<P>Graph theory is very much tied to the geometric properties of optimization and combinatorial optimization. Moreover, graph theory's geometric properties are at the core of many research interests in operations research and applied mathematics. Its techniques have been used in solving many classic
Column Generation (Gerad 25th Anniversary Series, Volume 5)
β Scribed by Guy Desaulniers, Jacques Desrosiers, Marius M. Solomon
- Publisher
- Springer
- Year
- 2005
- Tongue
- English
- Leaves
- 369
- Series
- Gerad 25th Anniversary 5
- Edition
- 1
- Category
- Library
No coin nor oath required. For personal study only.
β¦ Synopsis
Column Generation is an insightful overview of the state of the art in integer programming column generation and its many applications. The volume begins with "A Primer in Column Generation" which outlines the theory and ideas necessary to solve large-scale practical problems, illustrated with a variety of examples. Other chapters follow this introduction on "Shortest Path Problems with Resource Constraints," "Vehicle Routing Problem with Time Window," "Branch-and-Price Heuristics," "Cutting Stock Problems," each dealing with methodological aspects of the field. Three chapters deal with transportation applications: "Large-scale Models in the Airline Industry," "Robust Inventory Ship Routing by Column Generation," and "Ship Scheduling with Recurring Visits and Visit Separation Requirements." Production is the focus of another three chapters: "Combining Column Generation and Lagrangian Relaxation," "Dantzig-Wolfe Decomposition for Job Shop Scheduling," and "Applying Column Generation to Machine Scheduling." The final chapter by Fran?ois Vanderbeck, "Implementing Mixed Integer Column Generation," reviews how to set-up the Dantzig-Wolfe reformulation, adapt standard MIP techniques to the column generation context (branching, preprocessing, primal heuristics), and deal with specific column generation issues (initialization, stabilization, column management strategies).
β¦ Table of Contents
Contents......Page 10
Foreword......Page 6
Avant-propos......Page 8
Contributing Authors......Page 12
Preface......Page 14
1: A Primer in Column Generation......Page 17
2: Shortest Path Problems with Resource Constraints......Page 49
3: Vehicle Routing Problem with Time Windows......Page 82
4: Branch-and-Price Heuristics: A Case Study on the Vehicle Routing Problem with Time Windows......Page 114
5: Cutting Stock Problems......Page 145
6: Large-scale Models in the Airline Industry......Page 176
7: Robust Inventory Ship Routing by Column Generation......Page 209
8: Ship Scheduling With Recurring Visits And Visit Separation Requirements......Page 237
9: Combining Column Generation and Lagrangian Relaxation......Page 258
10: Dantzig-Wolfe Decomposition for Job Shop Scheduling......Page 282
11: Applying column generation to machine scheduling......Page 314
12: Implementing Mixed Integer Column Generation......Page 342
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