Column generation in the integral simplex method

Improvement of Column Generation Method for Railway Crew Scheduling Problems

The railway crew scheduling problem is to determine an optimal crew assignment to minimize the number of crews required to cover all of railway assignment satisfying several crew working constraints. The problem can be formulated as a huge set covering problem. Column generation method is commonly used to solve the railway crew scheduling problem. Conventional column generation method has a sho...

Solving the Master Linear Program in Column Generation Algorithms for Airline Crew Scheduling using a Subgradient Method

A subgradient method for solving large linear programs is implemented and analyzed in a column generation framework. A performance comparison of the implementation is made versus the commercial linear programming solver XPress. Computational results from tests using data from airline crew scheduling, in particular crew rostering, show that the method performs very well in a column generation sc...

Finding the best root node strategy for the approximation of the time-indexed bound in min-sum scheduling

— We identify the best root node strategy for the approximation of the time-indexed bound in min-sum scheduling by sorting through various options that involve the primal simplex, dual simplex, and barrier methods for linear programming, the network simplex method for network ow problems, and DantzigWolfe decomposition and column generation. Note to Practitioners— Min-sum scheduling problems ar...

 Abstract: Packing rectangular shapes into a rectangular space is one of the most important discussions on Cutting & Packing problems (C;P) such as: cutting problem, bin-packing problem and distributor's pallet loading problem, etc. Assume a set of rectangular pieces with specific lengths, widths and utility values. Also assume a rectangular packing space with specific width and length. The obj...

What is the Worst Case Behavior of the Simplex Algorithm?

The examples published by Klee and Minty in 1972 do not preclude the existence of a pivot rule which will make the simplex method, at worst, polynomial. In fact, the continuing success of Dantzig's method suggests that such a rule does exist. A study of known examples shows that (a) those which use selective pivot rules require exponentially large coe cients, and (b) none of the examples' pivot...