Book ChapterDOI
Lagrangian Relaxation for Integer Programming
Arthur M. Geoffrion
- pp 243-281
Reads0
Chats0
TLDR
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
More filters
Journal ArticleDOI
A multicriteria approach to the location of public facilities
G. Terry Ross,Richard M. Soland +1 more
TL;DR: This paper treats multicriteria questions in the framework of a model for selecting a subset of M sites at which to establish public facilities in order to serve client groups located at N distinct points and shows that for some combinations of specific criteria, parametric solutions of a generalized assignment problem (GAP) will yield all efficient solution.
Journal ArticleDOI
Branching in branch-and-price: a generic scheme
TL;DR: This paper presents a generic branching scheme in which the pricing oracle of the root node remains of use after branching and is the first branch-and-price algorithm capable of solving such problems to integrality without modifying the subproblem or expanding its variable space.
Journal ArticleDOI
The time-dependent traveling salesman problem and single machine scheduling problems with sequence dependent setup times
TL;DR: An exact branch-and-bound algorithm able to solve instances of 1|s"i"j|@?C"j and 1-1-1, having up to 50 and 45 jobs respectively is proposed.
Journal ArticleDOI
A comparison of two dual-based procedures for solving the p-median problem
Pierre Hanjoul,Dominique Peeters +1 more
TL;DR: Two dual-based procedures for solving the p -median problem rely upon alternative Lagrangean relaxations of the problem and describe the algorithms and report on the computational experiments.
Journal ArticleDOI
Integer linear programming models for 2-staged two-dimensional Knapsack problems
Andrea Lodi,Michele Monaci +1 more
TL;DR: This work considers the classical variant of TDK in which the maximum number of cuts allowed to obtain each item is fixed to 2, and refers to this problem as 2-staged TDK (2TDK).
References
More filters
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.