This survey reviews the forty-year history of research on transportation revenue management (also known as yield management). We cover developments in forecasting, overbooking, seat inventory control, and pricing, as they relate to revenue management, and suggest future research directions. The survey includes a glossary of revenue management terminology and a bibliography of over 190 references.

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Revenue Management: Research Overview and Prospects

Given a flight schedule and set of aircraft, the fleet assignment problem is to determine which type of aircraft should fly each flight segment. This paper describes a basic daily, domestic fleet assignment problem and then presents chronologically the steps taken to solve it efficiently. Our model of the fleet assignment problem is a large multi-commodity flow problem with side constraints defined on a time-expanded network. These problems are often severely degenerate, which leads to poor performance of standard linear programming techniques. Also, the large number of integer variables can make finding optimal integer solutions difficult and time-consuming. The methods used to attack this problem include an interior-point algorithm, dual steepest edge simplex, cost perturbation, model aggregation, branching on set-partitioning constraints and prioritizing the order of branching. The computational results show that the algorithm finds solutions with a maximum optimality gap of 0.02% and is more than two orders of magnitude faster than using default options of a standard LP-based branch-and-bound code.

The fleet assignment problem: Solving a large-scale integer program

Disruptions in airline transportation systems can prevent airlines from executing their schedules as planned. Adverse weather conditions, congestion at airports, and mechanical failures often hinder a flight schedule. During such events, decision makers must reschedule flight legs, and reroute aircraft, pilots, and passengers. We present an optimization model that reschedules legs and reroutes aircraft by minimizing an objective function involving rerouting and cancellation costs. We develop a heuristic for selecting which aircraft are rerouted, and we provide proof of concept by evaluating our model using a simulation of airline operations. Finally, we revise the model to minimize crew and passenger disruptions.

Rerouting Aircraft for Airline Recovery

We consider the airline fleet assignment problem involving the profit maximizing assignment of aircraft types to flight legs. Although several basic formulations have been proposed, important network considerations are insufficiently treated in these formulations and the resulting solutions are often suboptimal. We propose a new formulation and solution approach that captures network effects and generates superior solutions. We quantify the benefits of our proposed approach in a case study using data from a major United States airline.

Itinerary-Based Airline Fleet Assignment

Recognizing that allowing variability in scheduled flight departure times can result in improved flight connection opportunities and a more cost effective fleet assignment, we present a generalized fleet assignment model for simultaneously assigning aircraft types to flights and scheduling flight departures. Our model, a simple variant of basic fleet assignment models, assigns a time window to each flight and then discretizes each window, allowing flight departure times to be optimized. Because problem size can become formidable, much larger than basic fleet assignment models, we develop two algorithmic approaches for solving the model. Our direct solution approach is good for speed and simplicity, whereas our iterative technique minimizes memory usage. Using data from a major U.S. airline, we show that our model can solve real, large-scale problems, and we evaluate the effects of schedule flexibility. In every test scenario, the model produces a fleet assignment with significantly lower costs than the basic model, and, in a separate analysis, the model is used to tighten the schedule, potentially saving aircraft.

Airline Fleet Assignment with Time Windows

A major problem for the airline industry is the assignment of airplane capacity to flight schedules to meet fluctuating market needs. Demand Driven Dispatch (D3) is an operating concept that addresses this problem. Utilizing a demand forecast which improves as flight departure approaches, aircraft are dynamically assigned to flights to better match the predicted final demands. The result, demonstrated in studies of actual airline systems, is an increase in passenger loads and revenues with simultaneously reduced costs for a net of 1–5% improvement in operating profits. Concept implementation is simplified by the prevalence of yield management systems which provide the forecasting capability, and the emergence of airplane families which provide the necessary operational flexibility. Implementation also requires frequent solution of extremely large aircraft assignment problems. These problems, which can be formulated in terms of a multicommodity network flow, can be solved with heuristic algorithms shown to...

Matthew E. Berge

Papers

Demand driven dispatch: a method for dynamic aircraft capacity assignment, models, and algorithms