Neur2RO: Neural Two-Stage Robust Optimization

Robust optimization provides a mathematical framework for modeling and solving decision-making problems under worst-case uncertainty. This work addresses two-stage robust optimization (2RO) problems (also called adjustable robust optimization), wherein first-stage and second-stage decisions are made before and after uncertainty is realized, respectively. This results in a nested min-max-min optimization problem which is extremely challenging computationally, especially when the decisions are discrete. We propose Neur2RO, an efficient machine learning-driven instantiation of column-and-constraint generation (CCG), a classical iterative algorithm for 2RO. Specifically, we learn to estimate the value function of the second-stage problem via a novel neural network architecture that is easy to optimize over by design. Embedding our neural network into CCG yields high-quality solutions quickly as evidenced by experiments on two 2RO benchmarks, knapsack and capital budgeting. For knapsack, Neur2RO finds solutions that are within roughly $2\%$ of the best-known values in a few seconds compared to the three hours of the state-of-the-art exact branch-and-price algorithm; for larger and more complex instances, Neur2RO finds even better solutions. For capital budgeting, Neur2RO outperforms three variants of the $k$-adaptability algorithm, particularly on the largest instances, with a 5 to 10-fold reduction in solution time. Our code and data are available at https://github.com/khalil-research/Neur2RO

Machine Learning for Booking Control

RÉSUMÉ: La gestion des revenus est une approche analytique que les entreprises utilisent pour maximiser leurs profits. Cette thèse se concentre sur le problème du contrôle de l’acceptation et de rejet de réservations : Étant donné une capacité limitée, accepter une demande de réservation ou la rejeter afin de réserver de la capacité pour de futures réservations avec des revenus potentiellement plus élevés. Ce problème peut être formulé comme un programme dynamique stochastique à horizon fini, où l’acceptation d’une demande entraîne un profit et, à la fin de la période de réservation, le coût d’exécution des réservations acceptées est encouru. Le coût de l’exécution des demandes est appelé le problème de la prise de décision opérationnelle et, dans de nombreuses applications, il nécessite la résolution de problèmes non triviaux de programmation en nombres entiers mixtes. Ce travail propose d’entraîner un modèle prédictif pour approximer la valeur de la solution du problème de prise de décision opératioNnelle par l’apprentissage supervisé. Les prédictions peuvent ensuite être exploitées par de la programmation dynamique approximative générale et de l’apprentissage par renforcement pour résoudre le problème du contrôle des réservations. Cette méthodologie est ensuite évaluée sur deux problèmes de contrôle de réservation issus de la littérature. Le premier problème est un problème de logistique de distribution, pour lequel cette méthodologie produit des politiques qui permettent d’obtenir des bénéfices significativement plus élevés avec un temps de calcul réduit par rapport aux solutions de base. La deuxième application est une application de fret aérien, où la performance de cette approche se situe juste en dessous de l’état de l’art. Bien que les résultats obtenus dans cette thèse ne soient pas complètement compétitifs par rapport à l’état de l’art, plusieurs directions pour les travaux futurs existent qui pourraient, nous l’espérons, conduire à une amélioration supplémentaire. En outre, la méthodologie présentée dans cette thèse est générale, c’est-à-dire qu’elle peut facilement être étendue à de nombreux problèmes à horizon fini et, pour cette raison, elle apporte une contribution notable au contrôle des réservations.----------ABSTRACT : Revenue management is an analytic approach which companies utilize to maximize profit. This thesis focuses on the problem of controlling booking accept/reject decisions: Given a limited capacity, accept a booking request or reject it to reserve capacity for future bookings with potentially higher revenue. This problem can be formulated as a finite-horizon stochastic dynamic program, where accepting a request results in a profit and at the end of the booking period the cost of fulfilling the accepted bookings is incurred. The cost of fulfilling requests is referred to as the operational decision-making problem, and in many applications requires the solution of non-trivial mixed-integer programming problems. This work proposes to train a predictor to approximate the solution value of the operational decision-making problem through supervised learning. The predictions can then be leveraged within general-purpose approximate dynamic programming and reinforcement learning to solve the booking control problem. This methodology is then evaluated on two booking control problems from the literature. The first problem is a distributional logistics problem, where this methodology produces policies that result in significantly higher profit at a reduced computing time when compared to baselines. The second application is an airline cargo application, where this approach falls just short of state-of-the-art baselines. Although the results achieved in this thesis are not competitive with the state-of-the-art, there are several directions for future work that can hopefully lead to further improvement. Furthermore, the methodology presented in this thesis is general, i.e., can easily be extended to many end-of-horizon problems and for this reason, it provides a valuable contribution to booking control

Can Machine Learning Help in Solving Cargo Capacity Management Booking Control Problems?

Revenue management is important for carriers (e.g., airlines and railroads). In this paper, we focus on cargo capacity management which has received less attention in the literature than its passenger counterpart. More precisely, we focus on the problem of controlling booking accept/reject decisions: Given a limited capacity, accept a booking request or reject it to reserve capacity for future bookings with potentially higher revenue. We formulate the problem as a finite-horizon stochastic dynamic program. The cost of fulfilling the accepted bookings, incurred at the end of the horizon, depends on the packing and routing of the cargo. This is a computationally challenging aspect as the latter are solutions to an operational decision-making problem, in our application a vehicle routing problem (VRP). Seeking a balance between online and offline computation, we propose to train a predictor of the solution costs to the VRPs using supervised learning. In turn, we use the predictions online in approximate dynamic programming and reinforcement learning algorithms to solve the booking control problem. We compare the results to an existing approach in the literature and show that we are able to obtain control policies that provide increased profit at a reduced evaluation time. This is achieved thanks to accurate approximation of the operational costs and negligible computing time in comparison to solving the VRPs