Benders Decomposition for Simultaneous Aircraft Routing and Crew Scheduling

Abstract

G iven a set of flight legs to be flown by a single type of aircraft, the simultaneous aircraft routing and crew scheduling problem consists of determining a minimum-cost set of aircraft routes and crew pairings such that each flight leg is covered by one aircraft and one crew, and side constraints are satisfied. While some side constraints such as maximum flight time and maintenance requirements involve only crews or aircraft, linking constraints impose minimum connection times for crews that depend on aircraft connections. To handle these linking constraints, a solution approach based on Benders decomposition is proposed. The solution process iterates between a master problem that solves the aircraft routing problem, and a subproblem that solves the crew pairing problem. Because of their particular structure, both of these problems are solved by column generation. A heuristic branch-and-bound method is used to compute integer solutions. On a set of test instances based on data provided by an airline, the integrated approach produced significant cost savings in comparison with the sequential planning process commonly used in practice. The largest instance solved contains more than 500 flight legs over a 3-day period.

The robust shortest path problem with interval data via Benders decomposition

“…Geoffrion and Graves (1974) confirmed that the method is suitable to solve large scale multicommodity distribution system design models. Many other applications of Benders decomposition have been proposed since then (see, for example, Richardson 1976;Magnanti et al 1986;Cordeau et al 2000;Cordeau et al 2001). Methodologies for improving the performance of the method have been proposed in McDaniel and Devine (1977) and Magnanti and Wong (1981).…”

Modeling and Solving Vehicle Routing Problems with Many Available Vehicle Types

“…For routing and scheduling problems arising in areas such as airline planning, Benders' decomposition together with column generation has successfully been applied by Cordeau et al in [6] to simultaneously consider both the aircraft routing problem and the crew pairing problem something that traditionally have been done sequentially due to the large complexity of the problem. Their implementation rst uses a linear programming (LP) relaxation of both Benders master problem and Benders subproblem, and later reintroduces the integer requirements and performs a heuristic branching on the integer variables.…”

“…The altered image in Figure 1 is thus available under the same license. 6 to more satis ed customers. This type of optimization tool can also help Volvo to better understand their customers' needs, which may then in uence strategic vehicle development decisions and make Volvo even more competitive on the tough global vehicle market.…”

“…Benders' decomposition algorithm, which can solve integer programs to optimality, is presented in Section 2.3. To the best of our knowledge, Benders' decomposition has not previously been applied to the hVRP; it has, however, been applied to other related problems, such as the simultaneous aircraft routing and crew scheduling problem ( [6]) and network optimization problems (see [7]). …”

“…This is formalized in Claim 1, the proof of which is essentially the same proof as that of [13,Claim 1]. Claim 1 is the basis for the criteria for 6 The notation`…”