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25
Branchandprice: Column generation for solving huge integer programs
 Oper. Res
, 1998
"... We discuss formulations of integer programs with a huge number of variables and their solution by column generation methods, i.e., implicit pricing of nonbasic variables to generate new columns or to prove LP optimality at a node of the branchandbound tree. We present classes of models for which th ..."
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Cited by 348 (13 self)
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We discuss formulations of integer programs with a huge number of variables and their solution by column generation methods, i.e., implicit pricing of nonbasic variables to generate new columns or to prove LP optimality at a node of the branchandbound tree. We present classes of models for which this approach decomposes the problem, provides tighter LP relaxations, and eliminates symmetry. Wethen discuss computational issues and implementation of column generation, branchandbound algorithms, including special branching rules and e cient ways to solve the LP relaxation. We also discuss the relationship with Lagrangian duality. 1
A Parallel Genetic Algorithm for the Set Partitioning Problem
, 1994
"... In this dissertation we report on our efforts to develop a parallel genetic algorithm and apply it to the solution of the set partitioning problema difficult combinatorial optimization problem used by many airlines as a mathematical model for flight crew scheduling. We developed a distributed stea ..."
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Cited by 81 (2 self)
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In this dissertation we report on our efforts to develop a parallel genetic algorithm and apply it to the solution of the set partitioning problema difficult combinatorial optimization problem used by many airlines as a mathematical model for flight crew scheduling. We developed a distributed steadystate genetic algorithm in conjunction with a specialized local search heuristic for solving the set partitioning problem. The genetic algorithm is based on an island model where multiple independent subpopulations each run a steadystate genetic algorithm on their own subpopulation and occasionally fit strings migrate between the subpopulations. Tests on forty realworld set partitioning problems were carried out on up to 128 nodes of an IBM SP1 parallel computer. We found that performance, as measured by the quality of the solution found and the iteration on which it was found, improved as additional subpopulations were added to the computation. With larger numbers of subpopulations the genetic algorithm was regularly able to find the optimal solution to problems having up to a few thousand integer variables. In two cases, highquality integer feasible solutions were found for problems with 36,699 and 43,749 integer variables, respectively. A notable limitation we found was the difficulty solving problems with many constraints.
DRIVE: Dynamic Routing of Independent VEhicles
, 1996
"... We present DRIVE (Dynamic Routing of Independent VEhicles), a planning module to be incorporated in a decision support system for the direct transportation at Van Gend & Loos BV. Van Gend & Loos BV is the largest company providing road transportation in the Benelux with about 1400 vehicles t ..."
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Cited by 73 (2 self)
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We present DRIVE (Dynamic Routing of Independent VEhicles), a planning module to be incorporated in a decision support system for the direct transportation at Van Gend & Loos BV. Van Gend & Loos BV is the largest company providing road transportation in the Benelux with about 1400 vehicles transporting 160,000 packages from thousands of senders to tens of thousands of addressees per day. The heart of DRIVE is a branchandprice algorithm. Approximation and incomplete optimization techniques as well as a sophisticated column management scheme have been employed to create the right balance between solution speed and solution quality. DRIVE has been tested by simulating a dynamic planning environment with reallife data and has produced very encouraging results.
Application of a Hybrid Genetic Algorithm to Airline Crew Scheduling
 Computers & Operations Research
, 1996
"... This paper discusses the development and application of a hybrid genetic algorithm to airline crew scheduling problems. The hybrid algorithm consists of a steadystate genetic algorithm and a local search heuristic. The hybrid algorithm was tested on a set of forty realworld problems. It found the ..."
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Cited by 30 (0 self)
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This paper discusses the development and application of a hybrid genetic algorithm to airline crew scheduling problems. The hybrid algorithm consists of a steadystate genetic algorithm and a local search heuristic. The hybrid algorithm was tested on a set of forty realworld problems. It found the optimal solution for half the problems, and good solutions for nine others. The results were compared to those obtained with branchandcut and branchand bound algorithms. The branchandcut algorithm was significantly more successful than the hybrid algorithm, and the branchandbound algorithm slightly better. 1 Introduction Genetic algorithms (GAs) are search algorithms that were developed by John Holland [17]. They are based on an analogy with natural selection and population genetics. One common application of GAs is for finding approximate solutions to difficult optimization problems. In this paper we describe the application of a hybrid GA (a genetic algorithm combined with a local s...
A stochastic programming approach to the airline crew scheduling problem
 Transportation Science
, 2000
"... Traditional methods model the billiondollar airline crew scheduling problem as deterministic and do not explicitly include information on potential disruptions. Instead of modelling the crew scheduling problem as deterministic, we consider a stochastic crew scheduling model and devise a solution me ..."
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Cited by 25 (0 self)
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Traditional methods model the billiondollar airline crew scheduling problem as deterministic and do not explicitly include information on potential disruptions. Instead of modelling the crew scheduling problem as deterministic, we consider a stochastic crew scheduling model and devise a solution methodology for integrating disruptions in the evaluation of crew schedules. The goal is to use that information to find robust solutions that better withstand disruptions. Such an approach is important because we can proactively consider the effects of certain scheduling decisions. By identifying more robust schedules, cascading delay effects will be minimized. In this paper we describe our stochastic integer programming model for the airline crew scheduling problem and develop a branching algorithm to identify expensive flight connections and find alternative solutions. The branching algorithm uses the structure of the problem to branch simultaneously on multiple variables without invalidating the optimality of the algorithm. We present computational results demonstrating the effectiveness of our branching algorithm. 1
Crew Pairing Optimization
 OR IN AIRLINE INDUSTRY, GANG YU (ED.)
"... Next to fuel costs, crew costs are the largest direct operating cost of airlines. Therefore much research has been devoted to the planning and scheduling of crews over the last thirty years. The planning and scheduling of crews is usually considered as two problems: the crew pairing problem and the ..."
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Cited by 17 (2 self)
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Next to fuel costs, crew costs are the largest direct operating cost of airlines. Therefore much research has been devoted to the planning and scheduling of crews over the last thirty years. The planning and scheduling of crews is usually considered as two problems: the crew pairing problem and the crew assignment (rostering) problem. These problems are solved sequentially. In this paper we focus on the pairing problem. The aim of the paper is twofold. First, we give an overview of the crew pairing problem and synthesize the optimization methods that have been published previously. Second, we present the Carmen pairing construction system which is in operation at most major European airlines. Our purpose is to identify the particular properties of the Carmen system that have made this system the preferred decision support system for crew pairing optimization in Europe.
Column generation and the airline crew pairing problem
 Documenta Mathematica, Extra Volume ICM
, 1998
"... ..."
Integrated Airline Fleet and Crew Robust Planning
"... The airline fleet assignment problem involves assigning aircrafts to flights to maximize profit. Different fleet assignment solutions cause dramatically different performance in subsequent crew planning and operational processes. We have developed an integrated fleet and crew robust planning method ..."
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Cited by 5 (0 self)
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The airline fleet assignment problem involves assigning aircrafts to flights to maximize profit. Different fleet assignment solutions cause dramatically different performance in subsequent crew planning and operational processes. We have developed an integrated fleet and crew robust planning method to provide fleet assignment solutions that are both friendly to crew planning and robust to real time operations. The three challenges of this work are 1) to understand the influence of fleet assignment on crew scheduling; 2) to address crew scheduling in a tractable way in the integrated model; and 3) to achieve robustness. We address these challenges by developing a new approach that integrates crew connections within the fleet assignment model and imposes station purity by limiting the number of fleet types and crew bases allowed to serve each airport. Computational results demonstrate that the proposed approach can reduce crew planning cost, improve robustness, and solve industrial size problems with good computational efficiency. 1 1
A Parallel, Linear Programming Based Heuristic for Large Scale Set Partitioning Problems
, 2000
"... We describe a parallel, linear programming and implication based heuristic for solving set partitioning problems on distributed memory computer architectures. Our implementation is carefully designed to exploit parallelism to greatest advantage in advanced techniques like preprocessing and probing, ..."
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Cited by 2 (0 self)
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We describe a parallel, linear programming and implication based heuristic for solving set partitioning problems on distributed memory computer architectures. Our implementation is carefully designed to exploit parallelism to greatest advantage in advanced techniques like preprocessing and probing, primal heuristics, and cut generation. A primaldual subproblem simplex method is used for solving the linear programming relaxation, which breaks the linear programming solution process into natural phases from which we can exploit information to nd good solutions on the various processors. Implications from the probing operation are shared among the processors. Combining these techniques allows us to obtain solutions to large and difficult problems in a reasonable amount of computing time.