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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Book ChapterDOI
SDP Relaxations in Combinatorial Optimization from a Lagrangian Viewpoint
TL;DR: This work synthesizes various operations of SDP relaxation, an operation pioneered by N.Z. Shor, in a language close to that of nonlinear programming, and shows how the approach can be applied to general combinatorial problems.
Journal ArticleDOI
Single machine scheduling with symmetric earliness and tardiness penalties
TL;DR: This research focuses on scheduling jobs with varying processing times and distinct due dates on a single machine subject to earliness and tardiness penalties, and finds application in a just-in-time (JIT) production environment.
Journal ArticleDOI
An integrated approach to dynamic plant location and capacity planning
S.-K. Lim,Yeong-Dae Kim +1 more
TL;DR: The dynamic capacitated plant location problem is formulated as a mixed integer linear program and solved by a heuristic algorithm based on Lagrangian relaxation and a cut and branch algorithm which uses Gomory cuts.
Posted Content
Reliable design of an integrated supply chain with expedited shipments under disruption risks
TL;DR: In this article, a mathematical model for the design of a two-echelon supply chain where suppliers serve a set of terminal facilities that receive uncertain customer demands is proposed, and a customized solution algorithm based on the Lagrangian relaxation is developed to efficiently solve this model.
Journal ArticleDOI
Formulation and solution of a selection and sequencing problem in car manufacture
TL;DR: In this article, two problems that arise in production planning in car manufacture are addressed: (1) selecting a subset of cars from the order bank for manufacture in the next planning period such that a required number of cars belonging to each model/market group is chosen without violating resource constraints; (2) sequencing a set of cars on an assembly line such that the line is not slowed down by subsequences that overload its capacity to cope with certain features.
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.