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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Lotsizing and scheduling in the glass container industry
TL;DR: In this paper, the glass container industry production planning and scheduling problem is studied in depth, and the system is decomposed into a two-level hierarchically organized planning structure: long-term and short-term levels.
Dissertation
Protein Structure Comparison: From Contact Map Overlap Maximisation to Distance-based Alignment Search Tool
TL;DR: This thesis focuses on the similarity measure called Contact Map Overlap maximisation (CMO), which provides scores which can be used for obtaining good automatic classifications of the protein structures and proposes a hierarchical approach for CMO which is based on the secondary structure of the proteins.
Journal ArticleDOI
A generalized assignment model for dynamic supply chain capacity planning
Joseph B. Mazzola,Alan W. Neebe +1 more
TL;DR: The resulting model, MultiGAP, addresses the assignment of tasks to agents within each time period, with the attendant single-period assignment costs and agent-capacity constraint requirements, in conjunction with transition costs arising between any two consecutive periods in which a task is reassigned to a different agent.
Journal ArticleDOI
Optimizing the Strategic Decisions for One-Way Station-Based Carsharing Systems: A Mean-CVaR Approach
TL;DR: In this paper, a two-stage risk-averse stochastic model is proposed to maximize the mean return and minimize the risk, where the conditional value-at-risk (CVaR) is specified as the risk measure.
Proceedings Article
On Approximate Non-submodular Minimization via Tree-Structured Supermodularity
TL;DR: This work addresses the problem of minimizing nonsubmodular functions where the supermodularity is restricted to tree-structured pairwise terms, and develops several practical algorithms to provide approximate and near-optimal solutions.
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.