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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Journal ArticleDOI
A relax‐and‐price heuristic for the inventory‐location‐routing problem
William J. Guerrero,William J. Guerrero,William J. Guerrero,Caroline Prodhon,Nubia Velasco,Nubia Velasco,Ciro Alberto Amaya +6 more
TL;DR: Results demonstrate the capability of the algorithm to compute high quality solutions and empirically estimate the improvement in the cost function of the proposed model at up to 9% compared to the sequential approach.
Journal ArticleDOI
Iterative semi-continuous relaxation heuristics for the multiple-choice multidimensional knapsack problem
TL;DR: New iterative relaxation-based heuristics for the 0-1 Mixed Integer Programming problem (0-1 MIP), which generate a sequence of lower and upper bounds, and several variants of the new iterative semi-continuous relaxation based heuristic can be designed by a given update procedure of multiplier of SCR.
Seasonal Production and Sales Planning with Limited Shared Tooling at the Key Operation.
TL;DR: In this paper, Lagrangian relaxation is applied to a class of very large mixed integer linear programming problems representing seasonal production and sales planning in a situation where limited tooling is available at the key production operation.
Journal ArticleDOI
On the coordination of product and by-product flows in two-level distribution networks: Model formulations and solution procedures
TL;DR: In this article, the problem of coordinating product and byproduct flows in a two-level distribution network is studied, where a single product is produced at multiple plants in order to fulfill customer demands, and a byproduct is produced, that must be transported to, and processed at a postprocessing unit.
Journal ArticleDOI
The Capacitated Vehicle Routing Problem: Stronger bounds in pseudo-polynomial time
TL;DR: This work considers several old and new relaxations of this kind, all of which are based on column generation, and analyzes the effect of adding some known inequalities.
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.