Network Revenue Management Problem Research Articles

A New Dynamic Programming Decomposition Method for the Network Revenue Management Problem with Customer Choice Behavior

In this paper, we propose a new dynamic programming decomposition method for the network revenue management problem with customer choice behavior. The fundamental idea behind our dynamic programming decomposition method is to allocate the revenue associated with an itinerary among the different flight legs and to solve a single‐leg revenue management problem for each flight leg in the airline network. The novel aspect of our approach is that it chooses the revenue allocations by solving an auxiliary optimization problem that takes the probabilistic nature of the customer choices into consideration. We compare our approach with two standard benchmark methods. The first benchmark method uses a deterministic linear programming formulation. The second benchmark method is a dynamic programming decomposition idea that is similar to our approach, but it chooses the revenue allocations in an ad hoc manner. We establish that our approach provides an upper bound on the optimal total expected revenue, and this upper bound is tighter than the ones obtained by the two benchmark methods. Computational experiments indicate that our approach provides significant improvements over the performances of the benchmark methods.

A randomized linear program for the network revenue management problem with customer choice behavior

In this article, we propose a randomized linear program to obtain bid prices for the network revenue management problem with customer choice behavior. Our development proceeds in two stages. We first formulate a mixed integer program that can be viewed as a deterministic approximation to the network revenue management problem. We then use the optimal solution to the mixed integer program to formulate a linear program that can be easily randomized. We establish that our solution method approximates the optimal total expected revenue arbitrarily closely in an asymptotic regime where the leg capacities and the number of time periods in the decision horizon increase linearly with the same rate. Numerical experiments indicate that our approach may be available alternative to the standard deterministic linear program that appears in the existing literature.

Network capacity management under competition

We consider capacity management games between airlines who transport passengers over a joint airline network. Passengers are likely to purchase alternative tickets of the same class from competing airlines if they do not get tickets from their preferred airlines. We propose a Nash and a generalized Nash game model to address the competitive network revenue management problem. These two models are based on well-known deterministic linear programming and probabilistic nonlinear programming approximations for the non-competitive network capacity management problem. We prove the existence of a Nash equilibrium for both games and investigate the uniqueness of a Nash equilibrium for the Nash game. We provide some further uniqueness and comparative statics analysis when the network is reduced to a single-leg flight structure with two products. The comparative statics analysis reveals some useful insights on how Nash equilibrium booking limits change monotonically in the prices of products. Our numerical results indicate that airlines can generate higher and more stable revenues from a booking scheme that is based on the combination of the partitioned booking-limit policy and the generalized Nash game model. The results also show that this booking scheme is robust irrespective of which booking scheme the competitor takes.

Computing Time-Dependent Bid Prices in Network Revenue Management Problems

We propose a new method to compute bid prices in network revenue management problems. The novel aspect of our method is that it naturally provides dynamic bid prices that depend on how much time is left until departure. We show that our method provides an upper bound on the optimal total expected revenue and that this upper bound is tighter than the one provided by the widely known deterministic linear programming approach. Furthermore, it is possible to use the bid prices computed by our method as a starting point in a dynamic programming decomposition-like idea to decompose the network revenue management problem by the flight legs and to obtain dynamic and capacity-dependent bid prices. Our computational experiments indicate that the proposed method improves on many standard benchmarks.

Using decomposition methods to solve pricing problems in network revenue management

In this article, we develop two methods for making pricing decisions in network revenue management problems. We consider a setting where the probability of observing a request for an itinerary depends on the prices and the objective is to dynamically adjust the prices so as to maximize the total expected revenue. The idea behind both of our methods is to decompose the dynamic programming formulation of the pricing problem by the flight legs and to obtain value function approximations by focusing on one flight leg at a time. We show that our methods provide upper bounds on the optimal total expected revenue and these upper bounds are tighter than the one provided by a deterministic linear program commonly used in practice. Our computational experiments yield two important results. First, our methods provide substantial improvements over the deterministic linear program. The average gap between the total expected revenues obtained by our methods and the deterministic linear program is 7.11 per cent. On average, our methods tighten the upper bounds obtained by the deterministic linear program by 3.66 per cent. Second, the two methods that we develop have different strengths. In particular, while one method is able to obtain tighter upper bounds, the other one is able to obtain pricing policies that yield higher total expected revenues.

On the asymptotic optimality of the randomized linear program for network revenue management

For network revenue management problems, it is known that the bid prices computed through the so-called deterministic linear program are asymptotically optimal as the capacities on the flight legs and the expected numbers of product requests increase linearly with the same rate. In this paper, we show that the same asymptotic optimality result holds for the bid prices computed through the so-called randomized linear program. We computationally investigate how the performance of the randomized linear program changes with different problem parameters and with the number of samples. The hope is that our asymptotic optimality result and computational experiments will raise awareness for the randomized linear program, which has yet not been popular in the research community or industry.

An Approximate Dynamic Programming Approach to Network Revenue Management with Customer Choice

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 choice-based linear program. We develop a column generation algorithm to solve the problem for a multinomial logit choice model with disjoint consideration sets (MNLD). We also derive a bound as a by-product of a decomposition heuristic. Our numerical study shows the policies from our solution approach can significantly outperform heuristics from the choice-based linear program.

Using Lagrangian Relaxation to Compute Capacity-Dependent Bid Prices in Network Revenue Management

We propose a new method to compute bid prices in network revenue management problems. The novel aspect of our method is that it explicitly considers the temporal dynamics of the arrivals of the itinerary requests and generates bid prices that depend on the remaining leg capacities. Our method is based on relaxing certain constraints that link the decisions for different flight legs by associating Lagrange multipliers with them. In this case, the network revenue management problem decomposes by the flight legs, and we can concentrate on one flight leg at a time. When compared with the so-called deterministic linear program, we show that our method provides a tighter upper bound on the optimal objective value of the network revenue management problem. Computational experiments indicate that the bid prices obtained by our method perform significantly better than the ones obtained by standard benchmark methods.

Separable approximations for joint capacity control and overbooking decisions in network revenue management

We develop a network revenue management model to jointly make capacity control and overbooking decisions. Our approach is based on the observation that if the penalty cost of denying boarding to the reservations at the departure time were given by a separable function, then the dynamic programming formulation of the network revenue management problem would decompose by the itineraries and it could be solved by focusing on one itinerary at a time. Motivated by this observation, we use an iterative and simulation-based method to build separable approximations to the penalty cost that we incur at the departure time. Computational experiments compare our model with two benchmark strategies that are based on a deterministic linear programming formulation. The profits obtained by our model improve over those obtained by the benchmark strategies by about 3 per cent on the average, which is a significant figure in the network revenue management setting. For the test problems with tight leg capacities, the profit improvements can be as high as 13 per cent.

A Stochastic Approximation Method to Compute Bid Prices in Network Revenue Management Problems

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 path-based 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.

A refined deterministic linear program for the network revenue management problem with customer choice behavior

AbstractWe present a new deterministic linear program for the network revenue management problem with customer choice behavior. The novel aspect of our linear program is that it naturally generates bid prices that depend on how much time is left until the time of departure. Similar to the earlier linear program used by van Ryzin and Liu (2004), the optimal objective value of our linear program provides an upper bound on the optimal total expected revenue over the planning horizon. In addition, the percent gap between the optimal objective value of our linear program and the optimal total expected revenue diminishes in an asymptotic regime where the leg capacities and the number of time periods in the planning horizon increase linearly with the same rate. Computational experiments indicate that when compared with the linear program that appears in the existing literature, our linear program can provide tighter upper bounds, and the control policies that are based on our linear program can obtain higher total expected revenues. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008

Simulation of stochastic demand data streams for network revenue management problems

For evaluating heuristic and optimal network revenue management procedures test-instances are needed. As a consequence when trying to create instances for network revenue management problems it turns out that among other things a stream of stochastic demand data is required. But, developing and implementing a generator for demand data that fits to a given network, a given set of products, and a given set of capacity constraints is far from being easy. Since to the best of our knowledge no such demand data generator is available to the public, we specify an algorithm to generate this data and we also make this algorithm available upon request. This, we hope, facilitates future research work.