Robust Optimization for Airline Scheduling and Vehicle Routing
Robust optimization is an emerging modeling approach to make decisions under uncertainty. It provides an alternative framework to stochastic optimization where operational parameters are random and do not assume any probability distribution. In this thesis, we study three important problems in routing and scheduling under uncertainty, namely, the crew pairing problem, the shortest path problem with resource constraints, and the vehicle routing problem with time windows. We present robust optimization models and propose novel solution approaches, and perform extensive numerical testing to validate the models and solutions. The crew pairing problem finds a set of legal pairings with minimum cost to cover a set of flights. An optimal solution for the deterministic case, however, is often found to be far from optimal or even infeasible when implemented due to the several uncertainties inherent to the airline industry. We present a robust crew pairing formulation where time between flights may vary within an interval. The robust model determines a solution that minimizes crew cost and provides protection against disruptions with a specified level. A column generation approach is presented to solve the robust crew pairing problem. The robust model and the solution approach are tested on a set of instances based on an European airline. The solutions are more robust than the deterministic ones under simulated disruptions. The shortest path problem with resource constraints (SPPRC) is an important problem that appears as a subproblem in many routing and scheduling problems. The second study in the thesis focuses on the robust SPPRC where both cost and resource consumptions are random. The robust SPPRC determines a minimum cost path that is feasible when a number of variations occur for each resource. We present a mixed-integer programming (MIP) model that is equivalent to the robust SPPRC model, and develop graph reduction techniques and two solution methods. The first solution method is a sequential algorithm that solves a series of deterministic SPPRC. The second is a modified label-setting algorithm that uses a new dominance rule. Numerical testing shows that the modified label-setting algorithm outperforms the sequential algorithm and the MIP model. The third problem studied is the vehicle routing problem with time windows under uncertain customer demands. The robust model determines a set of routes with minimum cost such that each customer is served exactly once within the time window and each route is feasible when a number of customers change their demands. We propose a branch-and-price-and-cut algorithm and a novel separation strategy to determine valid inequalities that make use of data uncertainty. The model and solution methodology are tested on instances generated based on the Solomon instances. The robust solutions provide significant protection against random changes in customer demands compared to the deterministic solutions.