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An approximate dynamic programming approach to network revenue management with customer choice. Transportation Science, 43:381–394, 2009. Use of Approximate Dynamic Programming for Production Optimization SPE 141677 (a) Comparison with baseline strategy (
"... We consider a network revenue management problem where customers choose among open fare products according to some prespecified choice model. Starting with a Markov decision process (MDP) formulation, we approximate the value function with an affine function of the state vector. We show that the re ..."
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Cited by 30 (1 self)
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We consider a network revenue management problem where customers choose among open fare products according to some prespecified choice model. Starting with a Markov decision process (MDP) formulation, we approximate the value function with an affine function of the state vector. We show that the resulting problem provides a tighter bound for the MDP value than the choicebased linear program proposed by Gallego et al. (2004) and Liu and van Ryzin (2007). We develop a column generation algorithm to solve the problem for a multinomial logit choice model with disjoint consideration sets. We also derive a bound as a byproduct of a decomposition heuristic. Our numerical study shows the policies from our solution approach can significantly outperform heuristics from the choicebased linear program. While a substantial amount of research has been done on methods for solving the network revenue management problem, much less work has been done in solving the version where customers choose among available network products. Usually, when airlines open up a menu of fares for a given set of flights, customers will make substitutions between those available, or purchase nothing. Although incorporating customer choice is important in practice, methodologically it is
Robust Controls for Network Revenue Management
"... Revenue management models traditionally assume that future demand is unknown, but can be represented by a stochastic process or a probability distribution. Demand is however often difficult to characterize, especially in new or nonstationary markets. In this paper, we develop robust formulations for ..."
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Cited by 13 (0 self)
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Revenue management models traditionally assume that future demand is unknown, but can be represented by a stochastic process or a probability distribution. Demand is however often difficult to characterize, especially in new or nonstationary markets. In this paper, we develop robust formulations for the capacity allocation problem in revenue management, using the maximin and the minimax regret criteria, under general polyhedral uncertainty sets. Our approach encompasses the following openloop controls: partitioned booking limits, nested fare classes by origindestination pairs, DisplacementAdjusted Virtual Nesting, and fixed bid prices. We also characterize the optimal booking policy under interval uncertainty; while partitioned booking limits are optimal under the maximin criterion, some nesting is desirable under the minimax regret criterion. Our numerical analysis reveals that robust controls can outperform the classical heuristics for network revenue management, while achieving the best performance in the worst case. Our models are scalable to solve practical problems, because they combine efficient solution methods (small mixedinteger and linear optimization problems) with very modest data requirements. 1.
Pricing substitutable flights in airline revenue management
 European Journal of Operational Research
, 2007
"... We develop a Markov decision process formulation of a dynamic pricing problem for multiple substitutable flights between the same origin and destination, taking into account customer choice among the flights. The model is rendered computationally intractable for exact solution by its multidimensiona ..."
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Cited by 8 (2 self)
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We develop a Markov decision process formulation of a dynamic pricing problem for multiple substitutable flights between the same origin and destination, taking into account customer choice among the flights. The model is rendered computationally intractable for exact solution by its multidimensional state and action spaces, so we develop and analyze various bounds and heuristics. We first describe three related models, each based on some form of pooling, and introduce heuristics suggested by these models. We also develop separable bounds for the value function which are used to construct value and policyapproximation heuristics. Extensive numerical experiments show the value and policyapproximation approaches to work well across a wide range of problem parameters, and to outperform the poolingbased heuristics in most cases. The methods are applicable even for large problems, and are potentially useful for practical applications.
Resolving stochastic programming models for airline revenue management
, 2006
"... We study some mathematical programming formulations for the origindestination 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 twostage stochastic programs with si ..."
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Cited by 7 (1 self)
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We study some mathematical programming formulations for the origindestination 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 twostage stochastic programs with simple recourse, which can be viewed as an approximation to a multistage 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 twostage 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 bidprice policies. In addition, we propose a heuristic method to choose the resolving points, rather than resolving at equallyspaced times as customary. Numerical results are presented to illustrate the effectiveness of the proposed approach.
A stochastic approximation method to compute bid prices in network revenue management problems
 INFORMS Journal on Computing
"... We present a stochastic approximation method to compute bid prices in network revenue management problems. The key idea is to visualize the total expected revenue as a function of the bid prices and to use sample pathbased derivatives to search for a good set of bid prices. We deal with the discret ..."
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Cited by 7 (3 self)
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We present a stochastic approximation method to compute bid prices in network revenue management problems. The key idea is to visualize the total expected revenue as a function of the bid prices and to use sample pathbased derivatives to search for a good set of bid prices. We deal with the discrete nature of the network revenue management setting by formulating a smoothed version of the problem, which assumes that it is possible to accept a fraction of an itinerary request. We show that the iterates of our method converge to a stationary point of the total expected revenue function of the smoothed version. Computational experiments demonstrate that the bid prices obtained by our method outperform the ones obtained by standard benchmark methods and our method is especially advantageous when the bid prices are not recomputed frequently. The notion of bid prices forms a powerful tool to construct good policies for network revenue management problems. The idea is to associate a bid price with each flight leg that captures the opportunity cost of a unit of capacity. An itinerary request is accepted if and only if there is enough capacity and the revenue from the itinerary request exceeds the sum of the bid prices associated with the flight legs in the requested itinerary; see Williamson (1992) and Talluri and van Ryzin (2004).
A stochastic approximation method for the singleleg revenue management problem with discrete demand distributions
 Mathematical Methods of Operations Research
, 2009
"... We consider the problem of optimally allocating the seats on a single flight leg to the demands from multiple fare classes that arrive sequentially. It is wellknown that the optimal policy for this problem is characterized by a set of protection levels. In this paper, we develop a new stochastic ap ..."
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Cited by 5 (0 self)
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We consider the problem of optimally allocating the seats on a single flight leg to the demands from multiple fare classes that arrive sequentially. It is wellknown that the optimal policy for this problem is characterized by a set of protection levels. In this paper, we develop a new stochastic approximation method to compute the optimal protection levels under the assumption that the demand distributions are not known and we only have access to the samples from the demand distributions. The novel aspect of our method is that it works with the nonsmooth version of the problem where the capacity can only be allocated in integer quantities. We show that the sequence of protection levels generated by our method converges to a set of optimal protection levels with probability one. We discuss applications to the case where the demand information is censored by the seat availability. Computational experiments indicate that our method is especially advantageous when the total expected demand exceeds the capacity by a significant margin and we do not have good a priori estimates of the optimal protection levels.
Dynamic Assortment Customization with Limited Inventories
, 2010
"... We consider a retailer with limited inventories of identically priced, substitutable products. Customers arrive sequentially and the firm decides which subset of the products to o¤er to each arriving customer depending on the customer’s preferences, the inventory levels and the remaining time in the ..."
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Cited by 5 (0 self)
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We consider a retailer with limited inventories of identically priced, substitutable products. Customers arrive sequentially and the firm decides which subset of the products to o¤er to each arriving customer depending on the customer’s preferences, the inventory levels and the remaining time in the season. We show that the optimal assortment policy is to offer all available products if the customer base is homogeneous with respect to their product preferences. However, with multiple customer segments characterized by different product preferences, it may be optimal to limit the choice set of some customers. That is, it may be optimal not to o¤er products with low inventories to some customer segments and reserve them for future customers (who may have a stronger preference for those products). For the case of two products and two customer segments and for a special case with multiple products and multiple customer segments, we show that the optimal assortment policy is a threshold policy under which a product is offered to a customer segment if its inventory level is higher than a threshold value. The threshold levels are decreasing in time and increasing in the inventory levels of other products. For the general case, we perform a large numerical study, and confirm that the optimal policy continues to be of the threshold type. We find that the revenue impact of assortment customization can be significant, especially when customer heterogeneity is high and the starting inventory levels of the products are asymmetric. This demonstrates the use of assortment customization as another lever for revenue maximization in addition to pricing.
Using stochastic approximation methods to compute optimal basestock levels in inventory inventory control problems
 Operations Research
, 2008
"... In this paper, we consider numerous inventory control problems for which the basestock policies are known to be optimal and we propose stochastic approximation methods to compute the optimal basestock levels. The existing stochastic approximation methods in the literature guarantee that their iter ..."
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Cited by 4 (0 self)
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In this paper, we consider numerous inventory control problems for which the basestock policies are known to be optimal and we propose stochastic approximation methods to compute the optimal basestock levels. The existing stochastic approximation methods in the literature guarantee that their iterates converge, but not necessarily to the optimal basestock levels. In contrast, we prove that the iterates of our methods converge to the optimal basestock levels. Moreover, our methods continue to enjoy the wellknown advantages of the existing stochastic approximation methods. In particular, they only require the ability to obtain samples of the demand random variables, rather than to compute expectations explicitly and they are applicable even when the demand information is censored by the amount of available inventory. 1
Some decomposition methods for revenue management
 Transportation Sci
, 2007
"... doi 10.1287/trsc.1060.0184 ..."
Estimation of Choicebased Models Using Sales Data From a Single Firm. Working paper, Georgia Tech
, 2010
"... Choicebased revenue management (RM) problems use discrete choice models to predict productlevel demands. The estimation of choicebased RM models involves solving for choice parameters as well as an arrival rate. The latter represents a measure of unconstrained demand, i.e., the population of cust ..."
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Cited by 3 (0 self)
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Choicebased revenue management (RM) problems use discrete choice models to predict productlevel demands. The estimation of choicebased RM models involves solving for choice parameters as well as an arrival rate. The latter represents a measure of unconstrained demand, i.e., the population of customers who arrive and purchase a product from our firm as well as those who arrive and either decide to purchase a product from a competitor or not to purchase at all. Talluri and van Ryzin were the first to propose a parameter estimation method for this problem in 2004. However, their method, which uses ExpectationMaximization (EM) routines to solve an expected log likelihood function, exhibits prohibitively long estimation times and often leads to counterintuitive results. We reformulate the Talluri and van Ryzin parameter estimation method using marginal (versus expected) log likelihood functions. This enables us to eliminate the use of the EM algorithm, which results in solution times that are improved by orders of magnitude. The marginal log likelihood formulation allows us to decompose the problem into two steps: one that estimates the discrete choice model parameters, and the other that estimates the arrival rate and overall market share. We discuss theoretical properties of our marginal log likelihood formulation and prove that it converges to a local (and often global) optima. The proof is based on showing how the multidimensional