Journal Article10.1016/S0167-6377(00)00017-1
A parallel primal-dual simplex algorithm
TL;DR: This work presents a parallel primal-dual simplex algorithm that is capable of solving linear programs with at least an order of magnitude more columns than the previous work and repeatedly solves several linear programs in parallel to obtain a new dual feasible solution.
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About: This article is published in Operations Research Letters. The article was published on 01 Sep 2000. The article focuses on the topics: Simplex algorithm & Big M method.
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Citations
Airline crew scheduling : State-of-the-art
TL;DR: This paper surveys different approaches studied and discusses the state-of-the-art in solution methodology for the airline crew scheduling problem.
Airline Crew Scheduling Under Uncertainty
TL;DR: This work provides a lower bound on the cost of an optimal crew schedule in operations, and it is demonstrated that some of the crew schedules found using the method perform very well relative to this lower bound.
186
Robust Airline Fleet Assignment: Imposing Station Purity Using Station Decomposition
Barry C. Smith,Ellis L. Johnson +1 more
TL;DR: It is demonstrated that imposing station purity on the FAM can limit aircraft dispersion in the network and make solutions more robust relative to crew planning, maintenance planning, and operations, and a solution approach, station decomposition, which takes advantage of airline network structure is developed.
121
A Parallel Implementation of the Simplex Function Minimization Routine
Donghoon Lee,Matthew Wiswall +1 more
TL;DR: The parallel simplex algorithm is generic and can be applied, without re-writing computer code, to any optimization problem which the non-parallel Nelder–Mead is applicable, and is also easily scalable to any degree of parallelization up to the number of parameters.
85
Lead time considerations for the multi-level capacitated lot-sizing problem
TL;DR: Two models are presented; one considering batch production and the other one allowing lot-streaming, which demonstrate the capability of the new approach in delivering more realistic results.
54
References
Branch-And-Price: Column Generation for Solving Huge Integer Programs
Cynthia Barnhart,Ellis L. Johnson,George L. Nemhauser,Martin W. P. Savelsbergh,Pamela H. Vance +4 more
TL;DR: In this paper, column generation methods for integer programs with a huge number of variables are discussed, including implicit pricing of nonbasic variables to generate new columns or to prove LP optimality at a node of the branch-and-bound tree.
Practical parallel algorithms for dynamic data redistribution, median finding, and selection
David A. Bader,Joseph JaJa +1 more
- 15 Apr 1996
TL;DR: This paper presents a fast and portable parallel algorithm for finding the median given a set of elements distributed across a parallel machine that solves the general selection problem that requires the determination of the element of rank i, for an arbitrarily given integer i.
Parallelizing the Dual Simplex Method
Robert E. Bixby,Alex Martin +1 more
TL;DR: This work studies the parallelization of the steepest-edge version of the dual simplex algorithm, each of which is derived from the CPLEX dualsimplex implementation, and tests three different parallel implementations.
•Dissertation
Topics in airline crew scheduling and large scale optimization
Diego Klabjan
- 01 Aug 1999
11