A Column Generation Approach for Large-Scale Aircrew Rostering Problems

Abstract

This article describes a method for solving the crew rostering problem in air transportation. This problem consists of constructing personalized schedules that assign pairings, days off, and other activities to airline crew members. A generalized set partitioning model and a method using column generation have been used. This method has been adapted in a number of ways to take advantage of the nature of the problem and to accelerate solution. Numerical tests on problems from Air France have demonstrated that this method is capable of solving very large scale problems with thousands of constraints and hundreds of subproblems. The tests have also shown that these adaptations are capable of reducing solution time by a factor of about a thousand. Finally, results from this method are compared with those obtained with the method currently used at Air France.

Selected Topics in Column Generation

“…Column generation is a pricing scheme for large scale linear programs. In Gamache et al (1999) up to 300 N P-hard subproblems arise, and partial column generation is used. That is, only a subset of subproblems is chosen at each iteration to generate new columns.…”

A heuristic procedure to solve the project staffing problem with discrete time/resource trade-offs and personnel scheduling constraints

“…The objective is to minimise the number of employees required to perform all daily assignments in the horizon. Several authors have solved personnel scheduling problems using column generation and closely connected branchand-price approaches (Gamache et al, 1999;Mehrotra et al, 2000;Caprara et al, 2003;Beliën and Demeulemeester, 2006;Maenhout and Vanhoucke, 2010).…”

Uma proposta de solução para o problema da construção de escalas de motoristas e cobradores de ônibus por meio do algoritmo do matching de peso máximo

“…Uma aplicação da Pesquisa Operacional na construção de escalas para tripulação aérea pode ser encontrada em Gamache et al (1999). Os autores propõem a resolução deste problema em duas fases.…”