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
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Modèles et méthodes d'optimisation pour le problème de localisation- routage avec contraintes de stockage
William Javier,Guerrero Rueda +1 more
TL;DR: In this article, a methode cooperative approach is proposed to solve the problems of localisation-routage, tournees avec gestion of stocks, and plus court chemin generalise.
Book ChapterDOI
Single Machine Problems
Alessandro Agnetis,Jean-Charles Billaut,Stanisław Gawiejnowicz,Dario Pacciarelli,Ameur Soukhal +4 more
TL;DR: This chapter is devoted to single-machine agent scheduling problems and presents most of the results for the case of two agents (K = 2), for simplicity and because the most ofThe results found so far in the literature apply to this case.
Book ChapterDOI
Scheduling Problems with Variable Job Processing Times
Alessandro Agnetis,Jean-Charles Billaut,Stanisław Gawiejnowicz,Dario Pacciarelli,Ameur Soukhal +4 more
TL;DR: This chapter considers agent scheduling problems in which job processing times are variable, which means that the processing times, contrary to other chapters of the book, are not fixed and may change depending on such parameters as job starting times, job positions in schedule or the amount of resources allocated to jobs.
Journal ArticleDOI
Part selection and tool allocation in discrete parts manufacturing
TL;DR: This work develops a greedy type heuristic and demonstrates via extensive computational experimentation that the greedy heuristic produces near optimal solutions for a variety of problem instances.
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.