Re-Solving Stochastic Programming Models for Airline Revenue Management

We study some mathematical programming formulations for the origin-destination model in airline revenue management. In particular, we focus on the traditional probabilistic model proposed in the literature. The approach we study consists of solving a sequence of two-stage stochastic programs with simple recourse, which can be viewed as an approximation to a multi-stage stochastic programming formulation to the seat allocation problem. Our theoretical results show that the proposed approximation is robust, in the sense that solving more successive two-stage programs can never worsen the expected revenue obtained with the corresponding allocation policy. Although intuitive, such a property is known not to hold for the traditional deterministic linear programming model found in the literature. We also show that this property does not hold for some bid-price policies. In addition, we propose a heuristic method to choose the re-solving points, rather than re-solving at equally spaced times as customary. Numerical results are presented to illustrate the effectiveness of the proposed approach

Risk Minimization, Regret Minimization and Progressive Hedging Algorithms

This paper begins with a study on the dual representations of risk and regret measures and their impact on modeling multistage decision making under uncertainty. A relationship between risk envelopes and regret envelopes is established by using the Lagrangian duality theory. Such a relationship opens a door to a decomposition scheme, called progressive hedging, for solving multistage risk minimization and regret minimization problems. In particular, the classical progressive hedging algorithm is modified in order to handle a new class of linkage constraints that arises from reformulations and other applications of risk and regret minimization problems. Numerical results are provided to show the efficiency of the progressive hedging algorithms.Comment: 21 pages, 2 figure

Adaptive Two-stage Stochastic Programming with an Application to Capacity Expansion Planning

Multi-stage stochastic programming is a well-established framework for sequential decision making under uncertainty by seeking policies that are fully adapted to the uncertainty. Often such flexible policies are not desirable, and the decision maker may need to commit to a set of actions for a number of planning periods. Two-stage stochastic programming might be better suited to such settings, where the decisions for all periods are made here-and-now and do not adapt to the uncertainty realized. In this paper, we propose a novel alternative approach, where the stages are not predetermined but part of the optimization problem. Each component of the decision policy has an associated revision point, a period prior to which the decision is predetermined and after which it is revised to adjust to the uncertainty realized thus far. We motivate this setting using the multi-period newsvendor problem by deriving an optimal adaptive policy. We label the proposed approach as adaptive two-stage stochastic programming and provide a generic mixed-integer programming formulation for finite stochastic processes. We show that adaptive two-stage stochastic programming is NP-hard in general. Next, we derive bounds on the value of adaptive two-stage programming in comparison to the two-stage and multi-stage approaches for a specific problem structure inspired by the capacity expansion planning problem. Since directly solving the mixed-integer linear program associated with the adaptive two-stage approach might be very costly for large instances, we propose several heuristic solution algorithms based on the bound analysis. We provide approximation guarantees for these heuristics. Finally, we present an extensive computational study on an electricity generation capacity expansion planning problem and demonstrate the computational and practical impacts of the proposed approach from various perspectives

Restaurant Revenue Management: Examining Reservation Policy Implications at Fine Dining Restaurants

In the restaurant industry, some patrons do not honor their reservations, especially on holidays. Grounded in postpositivism and system theories, the purpose of this comparative study was to examine the impact of implementing a credit card payment policy for fine dining restaurants reservations and no shows after implementation of a credit card guarantee policy at a high-end hotel located in the southeast United States. Data were collected from archival records provided by the hotel executives. According to the results of a Wilcoxon Signed Rank test, there was a statistically significant decrease in the number of no shows, p \u3c .001, after the implementation of the credit card guarantee policy. In a paired sample t-test, there was a statistically significant decrease in the number of reservations, p \u3c .001, after implementation of the credit card guarantee policy. The implications for positive social change include the potential to increase understanding of payment policies as they relate to the restaurant industry. Service industry managers can benefit from implementing payment policies that can vary from specific dates, seasons, and type of services. Customers will also benefit by being able to make reservations not originally possible due to demand. The current study adds to service industry knowledge, increasing the understanding of payment policies as they relate to restaurant industry. Conducting a similar study in other service industries in the future may lead to a better understanding of the nature of policies and customers\u27 traits and behaviors

OPTIMIZATION MODELS AND METHODOLOGIES TO SUPPORT EMERGENCY PREPAREDNESS AND POST-DISASTER RESPONSE

This dissertation addresses three important optimization problems arising during the phases of pre-disaster emergency preparedness and post-disaster response in time-dependent, stochastic and dynamic environments. The first problem studied is the building evacuation problem with shared information (BEPSI), which seeks a set of evacuation routes and the assignment of evacuees to these routes with the minimum total evacuation time. The BEPSI incorporates the constraints of shared information in providing on-line instructions to evacuees and ensures that evacuees departing from an intermediate or source location at a mutual point in time receive common instructions. A mixed-integer linear program is formulated for the BEPSI and an exact technique based on Benders decomposition is proposed for its solution. Numerical experiments conducted on a mid-sized real-world example demonstrate the effectiveness of the proposed algorithm. The second problem addressed is the network resilience problem (NRP), involving an indicator of network resilience proposed to quantify the ability of a network to recover from randomly arising disruptions resulting from a disaster event. A stochastic, mixed integer program is proposed for quantifying network resilience and identifying the optimal post-event course of action to take. A solution technique based on concepts of Benders decomposition, column generation and Monte Carlo simulation is proposed. Experiments were conducted to illustrate the resilience concept and procedure for its measurement, and to assess the role of network topology in its magnitude. The last problem addressed is the urban search and rescue team deployment problem (USAR-TDP). The USAR-TDP seeks an optimal deployment of USAR teams to disaster sites, including the order of site visits, with the ultimate goal of maximizing the expected number of saved lives over the search and rescue period. A multistage stochastic program is proposed to capture problem uncertainty and dynamics. The solution technique involves the solution of a sequence of interrelated two-stage stochastic programs with recourse. A column generation-based technique is proposed for the solution of each problem instance arising as the start of each decision epoch over a time horizon. Numerical experiments conducted on an example of the 2010 Haiti earthquake are presented to illustrate the effectiveness of the proposed approach

Optimisation et simulation pour la gestion de disponibilite sous comportement d’achat

RÉSUMÉ: Nous nous intéressons dans ce doctorat à l’optimisation de la disponibilité de l’offre au cours d’une période de réservation pendant laquelle des ressources périssables sont vendues. Cette problématique appartient au domaine de la gestion de revenu plus communément désigné par le terme anglais de revenue management. Afin d’illustrer notre propos, considérons le siège d’un train effectuant un trajet entre deux villes à une certaine date et heure. Ce siège est une ressource périssable, car il ne peut pas être proposé une fois le train parti. Cette ressource doit donc être vendue avant son terme durant une période de réservation. Des clients arrivent pendant cette période pour éventuellement réserver cette ressource en achetant un des produits offerts. Les produits sont définis à l’avance par leur tarif et leurs conditions. Ces dernières portent sur l’annulation, l’échange, l’accès au wifi ou une offre de repas par exemple. Chaque client choisira éventuellement d’acheter l’un de ces produits en fonction d’un comportement d’achat qui lui est propre. Ce doctorat se résume à déterminer quels produits offrir à chaque arrivée de client afin de maximiser le revenu généré par l’ensemble des ventes réalisées au cours de la période de réservation. Pour se faire, les ressources et produits sont fixés ainsi que la demande qui est connue au moyen d’une prévision. L’optimisation des ressources et produits ainsi que la prévision de la demande ne font pas l’objet de ce doctorat et sont d’ailleurs presque toujours traitées séparément dans le domaine de gestion de revenu. Le dilemme suivant est soulevé. D’un côté en acceptant une requête, nous assurons un revenu, mais nous diminuons la capacité disponible pour des requêtes futures éventuellement de meilleur revenu. Il peut donc y avoir de la dilution. D’un autre côté, en refusant une requête, nous réservons de la capacité pour d’éventuelles requêtes futures à meilleur revenu tout en perdant la requête présente à revenu sûr. Il peut donc y avoir du gaspillage. Deux grandes évolutions ont successivement changé la modélisation de ce problème et ont amélioré la robustesse des solutions tout en le complexifiant. La première a pris en compte les ressources dans leur ensemble plutôt qu’individuellement. La deuxième a intégré le comportement d’achat de clients là où auparavant la demande était considérée de façon indépendante par produit. Aujourd’hui, une formulation exacte intégrant ces deux aspects existe, mais est trop rapidement insoluble. Des approximations ont donc été proposées. L’objectif est de retourner rapidement une politique de disponibilité générant le meilleur revenu espéré une fois simuler. Dans un premier temps, nous présentons une approximation pour un comportement d’achat non paramétrique. Ce type de demande est abondamment utilisé en pratique et modélise mieux les substitutions de produits que beaucoup de modèles paramétriques. Il jouit aussi de plus en plus de recherches sur son estimation, mais de peu de travaux en gestion de la disponibilité. Nous introduisons alors un des trois concepts importants de ce doctorat qui est l’utilisation de temps de fermeture par produit comme politique de disponibilité. Cette dernière s’adapte pleinement à la logique d’achat non paramétrique contrairement aux modèles existants. Nous arrivons à un modèle à nombres entiers dont les variables binaires rendent compte d’une hiérarchie de produit qui a un réel sens pratique. Cela nous permet de proposer de bonnes solutions initiales très facilement. La politique par temps de fermeture empêche naturellement la réouverture à la vente de produits au cours de la période de réservation. Il faut savoir que cet aspect est souvent désiré en pratique et nécessite la complexification des approches existantes contrairement à la nôtre. Dans le cas de non-réouverture, nous prouvons que notre approximation est une borne supérieure pour la formulation exacte et qu’elle est asymptotiquement optimale. Nous pouvons utiliser la politique retournée par notre approximation comme solution initiale de n’importe quelle approximation à réouverture. Des résultats numériques sur des instances de petites à grandes tailles montrent que notre approximation, par rapport aux approches existantes, retourne beaucoup plus rapidement une politique de disponibilité générant un revenu espéré légèrement supérieur. Ils mettent aussi en évidence l’accélération des approximations existantes lorsque notre approche est utilisée comme solution de départ. Dans un second temps, poussés par les résultats précédents, nous cherchons à généraliser l’approche précédente à tout comportement d’achat. Nous représentons d’abord toute demande sous la forme de chemins d’achats formant ainsi un arbre de demande. Cet arbre de demande est le second concept important de ce doctorat. Nous utilisons le fait que chaque chemin d’achat est non paramétrique pour construire une nouvelle approximation acceptant n’importe quel comportement d’achat. Notre nouvelle approximation hérite de la politique de disponibilité par temps de fermeture et donc de la non réouverture. Nous utilisons alors la même linéarisation et nous étendons les résultats théoriques précédents. Les modèles paramétriques retournent un arbre de demande immense qui rend notre approximation insoluble. Pour pallier cela, nous présentons une méthode de résolution itérative basée sur une construction progressive de l’arbre de demande par un ajout successif de chemins d’achats. Nous proposons plusieurs heuristiques pour déterminer quel chemin d’achat ajouter. Chaque ajout raffine la modélisation du comportement d’achat. Nous menons ensuite des expériences numériques sur des instances à comportement d’achat paramétrique de petite à grande taille. Les résultats montrent des résultats similaires à ceux pour le non paramétrique et la méthode itérative de résolution converge vers une bonne solution beaucoup plus rapidement que les autres approches. Dans un dernier temps, nous nous penchons sur la simulation pour la gestion de disponibilité. Nous proposons un nouvel estimateur à arrivées fluides pour le calcul du revenu espéré. Cette modélisation par arrivées fluides est le troisième concept important de ce doctorat. Notre modèle agrège alors les différentes arrivées par segment, et ce pour toute la période de réservation. Il ne subit donc pas l’aléatoire d’un ordre d’arrivées. Il nécessite alors une seule évaluation et est invariant alors que l’estimateur traditionnel à arrivées discrètes ne peut réduire la variance et donc augmenter la précision qu’en augmentant le nombre d’évaluations. En contrepartie, nous montrons que notre estimateur présente un biais, contrairement à l’estimateur traditionnel, pouvant être arbitrairement grand même si cela reste minime en pratique. Nous expérimentons alors des méthodes d’optimisation basées sur la simulation afin de résoudre le problème de contrôle de la disponibilité. Nous concluons rapidement que la bonne convergence de ces méthodes dépend largement du point de départ fourni par un modèle en programmation mathématique. Cette conclusion a été un moteur pour le développement des approximations précédentes. D’ailleurs, nous montrons que notre estimateur est équivalent à la plupart des approximations pour le contrôle de la disponibilité. En conséquence, nous évoquons quelques possibilités de notre estimateur pour appuyer l’optimisation. Les résultats numériques sur des instances de grandes tailles témoignent de la nette supériorité de notre estimateur en termes de temps de calcul. Nous constatons aussi peu de biais pour toutes les instances étudiées.----------ABSTRACT: This thesis focuses on the availability policy problem when selling perishable resources during a reservation period. This problem belongs to the revenue management topic. For example, a seat in a train between two cities at 9am on may 3rd 2018 is a perishable resource because it cannot be sold after the train departure. We must sell this resource through a reservation period before it expires and during which customers arrive to eventually buy a product. Many products can exist and are defined in advance by their terms and rates. For example, tickets for this seat can offer cancellation or exchange. A Meal or a wi-fi access can even be proposed at another cost. Each customer will then choose a product or not according to its own choice behaviour. This thesis aims to determinate which products to offer at each client arrival in order to maximize the income generated by the sales during the reservation period. Products and resources are fixed and demand is known. The products and resources optimization as well as the forecasting are not tackled in this thesis. Besides, they are almost always treated separately in revenue management. The following dilemma is raised. Accepting a request, provides an income, but removes one capacity for a future and potential higher request. This is called spillage. Whereas denying a request, protects a potential higher income but loses an immediate and safe income. This is named spoilage. Two major developments successively changed the model of this problem and improved the robustness of solutions while increasing the complexity. The first was to consider resources together rather than individually. The second is the integration of the customer choice behaviour rather than an independent demand by product. Today an exact formulation integrates both aspects but is too rapidly intractable. Approximations have therefore been proposed. The challenge is to quickly return an availability policy generating the best expected revenue when simulated. In a first part, we present an approximation for a non-parametric choice behaviour. This type of demand is widely used in practice and better accounts for products substitutions than many parametric models. It also benefits from recent research on its estimation and is rarely investigated for the availability policy problem. This approximation benefits from one of the three major concepts of this thesis which is an availability policy by closing times per product. This policy fully adapts to the non-parametric buying logic contrarily to existing models. The model is mixed integer with variables that account for a product hierarchy having a practical meaning. This allows us to easily offer good initial solutions in order to accelerate the resolution of our approximation. The closing time policy naturally prevents the reopening of products during the booking period. This aspect is often desired in practice. To force no reopening, existing approximations must be adapted and are thus more complex to solve. In the case of no reopening, we prove that our approximation is an upper bound for the exact formulation and that it is asymptotically optimal. We can use the policy returned by our approximation as an initial solution of any reopening approximation. Numerical results on small to large instances show that our approximation, compared to existing approaches, returns much faster an availability policy generating slightly higher expected revenue. They also highlight the acceleration of existing approximations when our approach is used as a starting solution. In a second part, driven by the previous results, we seek to generalize the previous approach to any choice behavior. We first represent any demand in the form of buying paths forming a demand tree. This demand tree is the second important concept of this thesis. Each buying path is non-parametric so that we extend previous results by introducing new approximation accepting any choice behavior. It inherits the closing time availability policy and by consequence the no reopening. We then use the same linearization and extend the previous theoretical results. Parametric choice models return huge and intractable demand tree. To overcome this, we present an iterative resolution method based on a progressive construction of the demand tree by a successive addition of buying paths. We propose several heuristics to determine which buying path to add. We then conduct numerical experiments on small to large instances with parametric choice behaviour. The results are similar to those for nonparametric and the iterative method of resolution converges much faster to a good solution than existing approximations. In the last part, we focus on simulation for the availability policy problem. We propose a new fluid arrivals estimator to determinate the expected revenue. This fluid arrivals aspect is the third major concept of this thesis. It aggregates the different arrivals by segment for the entire booking period. It thus does not suffer from the randomness of ordered arrivals. Consequently, it requires only one evaluation and is invariant whereas the traditional discrete arrivals estimator can only reduce the variance by increasing the number of evaluations. However, we show that our estimator has a bias, unlike the traditional estimator, which can be arbitrarily large even if remains minimal in practice. We then experiment optimization-based simulation methods to solve the availability policy problem. We quickly conclude that the good convergence of these methods highly depends on the starting point provided by a mathematical programming model. This conclusion has been a motivation for the development of the previous approximations. Moreover, we show that our estimator is equivalent to most of these approximations. As a result, we discuss some applications for our estimator to support optimization. The numerical results on large-scale instances highlight the superiority of our estimator in terms of computation time. We also found only a little bias for all instances studied

Network Revenue Management under Competition within Strategic Airline Alliances

Airlines often cooperate with partners within strategic alliances to offer their customers itineraries beyond their own networks. However, despite the cooperation, the alliance members often remain competitors on other routes and compete for customers. This thesis takes into account the competition between two alliance partners and models it in a linear program. An algorithm is developed to compute optimal capacity allocations in pure Nash equilibria based on the model. For cases, in which a Nash equilibrium does not exist or cannot be found within a pre-defined time, a heuristic approach is described to compute an approximate Nash equilibrium. Computational studies show the applicability of the approaches in real-sized airline networks. Finally, suggestions for future research are made

Dynamic Pricing under Operational Frictions

This dissertation investigates the tactical dynamic pricing decisions in industries where sellers sell multiple types of capacity-constrained products/services to their customers. Motivated by operational frictions posed by business considerations, I develop dynamic pricing heuristics that have both provably good revenue performance and nice features which can address these operational frictions. The first essay studies how to do effective dynamic pricing without too many price changes. In practice, many sellers have concerns about dynamic pricing due to the computational complexity of frequent re-optimizations, the negative perception of excessive price adjustments, and the lack of flexibility caused by existing business constraints. To address these concerns, I develop a pricing heuristic which is computationally easy to implement and only needs to adjust a small number of prices and do so infrequently to guarantee a strong revenue performance. In addition, when not all products are equally admissible to price adjustment, my heuristic can replace the price adjustment of some products by their similar products and maintain an equivalent revenue performance. These features allow the sellers to achieve most of the benefit of dynamic pricing with much fewer price changes and provide extra flexibility to manage prices. While the first essay assumes that the sellers know the underlying demand function, this information is sometimes unavailable to the sellers in practice. The second and the third essays study how to jointly learn the demand and dynamically price the products to minimize revenue loss compared to a standard revenue upper bound in the literature. The second essay addresses the parametric case where the seller knows the functional form of the demand but not the parameters; the third essay addresses the nonparametric case where the seller does not even know the functional form of the demand. There is a considerable gap between the revenue loss lower bound under any pricing policy and the performance bound of the best known heuristic in the literature. To close the gap, in my second essay, I propose a heuristic that exactly match the lower bound for the parametric case, and show that under a demand separation condition, a much sharper revenue loss bound can be obtained; in my third essay, I propose a heuristic whose performance is arbitrarily close to the lower bound for the nonparametric case. All the proposed heuristics are computationally very efficient and can be used as a baseline for developing more sophisticated heuristics for large-scale problems.PHDBusiness AdministrationUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/138561/1/georgeqc_1.pd