Stochastic programming in revenue management

Airline revenue management aims to assign the right seat to the right customer with right prices at the right time. Due to the existence of large uncertainty in customer demand and the unavailability of perfect information, decisions must be made in advance. Also, such decisions are subject to constraints, such as seat availability, demand forecasts, and customer preferences. The objective of revenue management is to maximize the long term booking revenue. In this research, we studied two models in detail, the seat allocation model and the customer choice model based on preference orders. The seat allocation model is to decide the number of seats available for booking at class level by assuming the demands among booking classes are independent. The customer choice model is to assign seats at class level without forecasting demands individually. Both research topics in revenue management, the seat allocation optimization and customer choice optimization, are built by stochastic programming models.; We present a multi-stage stochastic programming formulation to the seat allocation problem that extends the traditional probabilistic model proposed in the literature. Because of the lack of convexity properties, solving the multi-stage problem exactly may be difficult. In order to circumvent that obstacle, We use an approximation based on solving a sequence of two-stage stochastic programs with simple recourse. Our theoretical results show that the proposed approximation is robust, in the sense that solving more successive two-stage programs can only improve the expected revenue. We also discuss a heuristic method to choose the re-solving points. Numerical results are presented to illustrate the effectiveness of the proposed approach.; Besides the strong uncertainty in customer demand, the customer's preference can make a difference in total revenue too. In our research, we assume that customers make choices according to personal preferences, such as preferences for connected trips or direct trips. We realize the fact that different customers might possess similar preference and behave. It becomes the idea to construct the customer preference orders. Instead of forecasting the demands by classes in seat allocation model, our preference order model requires the distribution information by preference orders. Essentially, this model is also a stochastic programming model. With properly implementing the model recommendation, the numerical experiment indicates that the preference order method tends to generate no less operating revenue than independent demand methods by catching more valued customers.; In this text, we also gave a detailed literature review in the Chapter 1 for most up-to-date airline revenue management progresses. Compared with existing research, we have made two major contributions. First, we proposed a network heuristic to improve the rolling horizon method with analytic justification; second, we proposed the first solvable network customer choice behavior model by mathematical programming. Those contributions open a way to incorporate the demands' distributional information and the customer choice behavior into the real airline booking optimization process.