1. Introduction
During the one hundred years since the first flight of Orville and Wilbur Wright, the air transport industry has grown into a major sector of the global economy. Even more importantly, it has become essential to developing and maintaining cultural and economic links among countries and peoples. The airlines alone generated more than $300 billion in revenues in 2002, a lean year, and carried about 1.6 billion passengers, a number expected to grow at an annual rate of 4%-5% over the next 20 years according to most forecasts. According to the industry "air transport provides 28 million direct, indirect, and induced jobs world wide" and carries over 40% of the world trade of goods, by value" (Collaborative Forum 2003) After spending roughly its first 40 years trying to get off the ground, literally at times, the air transport industry has grown by leaps and bounds during the last 60, especially since the advent of the "jet age" in the late 1950s. Throughout that second period, operations research (OR) has played a critical role in helping the airline industry and its infrastructure sustain high growth rates and make the transition from a novelty that catered to an elite clientele to a service industry for the masses. More than 100 airlines and air transport associations are currently represented in AGIFORS, the Airline Group of Operational Research Societies, which has been active since 1961. Indeed, it is difficult to think of any single sector, other than perhaps military operations, with which operations research has been linked more closely. One of the reasons is that airline operations and, more generally, the air transport environment provide natural contexts for the application of OR techniques and models. A second is that the airline industry has consistently been a leader in the use of information technology and has relied heavily on the intensive use of computers over the years. The objective of this paper is to present a historical perspective on the contributions of operations research to the air transport industry, as well as to offer an assessment of some of the challenges that will be confronted next. Any reasonably thorough coverage of this subject would probably require an entire issue of this journal because the number of OR papers published on air transport easily exceeds 1,000 over the last 50 years. In view of the severe constraints on its length, the scope of the paper will instead be confined to a selected subset of air transport-related topics, where operations research has made some of its most significant contributions to date. Examples of important topics that are either not covered at all or are touched on peripherally include: aviation safety and security, airline fleet planning, airline staffing, airline maintenance planning, aircraft loading, and decision support tools for the management of airport operations (e.g., gate assignments). Moreover, the specific topics and contributions that are highlighted are presented in nonquantitative terms and largely reflect the authors' own interests. In addition to the bibliographic references associated with these contributions, other survey papers, which provide additional details and references, are cited whenever possible
Section 2 of the paper deals with the classical problems of scheduling, routing, and crew assignment in the airline industry. This is a context that is perfectly suited to the use of large-scale, discrete optimization approaches and, indeed, has motivated several methodological and computational developments in this vibrant area of OR over the years.
Section 3 covers airline revenue management, including overbooking, flight leg yield management and network revenue maximization. Through a combination of stochastic and optimization models, OR work in this area has generated significant additional revenues for the airlines ever since the late 1980s. Moreover, revenue management continues to be a field in which airlines are vying intensively for competitive advantage.
Section 4 surveys selected applications of OR to the study, planning, and design of the two major pieces of aviation infrastructure, the airports system and the air traffic management (ATM) system. Historically the emphasis here has been on stochastic models, as the questions addressed have focused on capacity, delays, and safety under conditions in which the probabilistic characteristics of the input parameters play a dominant role.
However, optimization models, both deterministic and stochastic, have found use in the intensive recent research on air traffic flow management, a topic also reviewed briefly in S4. Finally, S5 summarizes the main conclusions regarding the fundamental challenges faced by future research