Optimal solution of set covering/partitioning problems using dual heuristics
Management Science
A multiplier adjustment approach for the set partitioning problem
Operations Research - Supplement
Solving airline crew scheduling problems by branch-and-cut
Management Science
Computers and Operations Research
On some difficult linear programs coming from set partitioning
Discrete Applied Mathematics - Special issue: Third ALIO-EURO meeting on applied combinatorial optimization
Constraint Handling in Genetic Algorithms: The Set Partitioning Problem
Journal of Heuristics
A concurrent processing framework for the set partitioning problem
Computers and Operations Research
Branch-And-Price: Column Generation for Solving Huge Integer Programs
Operations Research
2-Path Cuts for the Vehicle Routing Problem with Time Windows
Transportation Science
A Set Partitioning Approach to the Crew Scheduling Problem
Operations Research
A Parallel, Linear Programming-based Heuristic for Large-Scale Set Partitioning Problems
INFORMS Journal on Computing
Performance of Various Computers Using Standard Linear Equations Software
Performance of Various Computers Using Standard Linear Equations Software
A Practical Algorithm for Computing a Subadditive Dual Function for Set Partitioning
Computational Optimization and Applications
Computational results with a primal-dual subproblem simplex method
Operations Research Letters
A parallel primal-dual simplex algorithm
Operations Research Letters
A least-squares primal-dual algorithm for solving linear programming problems
Operations Research Letters
Optimization of occupancy rate in dial-a-ride problems via linear fractional column generation
Computers and Operations Research
An Exact Algorithm for the Pickup and Delivery Problem with Time Windows
Operations Research
New Route Relaxation and Pricing Strategies for the Vehicle Routing Problem
Operations Research
Hi-index | 0.00 |
The set partitioning problem is a fundamental model for many important real-life transportation problems, including airline crew and bus driver scheduling and vehicle routing. In this paper we propose a new dual ascent heuristic and an exact method for the set partitioning problem. The dual ascent heuristic finds an effective dual solution of the linear relaxation of the set partitioning problem and it is faster than traditional simplex based methods. Moreover, we show that the lower bound achieved dominates the one achieved by the classic Lagrangean relaxation of the set partitioning constraints. We describe a simple exact method that uses the dual solution to define a sequence of reduced set partitioning problems that are solved by a general purpose integer programming solver. Our computational results indicate that the new bounding procedure is fast and produces very good dual solutions. Moreover, the exact method proposed is easy to implement and it is competitive with the best branch and cut algorithms published in the literature so far.