Book ChapterDOI
Lagrangian Relaxation for Integer Programming
Arthur M. Geoffrion
- pp 243-281
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It is a pleasure to write this commentary because it offers an opportunity to express my gratitude to several people who helped me in ways that turned out to be essential to the birth of [8].Abstract:
It is a pleasure to write this commentary because it offers an opportunity to express my gratitude to several people who helped me in ways that turned out to be essential to the birth of [8]. They also had a good deal to do with shaping my early career and, consequently, much of what followed.read more
Citations
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The collision avoidance problem: Methods and algorithms
Martín Campo,Francisco Javier +1 more
TL;DR: Tesis Doctoral leida en la Universidad Rey Juan Carlos en noviembre de 2010. Directores de la Tesis: Laureano F. Escudero y Antonio Alonso Ayuso as mentioned in this paper
Journal ArticleDOI
Scheduling web banner advertisements with multiple display frequencies
Ali Amiri,Syam Menon +1 more
TL;DR: The Lagrangian decomposition-based solution approaches presented in this paper are observed to provide good schedules in a reasonable period of time and could result in a considerable increase in profits.
Book ChapterDOI
An Approach to Vehicle Scheduling with Depot Capacity Constraints
TL;DR: Multiple-depot vehicle scheduling in public transport can be formulated as an integral multicommodity flow problem in a time-space network using a Lagrangean relaxation and subgradient optimization and an improved lower bound is determined.
Journal ArticleDOI
An Indirect Method for the Generalized k-Median Problem Applied to Lock-Box Location
TL;DR: An indirect method is given, using an algorithm for the uncapacitated problem to solve the k-median problem, which seems to be roughly as efficient as the underlying uncAPacitated algorithm.
Journal ArticleDOI
An integrated modeling framework for design of logistics networks with expedited shipment services
TL;DR: A customized solution approach based on Lagrangian relaxation is developed that can solve integrated logistics network problem efficiently and accurately and minimizes the expected total system cost.
References
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Journal ArticleDOI
The Traveling-Salesman Problem and Minimum Spanning Trees
Michael Held,Richard M. Karp +1 more
TL;DR: It is shown that maxπwπ = C* precisely when a certain well-known linear program has an optimal solution in integers.
Journal ArticleDOI
Validation of subgradient optimization
TL;DR: It is concluded that the “relaxation” procedure for approximately solving a large linear programming problem related to the traveling-salesman problem shows promise for large-scale linear programming.
Journal ArticleDOI
Generalized Lagrange Multiplier Method for Solving Problems of Optimum Allocation of Resources
TL;DR: The use of Lagrange multipliers for optimization in the presence of constraints is not limited to differentiable functions but can be applied to problems of maximizing an arbitrary real valued objective function over any set whatever, subject to bounds on the values of any other finite collection of real valued functions denned on the same set as mentioned in this paper.
Book ChapterDOI
Multicommodity Distribution System Design by Benders Decomposition
Arthur M. Geoffrion,G. W. Graves +1 more
TL;DR: In this paper, a multicommodity capacitated single-period version of the problem is formulated as a mixed integer linear program, and a solution technique based on Benders Decomposition is developed, implemented, and successfully applied to a real problem for a major food firm with 17 commodity classes, 14 plants, 45 possible distribution center sites, and 121 customer zones.
Journal ArticleDOI
The traveling-salesman problem and minimum spanning trees: Part II
Michael Held,Richard M. Karp +1 more
TL;DR: An efficient iterative method for approximating this bound closely from below is presented, and a branch-and-bound procedure based upon these considerations has easily produced proven optimum solutions to all traveling-salesman problems presented to it.