Search

The crew-pairing problem (CPP) is solved in the first step of the crew-scheduling process. It consists of creating a set of pairings (sequence of flights, connections, and rests forming one or multiple days of work for an anonymous crew member) that covers a given set of flights at minimum cost. Those pairings are assigned to crew members in a subsequent crew-rostering step. In this paper, we propose a new integral column-generation algorithm for the CPP, called improved integral column generation with prediction ([Formula: see text]), which leaps from one integer solution to another until a near-optimal solution is found. Our algorithm improves on previous integral column-generation algorithms by introducing a set of reduced subproblems. Those subproblems only contain flight connections that have a high probability of being selected in a near-optimal solution and are, therefore, solved faster. We predict flight-connection probabilities using a deep neural network trained in a supervised framework. We test [Formula: see text] on several real-life instances and show that it outperforms a state-of-the-art integral column-generation algorithm as well as a branch-and-price heuristic commonly used in commercial airline planning software, in terms of both solution costs and computing times. We highlight the contributions of the neural network to [Formula: see text].

In this paper, we study a warehouse-retailer network design (WRND) model that simultaneously makes the location, distribution, and warehouse-retailer echelon inventory replenishment decisions. Although a column generation algorithm was proposed recently in the literature, it remains a challenge to solve large size instances of this NP-hard problem efficiently and effectively. The purpose of this paper is to present a greedy algorithm. Computational results demonstrate that our greedy algorithm can solve large-scale WRND problems efficiently with errors within 3%–4% on average.

In a previous paper, Appelgren (Appelgren, L. 1969. A column generation algorithm for a ship scheduling problem. Trans. Sci. 3 53–68.), a decomposition algorithm for a class of vessel scheduling problems was presented. In some problems, the algorithm gives fractional solutions that cannot be interpreted as feasible schedules. This paper treats two integer programming methods that can be used to resolve these cases. The cutting plane method that was first tested was abandoned because it was not able to solve all the test problems. The second method is a branch-and-bound algorithm, where the branching is performed on one of the “essential” fractional variables and where the bounds are obtained by the decomposition algorithm. All fractional problems that have been found by simulation or in regular use of the algorithm have been solved, mostly with one branching only. There are fundamental difficulties in combining these integer programming methods with the Dantzig-Wolfe decomposition, since the constraints generated in the master program have to be taken into account in the solution of the subprograms. The success in this case is due to the simple structure of the master LP problem.

A column generation algorithm for solving a class of nonlinear traffic assignment problems is presented. The fundamental advantage of the algorithm is that it does not require the a priori generation of all paths joining each origin-destination pair. The algorithm is capable of handling rather large networks. Computational experience that contrasts column generation with the a priori generation of all paths and compares two different quadratic programming algorithms is reported.