Pricing by local search in column generation for the airline crew pairing problem

The airline crew pairing problem (ACP) is finding the least costly set of crew pairings so that each flight given in the flight schedule is covered. The ACP is traditionally modeled either as a set partitioning problem or a set covering problem. Due to the large number of possible pairings (columns), these models are usually solved by the column generation (CG) method. For the ACP, the pricing subproblem of the CG corresponds to a multi-label shortest path problem (MLSP) typically solved over a flight network. The MLSP over the flight network is NP-hard and it suffers from an exponential complexity even for moderate size flight networks. In order to overcome the complexity of the pricing subproblem, we propose a column generation method to solve the ACP, in which a hybrid pricing procedure is used. In this hybrid procedure, the pricing subproblem consists of three steps. First, we apply a local search mechanism on the partial duty period pool to construct pairings with negative reduced cost. In cases local search mechanism cannot find such a pairing, we execute a heuristic MLSP algorithm over the partial duty network to price out negative reduced cost pairings for the restricted master problem (RMP). If this method also fails, we solve the MLSP over the flight network. By adopting this hybrid approach, we aim to decrease the number of CG iterations where the MLSP is executed over the flight network, and reduce the computation time per iteration as well as the total computation time. We test the efficiency of our approach on real-life instances acquired from a local airline company, and present numerical results

Pricing in column generation for a robust airline crew pairing problem

The crew pairing problem is to find the least costly set of pairings so that each flight given in the flight schedule is covered. In this study, the robust crew pairing problem is considered. That is, the selected pairings cover the regular flights and also provide solutions to cover some extra flights which may be introduced into the flight schedule during the operation at a later point in time. The crew pairing problem is usually solved by column generation in which the pricing subproblem becomes a multi-label shortest path problem. For the robust crew pairing problem the multi-label shortest path problem requires some modifications to solve two column generation approaches proposed by Çoban [10]. These modifications of the pricing problem with associated labels and the domination rules are presented. The complexity of the multi-label shortest path problem grows exponentially as the number of flights (nodes) in the flight schedule increases. This curse of dimensionality is solved by using approximate and exact pruning rules. Also, a buffer column pool is formed as an intermediate step in order to find a negative reduced cost pairing without solving the multi-label shortest path problem at every iteration of the column generation algorithm. In the multi-label shortest path problem, the approximate rules based on the score-calculation are used for early pruning of the paths on the processed nodes. The optimal solution may be missed because of the coarse structure of the approximate rules. When a pairing that improves the objective function cannot be found by applying the approximate rules, we switch to the exact pruning. Another method is using a hybrid approach that applies both approximate and exact rules in the same iteration to find the optimal solution. The performance of our solution approach is demonstrated through a computational study by using actual data from a local airline

Algorithmes de résolution du problème de plus court chemin avec contraintes de ressources

Méthode exactes -- Méthodes heuristiques -- Le modèle unifié -- Méthode de résolution -- Applications -- Le problème de plus court chemin avec contraintes de ressource : espace des états -- Projection de l'espace des étiquettes -- Comparaison des différents algorithmes de résolution -- Algorithme d'amélioration dynamique de la borne supérieure -- Méthodes d'accélération -- Généralisation de l'algorithme ADBS