Seat Inventory Control Problem Research Articles

A deep reinforcement learning approach to seat inventory control for airline revenue management

Commercial airlines use revenue management systems to maximize their revenue by making real-time decisions on the booking limits of different fare classes offered in each of its scheduled flights. Traditional approaches—such as mathematical programming, dynamic programming, and heuristic rule-based decision models—heavily rely on external mathematical models of demand and passenger arrival, choice, and cancelation, making their performance sensitive to the accuracy of these model estimates. Moreover, many of these approaches scale poorly with increase in problem dimensionality. Additionally, they lack the ability to explore and “directly” learn the true market dynamics from interactions with passengers and adapt to changes in market conditions on their own. To overcome these limitations, this research uses deep reinforcement learning (DRL), a model-free decision-making framework, for finding the optimal policy of the seat inventory control problem. The DRL framework employs a deep neural network to approximate the expected optimal revenues for all possible state-action combinations, allowing it to handle the large state space of the problem. Multiple fare classes with stochastic demand, passenger arrivals, and booking cancelations have been considered in the problem. An air travel market simulator was developed based on the market dynamics and passenger behavior for training and testing the agent. The results demonstrate that the DRL agent is capable of learning the optimal airline revenue management policy through interactions with the market, matching the performance of exact dynamic programming methods. The revenue generated by the agent in different simulated market scenarios was found to be close to the maximum possible flight revenues and surpass that produced by the expected marginal seat revenue-b (EMSRb) method.

Deep reinforcement learning in seat inventory control problem: an action generation approach

Nowadays, firms intend to use customer choice-based models instead of an independent demand paradigm to generate more revenue. In this paper, we address choice-based seat inventory control problem with stochastic demand using a deep reinforcement learning technique named Deep Q-Network (DQN). DQN can naturally address large state space problems with its integrated function approximation. However, it becomes intractable in the case of large discrete action space. To address this issue, we propose an Action Generation (AGen) algorithm. AGen is a greedy heuristic algorithm designed to be integrated into DQN to overcome the complexity of the original problem. It aims to greedily generate a set of “effective” actions to replace the original action space. This leads to the main achievement of this study which is to dramatically decrease the complexity of the solution method without negatively affecting its performance in a large-scale choice-based seat inventory allocation problem.

A dynamic bid price approach for the seat inventory control problem in railway networks with consideration of passenger transfer

Railway seat inventory control aims to maximize ticket sale profits by determining a selling policy on the reservation horizon. This paper introduces a dynamic bid price approach in railway seat inventory control problem. Multi-dimensional demand is taken into consideration in modeling the problem, in which passenger transfer is our main focus. A new approximate approach is designed to this problem. Numerical examples are presented to evaluate the efficiency of this approach. Simulation experiments are conducted to verify the impact of transfer under different scenarios.

An Optimization Method for Train Seat Inventory Control

Railway passenger transportation plays a fundamental role in China, reasonable revenue is the guarantee of railway's regularly development such as equipment replacement, technology enhancement, etc. Although many studies on the railway revenue models have been conducted, there is a lack of effective modeling which considers the multiple trains and the multiple levels of seats in real operation. Aiming to improve the revenue of railway transportation industry, this paper proposes a new optimization method for the train seat inventory control problem with the consideration of the multiple trains and the multiple levels of seats. As the in-depth research of this problem, an integer linear programming model is formulated which aims to maximize the total revenue of rail industry. The commercial software MATLAB with CPLEX solver is employed to obtain the approximate optimal solutions. The effectiveness and performance of the proposed approaches are testified by two examples implemented on a simple railway corridor and Wuhan–Guangzhou high-speed railway corridor. Moreover, sensitivity analysis experiments are given to explore the impact on the revenue if the model parameters are changed.

Seat inventory control methods for Chinese passenger railways

Railway seat inventory control strategies play a crucial role in the growth of profit and train load factor. The railway passenger seat inventory control problem in China was addressed. Chinese passenger railway operation features and seat inventory control practice were analyzed firstly. A dynamic demand forecasting method was introduced to forecast the coming demand in a ticket booking period. By clustering, passengers’ historical ticket bookings were used to forecast the demand to come in a ticket booking period with least squares support vector machine. Three seat inventory control methods: non-nested booking limits, nested booking limits and bid-price control, were modeled under a single-fare class. Different seat inventory control methods were compared with the same demand based on ticket booking data of Train T15 from Beijing West to Guangzhou. The result shows that the dynamic non-nested booking limits control method performs the best, which gives railway operators evidence to adjust the remaining capacity in a ticket booking period.

Uncertain Programming for Network Revenue Management

The mathematical model for airline network seat inventory control problem is usually investigated to maximize the total revenue under some constraints such as capacities and demands. This paper presents a chance-constrained programming model based on the uncertainty theory for network revenue management, in which the fares and the demands are both uncertain variables rather than random variables. The uncertain programming model can be transformed into a deterministic form by taking expected value on objective function and confidence level on the constraint functions. Based on the strategy of nested booking limits, a solution method of booking control is developed to solve the problem. Finally, this paper gives a numerical example to show that the method is practical and efficient.

순차적으로 출발하는 여객노선에서 고객의 의사결정을 고려한 좌석재고 통제문제에 대한 모의실험 분석

We conduct the future studies suggested by Park and Seo (3). They considered a seat inventory control problem in which flights depart sequentially during a similar time-interval and passengers purchase available seats depending on individual customer choice behavior. Customer choice behavior can lead to one among a horizontal shift, a di- version-up, and a booking loss when a desired fare class is unavailable. We investigate how seat availability calculation method, booking limit control mechanism, seat inventory capacity, number of booking class, type of seat demand influence on revenues in an airline industry through thorough computer simulation experiments.

Research on Multi-Segment and Multi-Class Seat Inventory Control with Overbooking

In order to achieve a real-time control method and technical support for airlines, the integrated modeling issue of airlines about seat inventory control and overbooking has been researched in this paper. And the integrated control static model has been established by the stochastic programming method, based on ticket sales process to be simulated as a queue process and profit maximization to be objective function. So the problem is decomposed into a plurality of single-segment and single-class seat inventory control problem. Furthermore, the optimal decision-making equation of limiting reservation for each class has been deduced from the model. Finally, the validity of model and calculation method are shown by the full analysis of practical application of the model.

Seat inventory control for sequential multiple flights with customer choice behavior

This paper considers a seat inventory control problem in which flights depart sequentially and passengers purchase available seats depending on customer choice behavior. Customer choice behavior can lead to either a horizontal shift or a booking loss when a desired fare class is unavailable. This problem is mathematically challenging and intractable via exact mathematical models. As an alternative heuristic approach, this paper develops a simulation-based greedy grid-search algorithm and illustrates simulation experiments using the newly developed algorithm. This paper obtains encouraging numerical results with the approach proposed here, but additional studies are required for accommodating more general assumptions such as booking arrival patterns, booking control mechanisms (e.g., cancellation and overbooking) and strategic customer behavior.

Revenue management with aircraft reassignment flexibility

A well-studied problem in airline revenue management is the optimal allocation of seat inventory among different fare-classes, given a capacity for the flight and a demand distribution for each class. In practice, capacity on a flight does not have to be fixed; airlines can exercise some flexibility on the supply side by swapping aircraft of different capacities between flights as partial booking information is gathered. This provides the airline with the capability to more effectively match their supply and demand. In this paper, we study the seat inventory control problem considering the aircraft swapping option. For theoretical and practical purposes, we restrict our attention to the class of booking limit policies. Our analytical results demonstrate that booking limits considering the swapping option can be considerably different from those under fixed capacity. We also show that principles on the relationship between the optimal booking limits and demand characteristics (size and risk) developed for the fixed-capacity problem no longer hold when swapping is an option. We develop new principles and insights on how demand characteristics affect the optimal booking limits under the swapping possibility. We also develop an easy to implement heuristic for determining the booking limits under the swapping option and show, through a numerical study, that the heuristic generates revenues close to those under the optimal booking limits. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011

MILP Model For Network Revenue Management In Airlines

<p class="MsoNormal" style="text-justify: inter-ideograph; text-align: justify; margin: 0in 36.1pt 0pt 0.5in; layout-grid-mode: char;"><span style="mso-bidi-font-style: italic;"><span style="font-size: x-small;"><span style="font-family: Times New Roman;">Seat inventory control is an important problem in revenue management which is to decide whether to accept or reject a booking request during the booking horizon in airlines. The problem can be modeled as dynamic stochastic programs, which are computationally intractable in network settings. Various researches have been tried to solve it effectively. Even though dynamic (and stochastic) programming (DP) models can be solved it optimally, they are computationally intractable even for small sized networks. Therefore, in practice, DP models are approximated by various mathematical programming models. In this paper, we propose an approximation model for solving airline seat inventory control problem in network environments. Using Linear Approximation technique, we will transform our problem into a concave piecewise LP model. Based on the optimal solution of ours, we suggest how to implement it for airline inventory control policies such as booking limits, bid-price controls and virtual nesting controls.</span></span></span></p>

Airline Revenue Management Under Imperfect Market Segmentation

We study the dynamic seat inventory control problem for a single-leg flight with multiple fare classes under imperfect market segmentation, when customers book the lowest available class whose restrictions they can meet and whose fare they are willing to pay. This is more realistic than the usual assumption that each customer requests a particular fare class, and is lost when it is not available. We derive theoretical properties of the value functions and optimal policy for a generic single-resource revenue management problem, of which this problem is a special case. In particular, we show that a nested policy is not necessarily optimal when a fare class is underpriced or not sufficiently restricted. Numerical examples show that incorporating imperfections of the market segmentation in the booking policy leads to significant revenue gains.

Revenue Management Games: Horizontal and Vertical Competition

A well-studied problem in the literature on airline revenue (or yield) management is the optimal allocation of seat inventory among fare classes, given a demand distribution for each class. In practice, the seat allocation decisions of one airline affect the passenger demands for seats on other airlines. In this paper, we examine the seat inventory control problem under both horizontal competition (two airlines compete for passengers on the same flight leg) and vertical competition (different airlines fly different legs on a multileg itinerary). Such vertical competition can be the outcome of a code-sharing agreement between airlines, because each airline sells seats on the partner airlines’ flights but the airlines are unwilling, or unable, to coordinate yield management decisions. We provide a general sufficient condition under which a pure-strategy Nash equilibrium exists in these revenue management games, and we also compare the total number of seats available in each fare class with, and without, competition. Analytical results as well as numerical examples demonstrate that more seats are protected for higher-fare passengers under horizontal competition than when a single airline acts as a monopoly. Under vertical competition the booking limit may be higher or lower, however, than the monopoly level, depending on the demand for connecting flights in each fare class. Finally, we discuss revenue-sharing contracts that coordinate the actions of both airlines.

Dynamic two-leg airline seat inventory control with overbooking, cancellations and no-shows

This paper formulates a discrete time, finite horizon Markov decision process (dynamic programming), for the two-leg airline seat inventory control problem. The dynamics of the passenger reservation process together with realistic elements of customer behaviour such as cancellations, no-shows and overbooking are explicitly considered. Mirroring the dynamic seat inventory control models for the single-leg flight, it solves the two-leg seat allocation problem with multiple fare classes, and generalises the formulation to the multileg airline seat inventory control problem. A computationally efficient model is developed and is shown to provide solutions that are within a few percentage points of the optimal solution.

A Dynamic Airline Seat Inventory Control Model and Its Optimal Policy

We consider an airline seat inventory control problem with multiple origins, one hub, and one destination. Passengers from the origins fly to the destination via the hub. Seat capacity of the hub-destination flight is fixed. Demands at origins are assumed to obey the Poisson process. To maximize the expected revenue, management faces decisions on allocating seats among competing origin-destination routes. This study presents a stochastic control model and develops optimal control rules. The basic model is subsequently distended to consider multiple fares on each route, time-dependent demands, and booking control on an extended network. A numerical example shows that optimal seat control is simple and efficient.

Revenue Management Games

A well-studied problem in the literature on airline revenue (or yield) management is the optimal allocation of seat inventory among fare classes given a demand distribution for each class. In practice, the seat allocation decisions of one airline affect the passenger demands for seats on other airlines. In this paper we examine the seat inventory control problem under both horizontal competition (two airlines compete for passengers on the same flight leg) and vertical competition (different airlines fly different legs on a multi-leg itinerary). Such vertical competition can be the outcome of a code sharing agreement between airlines, for each airline sells seats on the partner airlines’ flights but the airlines are unwilling, or unable, to coordinate yield management decisions. We provide a quite general sufficient condition under which a pure-strategy Nash equilibrium exists in these 'revenue management games', and we also compare the total number of seats available in each fare class with, and without, competition. Analytical results as well as numerical examples demonstrate that under horizontal competition more seats are protected for higher-fare passengers than when a single airline acts as a monopoly, while under vertical competition the booking limit may be higher, or lower, than the monopoly level, depending upon the demand for connecting flights in each fare class. Finally, we discuss revenue-sharing contracts that coordinate the actions of both airlines.

OR Practice—Application of a Probabilistic Decision Model to Airline Seat Inventory Control

The application of booking limits on the number of seats available at different prices on the same flight allows airlines to increase revenues. Effective seat inventory control by an airline depends on forecasts of future bookings, the revenue values associated with each fare type, and an ability to make systematic tradeoffs between booking requests so as to maximize total flight revenues. This article describes the implementation of a computerized system for making these tradeoffs and setting booking limits on future flights at Western Airlines in early 1987. The Expected Marginal Seat Revenue (EMSR) decision model developed for this application takes account of the uncertainty associated with estimates of future demand as well as the nested structure of booking limits in airline reservations systems. The Automated Booking Limit System implemented at Western made use of the EMSR model to set and revise booking limits periodically prior to flight departure. Although the system did not take into account several important components of the seat inventory control problem, a revenue impact test on a sample of actual flights showed a significant revenue improvement over the judgmental methods used previously.