighborhood search improvement and Lagrangean relaxation based methods. This chapter ends with an in depth comparison of the results obtained by these various methods on a sample problem. In chapter 7 lixed costs are considered in addition to the transport costs, leading to fixed charge facility location problems, perhaps better known as the simple and the capacitated plant location problem. For the uncapacitated version, similar heuristic methods are described as before, now also including the dual-based approach. For the capacitated version, several different techniques are outlined. Langrangean relaxation of the capacity constraints leads to uncapacitated versions as subproblems, while relaxing the demand constraints leads to subproblems which decompose into easy knapsack problems; Bender’s decomposition is proposed as a third solution method. All the basic models having been introduced, chapter 8 now takes a quick look at several extensions in which these basic models lie at the heart. This comprises several classes of models like bi- or multi-objective models, location of hierarchical facility systems of various structures, other types of interactions like inter-facility flows/proximity, multiple product systems, integration of location and routing aspects for distribution modeling, hub location and undesirable facility location. In each case some formulations as mixed integer linear programming are worked out, but no direct information is given on special purpose solution strategies. This may hardly be considered as a disadvantage, the aim of this chapter being mainly to show the modeling versatility of integer programming by example, thereby introducing some of the standard tricks of the trade. The final chapter (chapter 9) is aimed at the starting practitioner. It puts the material developed in the book in its proper perspective within the whole decision process, and cautions against unreflected use of ready-made models. To quote “The problems faced by an enterprise may have little to do with the locations of the organization’s facilities. We must avoid falling into the trap of viewing every problem as a nail simply because all we have in our toolbox is a hammer”. The book ends with an 80 page reference manual for the use of the software accompanying the book as a 3.5” diskette. This software consists of three main parts: SITATION, MODDIST and MENU-OKF, all executables under MS-DOS. The first allows solution of maximum covering location problems, p-median problems and uncapacitated fixed charge location problems, by way of any of the heuristic methods described in this book. Branch and bound for a guaranteed exact optimal solution of these problems is not included, but this should not be a great drawback thanks to the availability of many general purpose mixed integer linear programming packages. The second is a utility to build networks, generate distance data and modify them selectively. The third is a network flow exact solution method based on the out-of-kilter method. The book is well structured for self-teaching and the accompanying software, although somewhat restricted in scope, makes the book directly useful in simple practical situations.
Book Review
119
Most models and methods are introduced and described with ample details, and each chapter ends with several exercises. As such it is well suited for students and practitioners who quickly want to become acquainted with the basic models and the standard techniques. However, some of the presented material is clearly of much higher technical level and less prepared readers will probably have a hard time with these parts. Conversely do not expect too much technical details and formal proofs. Mathematically oriented readers will probably remain somewhat frustrated and will have to turn elsewhere to find the hard theory behind it all. And the book is not very helpful in this respect; it offers only few references to further literature and these are quite restricted: in the final reference list only some 150 titles appear, which is clearly far below the thousands of papers published in the field. Non-native North Americans may also feel somewhat left-out, since all examples are clearly US oriented, and the nice graphical output of the software is restricted to northern America.