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E-raamat: Equitable Resource Allocation - Models, Algorithms and Applications: Models, Algorithms and Applications [Wiley Online]

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"This book focuses primarily on equitable resource allocation and is a valuable reference to those who work to solve diverse optimization problems"--

Resource allocation problems focus on the allocation of limited resources among competing activities with the intent of optimizing an objective function, says Luss, who is retired now from big technology companies. Taking as his objective function the equitable or fair distribution among all competing activities, he describes a large number of models that have special mathematical structures and can be solved by elegant efficient algorithms that take advantage of these structures. He covers nonlinear resource allocation, lexicographic minimax and maximin optimizations, substitutable resources, multi-period equitable resource allocation, network resources, and integer decisions. Annotation ©2013 Book News, Inc., Portland, OR (booknews.com)

A unique book that specifically addresses equitable resource allocation problems with applications in communication networks, manufacturing, emergency services, and more

Resource allocation problems focus on assigning limited resources in an economically beneficial way among competing activities. Solutions to such problems affect people and everyday activities with significant impact on the private and public sectors and on society at large.

Using diverse application areas as examples, Equitable Resource Allocation: Models, Algorithms, and Applications provides readers with great insight into a topic that is not widely known in the field. Starting with an overview of the topics covered, the book presents a large variety of resource allocation models with special mathematical structures and provides elegant, efficient algorithms that compute optimal solutions to these models.

Authored by one of the leading researchers in the field, Equitable Resource Allocation:

  • Is the only book that provides a comprehensive exposition of equitable resource allocation problems
  • Presents a collection of resource allocation models with applications in communication networks, transportation, content distribution, manufacturing, emergency services, and more
  • Exhibits practical algorithms for solving a variety of resource allocation models
  • Uses real-world applications and examples to explain important concepts
  • Includes end-of-chapter exercises

Bringing together much of the equitable resource allocation research from the past thirty years, this book is a valuable reference for anyone interested in solving diverse optimization problems.

Preface xi
Acknowledgments xvii
1 Introduction
1(40)
1.1 Perspective
1(2)
1.2 Equitable Resource Allocation: Lexicographic Minimax (Maximin) Optimization
3(11)
1.3 Examples and Applications
14(12)
1.3.1 Allocation of High-Tech Components
14(1)
1.3.2 Throughput in Communication and Computer Networks
15(3)
1.3.3 Point-to-Point Throughput Estimation in Networks
18(2)
1.3.4 Bandwidth Allocation for Content Distribution
20(3)
1.3.5 Location of Emergency Facilities
23(2)
1.3.6 Other Applications
25(1)
1.4 Related Fairness Criteria
26(4)
1.5 Outline of the Book
30(5)
1.5.1
Chapter 2: Nonlinear Resource Allocation
30(1)
1.5.2
Chapter 3: Equitable Resource Allocation: Lexicographic Minimax and Maximin Optimization
30(1)
1.5.3
Chapter 4: Equitable Resource Allocation with Substitutable Resources
31(1)
1.5.4
Chapter 5: Multiperiod Equitable Resource Allocation
32(1)
1.5.5
Chapter 6: Equitable Network Resource Allocation
33(1)
1.5.6
Chapter 7: Equitable Resource Allocation with Integer Decisions
34(1)
1.6 Concluding Remarks and Literature Review
35(6)
1.6.1 Equitable Allocation of High-Tech Components
38(1)
1.6.2 Equitable Throughput in Communication and Computer Networks
38(1)
1.6.3 Point-to-Point Throughput Estimation in Networks
39(1)
1.6.4 Equitable Bandwidth Allocation for Content Distribution
39(1)
1.6.5 Equitable Location of Emergency Facilities
39(1)
1.6.6 Other Applications
39(2)
2 Nonlinear Resource Allocation
41(36)
2.1 Formulation and Optimality Properties
42(6)
2.2 Algorithms
48(10)
2.2.1 The Activity Deletion Algorithm
48(5)
2.2.2 The Activity Addition Algorithm
53(2)
2.2.3 The Constraints Evaluation Algorithm
55(3)
2.2.4 Lower and Upper Bounds
58(1)
2.3 Nonlinear Resource-Usage Constraint
58(8)
2.3.1 Formulation and Optimality Properties
59(3)
2.3.2 Algorithms
62(4)
2.4 Multiple Resource Constraints: A Special Case
66(7)
2.5 Concluding Remarks and Literature Review
73(4)
Exercises
75(2)
3 Equitable Resource Allocation: Lexicographic Minimax and Maximin Optimization
77(46)
3.1 Formulation and Optimality Properties
78(6)
3.2 Minimax Algorithms
84(14)
3.2.1 The Minimax Activity Deletion Algorithm
84(6)
3.2.2 The Minimax Activity Addition Algorithm
90(4)
3.2.3 The Minimax Constraints Evaluation Algorithm
94(3)
3.2.4 Lower and Upper Bounds
97(1)
3.3 The Lexicographic Minimax Algorithm
98(9)
3.4 Extension to Nonseparable Objective Function
107(9)
3.5 Concluding Remarks and Literature Review
116(7)
Exercises
120(3)
4 Equitable Resource Allocation with Substitutable Resources
123(60)
4.1 Representations of Substitutable Resources
124(7)
4.1.1 Transitive Substitutable Resources Represented by Trees
124(1)
4.1.2 Transitive Substitutable Resources Represented by Acyclic Graphs
125(2)
4.1.3 Nontransitive Substitutable Resources Represented by Bipartite Graphs
127(1)
4.1.4 Activity-Dependent Substitutable Resources Represented by Bipartite Graphs
128(1)
4.1.5 Solution Approach
129(2)
4.2 Transitive Substitutable Resources Represented by Trees
131(22)
4.2.1 Formulation
131(3)
4.2.2 The Minimax Algorithm
134(9)
4.2.3 The Lexicographic Minimax Algorithm
143(8)
4.2.4 Lower and Upper Bounds
151(2)
4.3 Transitive Substitutable Resources Represented by Acyclic Graphs
153(19)
4.3.1 Formulation
154(1)
4.3.2 The Feasibility Problem
155(6)
4.3.3 The Minimax Algorithm
161(4)
4.3.4 The Lexicographic Minimax Algorithm
165(7)
4.4 Activity-Dependent Substitutable Resources Represented by Bipartite Graphs
172(8)
4.4.1 Formulation
173(2)
4.4.2 The Minimax Algorithm
175(4)
4.4.3 The Lexicographic Minimax Algorithm
179(1)
4.5 Concluding Remarks and Literature Review
180(3)
Exercises
181(2)
5 Multiperiod Equitable Resource Allocation
183(38)
5.1 Formulation for Storable Resource Allocation
184(3)
5.2 Minimax Algorithms for Storable Resources
187(16)
5.2.1 The Search-Based Algorithm
188(4)
5.2.2 The Transformation-Based Algorithm
192(8)
5.2.3 The Multiperiod Activity Deletion Algorithm: A Special Case
200(3)
5.3 The Lexicographic Minimax Algorithm
203(7)
5.4 Allocation of Nonstorable Resources
210(3)
5.5 Multiperiod Allocation of Substitutable Resources
213(5)
5.6 Concluding Remarks and Literature Review
218(3)
Exercises
219(2)
6 Equitable Allocation of Network Resources
221(38)
6.1 Multicommodity Network Flows with a Single Fixed Path
223(4)
6.2 Multicommodity Network Flows with Multiple Paths
227(10)
6.3 Bandwidth Allocation for Content Distribution
237(11)
6.4 Content Distribution with Node-Dependent Performance Functions
248(6)
6.5 Concluding Remarks and Literature Review
254(5)
Exercises
257(2)
7 Equitable Resource Allocation with Integer Decisions
259(54)
7.1 Knapsack Resource Constraints with Integer Variables
261(12)
7.1.1 Formulation and Challenges
261(3)
7.1.2 The Integer Minimax Problem
264(6)
7.1.3 The Integer Lexicographic Minimax Problem with One Resource Constraint
270(3)
7.2 Problems with a Limited Number of Distinct Outcomes
273(17)
7.2.1 The Equitable Facility Location Problem
273(6)
7.2.2 The Equitable Sensor Location Problem
279(2)
7.2.3 Lexicographic Minimization of Counting Functions
281(9)
7.3 Problems with a Large Number of Distinct Outcomes
290(17)
7.3.1 Examples
291(3)
7.3.2 Lexicographic Maximization of Performance Function Values
294(7)
7.3.3 The Conditional Maximin Approach
301(1)
7.3.4 The Ordered Weighted Averaging Approach
302(3)
7.3.5 The Convex Integer Optimization Approach
305(2)
7.4 Concluding Remarks and Literature Review
307(6)
Exercises
311(2)
Appendices
313(18)
Appendix A Summary of Models and Algorithms
315(8)
Appendix B The Kuhn-Tucker Conditions
323(4)
Appendix C Duality in Linear Programming
327(4)
References 331(12)
Author Index 343(4)
Subject Index 347
HANAN LUSS, PhD, serves as an Adjunct Professor, teaching operations research courses at Columbia University. Dr. Luss was at AT&T Bell Laboratories/AT&T Labs for twenty-five years, serving as technical manager of the Operations Research Studies Group, and at Telcordia Technologies for twelve years, serving as senior scientist. He led research activities and applied work with an emphasis on operations research methodologies for resource allocation, communication network design, capacity expansion, manufacturing, and related topics. A Fellow of the Institute for Operations Research and the Management Sciences (INFORMS), Dr. Luss has published over seventy papers in major refereed journals and books and has been granted more than ten patents.