A Brief History of Revenue Management and Pricing
Introduction
Providing a definition of revenue management and pricing (RMP) as a field of scientific research is challenging. A widespread short definition of revenue management as a business practice (selling the right product, to the right customer, at the right price, to increase revenue), arguably coming from Robert Cross’ popular business book (Cross (1997)), has the advantage of simplicity and non-technicality, and is a good starting point to understand what the science is about. Talluri and van Ryzin (2004a), in the introduction of their book, proposed a more developed version of this definition: revenue management is demand-management, the systems making automated decisions about which product to sell, to which customer, at what price, where and when, in order to increase revenue. This definition works well for the airlines, hotel and brick-and-mortar retail setups (the original setups for revenue management). But this definition was produced before the 2010s explosion of online marketplaces. Online marketplaces transformed the field, from demand management to marketplace management (as noted in Lobel (2021)), and this shift is what makes the development of an all-encompassing definition of RMP science challenging. In line with the historical focus of the present essay, RMP can be defined historically. RMP, as an academic field of research, since its inception in the 1980s has broadened its scope, from the study of systems for automatically allocating seats to different fare classes to maximize revenue, first developed by airlines in the 1980s in the context of electronic distribution systems, to the study of systems for the automated fine-grained matching of supply and demand through pricing and other forms of control, enabling complex profit-making strategies, in the context of online marketplaces.
There is a large literature on the history of RMP as a field of scientific research. First, participants in the development of actual revenue management systems wrote books based on their rich recollections of the events (Cross (1997), Boyd (2007), Vinod (2021)), discussing the science behind the practice. Second, the main books on RMP also include well-informed and carefully crafted historical considerations (Talluri and van Ryzin (2004a), Phillips (2021); there is less history in Gallego and Topaloglu (2019), but for the reader interested in a comprehensive and systematic technical coverage of the scientific field, with an extensive bibliography, this book is second to none). Lastly, practitioners and researchers of revenue management have written historical papers, see Boyd and Bilegan (2003), and all the papers in the July 2016 issue of the Journal of Revenue and Pricing Management. One recent paper on the history of RMP as an academic field, written for the 65th anniversary of Management Science, stands out: Lobel (2021). Given this rich body of literature, the brief history told below can only be incomplete.
The process of emergence and broadening of the scientific field follows the “algorithmization” of the economy (as argued in Lobel (2021)). Decisions on demand management (which product to sell, to which customer, at what price) have become, since the 1970s, increasingly automated, taken away from human managers and delegated to algorithms. Two related underlying processes explain the emergence and growth of the algorithmic economy, and help us understand the emergence and dynamic of RMP science. First, changing market circumstances: in the last quarter of the twentieth century, demand became more diverse, heterogeneous, uncertain (the ‘tough new customer’, uninterested in standard mass market products and asking for customized products, features prominently in Robert Cross’ account of revenue management: see Cross (1997), pp. 11-15; see also Talluri and van Ryzin (2004a), pp. 11-16). Second, technological shifts enabled the development of electronic commerce. Airlines transformed their computerized reservation systems into global distribution systems in the 1960s, way before the use of the Internet for e-commerce – which became widespread only in the early 2000s. This evolving market and technological environment fostered the use of the nascent e-commerce infrastructure to address the newly individualized demand, and triggered the development of new technological systems with a new economic function: forecasting demand and dynamically optimizing the prices and the offer set of products. In the process, forecasting and optimization have become the object of a science, called RMP.
The science has then shaped, and been shaped by, the practice. The tight integration of theory and practice is a distinctive feature of the field. In particular, new business models, invented to respond to the new market circumstances, and the evolution of the e-commerce technologies, worked both as affordances and as legacies for RMP science. The story told below seeks to highlight the rich dynamic of the science in its interplay with business practices: how specific historically situated ways of framing the business problem, and specific historically situated ways to use the technological e-commerce environment, interacted with scientific developments.
The Airlines Capacity Allocation Setup: The 1980s
The story of revenue management started at American Airlines after the deregulation of the sector in 1978, see Cross (1997), Boyd (2007). Airline deregulation in the U.S. got its start in 1977 when President Jimmy Carter appointed Alfred Kahn of Cornell University as the head of the Civil Aeronautics Board (CAB). Kahn immediately started relaxing rules on fare setting and on the introduction of new routes. U.S. airline deregulation became official on the 24th of October 1978 when President Carter signed the Airline Deregulation Act into law. The CAB was then dismantled in 1985. Before 1978, airlines were regulated almost as a public service. Any opening or closing of a line, and any price change, required filing a request to the CAB. Prices were controlled, based on some simple mechanism allowing for a guaranteed rate of return for the airline. Likewise, most companies in Europe were state-owned and their prices regulated in the same way. Deregulation was, therefore, a necessary precondition for the airlines to be allowed to change prices quickly, and more broadly to set their prices as they wished, without providing a justification and disclosing their costs to the regulator. However, this is only one aspect of the story. Factors other than deregulation, i.e., already existing practices and technological factors, played an important role in the invention of revenue management in the airlines. Furthermore, deregulation shaped the pricing revolution in a more indirect way than just allowing for price changes, by triggering the emergence of new business models.
The Origins of Revenue Management
An early predecessor, or form of revenue management, was the overbooking methodology used in airlines in the 1970s. In the regulated world, customers could cancel their reservation, or just not show up, without incurring any financial penalty. In this context, overbooking (the practice of overselling, expecting a number of cancellations and no-shows) was a standard practice in the industry. According to Marvin Rothstein (1985), who was part of the operations research team at American Airlines which initiated research into overbooking as early as the mid-1960s in order to develop a scientific and systematic approach to the problem, Leendert Kosten, from Delft University in the Netherlands, was one of the first to describe the problem and provide a general model (Kosten (1960)). In the introduction of his paper, Kosten wrote: “Airlines have several problems in connection with booking. Customers may book for a certain flight some time in advance and are also allowed to cancel their bookings. As a result of this it is possible that an airplane leaves with some seats empty or that the airline, expecting some of its customers to cancel their booking, has sold too many seats. In both cases losses are the result. In this paper a booking policy that minimizes the expected losses is developed.” Kosten here is framing the airlines’ overbooking problem as the newsvendor problem, the balancing of the possible costs of carrying or selling too much vs. too little. The expression “newsvendor problem” comes from Morse and Kimball book (Morse and Kimball (1951)), where they were, apparently, the first to use the example of the newsboy (the newsvendor needs to decide how many copies of the daily newspaper to buy, or stock, at the beginning of the day, knowing the price, facing uncertain demand, with a perishable product, unsold copies being worthless at the end of the day). The problem itself had been framed by the British political economist Francis Edgeworth in the late nineteenth century, to determine the optimal cash reserve a bank should keep to meet uncertain demand for cash withdrawal by customers (Edgeworth (1888)). Arrow, Harris and Marschak (1951) are credited with the modern formulation of the optimal inventory problem: with fixed prices and an uncertain demand, what is the best amount to stock? Kosten used the newsvendor framing to address the airlines overbooking problem, inspiring the research into implementable models, and actual overbooking policies, at American Airlines and then elsewhere, in the 1960s and 1970s.
Rothstein actually mentions an earlier model which inspired the operations researchers working on overbooking in the 1960s at American Airlines, a model by Martin Beckmann (Beckmann (1958)). Beckmann’s model was more general and therefore less implementable than Kosten’s model. But Beckmann, a German economist, developed the model when working for the Cowles Commission, recently relocated at Yale University from the University of Chicago. Beckmann wrote on the airline overbooking problem while working closely with Arrow and Marschak, under the mentorship of the Dutch mathematician and economist Tjalling Koopmans, who was at the time pushing for the application of mathematical programming approaches to various economic problems, with a keen interest for transportation. Beckmann’s work shows the link with some fundamental and cutting-edge ideas, born in wartime planning, at the intersection of mathematics, economics, and operations research, ideas which would have a lasting effect on all these disciplines (both Koopmans and Arrow would later win the Nobel Memorial Prize in Economic Sciences).
For the history of revenue management properly speaking, a crucial step was the work of Ken Littlewood in the early 1970s. Littlewood worked in the operations research team at the British Overseas Airways Corporation, which would become British Airways in 1974. He presented the first newsvendor-like analysis of booking policies for airlines, yet instead of controlling bookings to maximize the number of passengers carried by flights, as in Kosten’s framing of the problem and in subsequent overbooking methodologies, he proposed to control bookings in order to maximize revenue, in a two-class ticketing system (Littlewood (1972)). The solution to this problem, the so-called Littlewood’s rule, later became crucial for the implementation of American Airlines revenue management system, when deregulation made the creation of new fares both easier and necessary for American Airlines survival, as explained below.
Therefore, before deregulation, there was a well-developed body of research and practices in overbooking for air travel. In the 1970s these models and methodologies were quite close to a form of revenue management.
On the computer technology side, long before deregulation, in the late 1950s, American Airlines partnered with IBM to develop a computerized system for flight booking. It was a crucial technological innovation, enabling airlines to manage a lot more reservations. SABRE (for Semi-Automatic Business Research Environment) was fully operational in 1964. The SABRE system made booking information available in real time in a centralized system. It processed thousands of reservations per hour whereby customers placed telephone calls to SABRE operators. In the mid-1970s, SABRE terminals were installed in travel agencies, as a response to the deployment of Apollo, United’s reservation system, in those same travel agencies and in large corporate customers’ offices. For the development of RMP, this new technological environment was crucial. The systems produced a wealth of data on customers’ booking and flying behavior, in a form more suitable to analysis than small paper cards. Besides, these systems made it possible for travel agents and large corporate customers to ‘see’ the flights directly. The booking systems used by major U.S. airlines had become global distribution systems in the mid-1970s; these were the first electronic marketplaces.
On the business side, deregulation mattered not just because it allowed “price freedom” but because, almost immediately afterwards, low-cost carriers entered the market. The spectacular story of the rise and fall of People Express has been told in many books and papers. A company like People Express operated at a much lower cost than American Airlines. People Express used a single model of plane to lower the cost of maintenance, operated only on the most popular routes between big cities, cross trained its staff so that gate agents could serve as flight attendants and had a non-unionized workforce. American Airlines could not possibly start a price war and match the low prices of People Express, nor could American carry on with much higher prices than its competition.
Robert Crandall, American Airlines CFO at the time (and soon-to-be CEO, in 1985), is credited with the “surplus seats” and segmentation ideas. Even though Crandall did not put it that way, his business intuition was what today we would call value-based pricing, i.e., charge more to customers who value the product or service more. Arguably, the practice is as old as business. The challenge is how to identify and separate customers into market segments according to the differences in customers’ valuations, or in the buyers’ “reservation prices.” In a recent paper, Haan et al. (2012) study an interesting example, one that shows both the ingenuity deployed to overcome this challenge, and how old value-based pricing is. Starting in 1429, Denmark charged a toll on ships passing through the Øresund Strait separating Denmark from Sweden. In 1567 the toll was changed from essentially a per-ship toll to a toll that was about 1.5% of the value of the cargo on the ship. To encourage ship captains to accurately estimate the value of their ship's cargo, Denmark stipulated that it had the right to buy the ship's cargo at the price given by the captain. This gave a strong incentive to the captain not to severely understate the value of his cargo. This was a form of self-selection mechanism. This form of taxation or pricing was later referred to as a Harberger(1965) tax. The business history is full of innovations in self-selection mechanisms like this one, explicitly designed in order to implement value-based pricing. Closer to Crandall’s problem, other famous examples of self-selection mechanisms are King Gillette in early 1900s, selling razor holders cheaply. He made his profit from selling razor blades over time. Wealthy people who shaved daily paid more than low-income customers who shaved only on Saturday. Another famous example is the IBM punched card and associated punch card machine, introduced in 1928. IBM made more money from the sale of punched cards than from the sale of the model 016, 024, 026, and 029 card punch machines. Big wealthy firms used a lot more cards than small, poor struggling firms, though they might have a similar number of 026 card punches. In all these examples, the firm finds ways to segment the market in order to exploit differences in willingness-to-pay, yet the firm does not create explicit segments or groups.
Value-based pricing, and the associated strategies to discover the differences in willingness-to-pay amongst customers, are therefore old, and widespread. When Crandall was facing competition by People Express, the phenomenon was also well-studied in economics. Economists use the notion of price discrimination. Crandall himself did not use that notion and the associated theory, yet since these ideas in economics provide insights into what he did, and into RMP more generally, it is worth reviewing them. The notion of price discrimination refers to the same process as value-based pricing, yet business practitioners usually prefer to use the term value-based pricing, in order to avoid the negative connotations associated with the word “discrimination”. Value-based pricing offers a more positive outlook: charging more to customers who value the product or service more. Value-based pricing also points towards a business strategy, while price discrimination is a concept in economics, built to answer a “why” question. Price discrimination in economics describes the practice of charging customers not based on costs but on their willingness to pay, thereby extracting more of the consumers’ surplus. More technically, a monopolist engages in price discrimination when prices for a similar product are in a variable proportion to marginal costs. Price discrimination therefore requires some kind of market power – which does not imply that price discrimination is necessarily detrimental to welfare, as for instance in the extreme case where firms could not survive if they do not engage in price discrimination. Price discrimination, and the economics of it, is a fundamental idea to understand RMP.
The earliest model comes from the nineteenth century French engineer Jules Dupuit’s pricing model for roads and bridges (Dupuit (1844)). Dupuit was a state engineer in charge of the design, construction and maintenance of roads, bridges, and canals. He argued that the decision on public works should not be made according to some measurement of the reduction in transportation costs for the goods carried by the vehicles using the road, bridge or canal, but according to a measure of the utility of the public work for those who use it. For Dupuit, the cost of construction should be covered by a toll, and the toll should be based on the utility, expressed in monetary value, of the various users, what we would call today their willingness to pay. In his paper, Dupuit explicitly draws inspiration from business practices of segmenting the market. Dupuit’s paper mattered a lot for the history of economics, as it is one of the first indications of the idea that the firm is facing a demand curve. He also hints at the ideas of marginal utility, and consumers’ surplus, away from the labor cost of production theory that dominated British classical political economy since Adam Smith.
The full theory of price discrimination is usually attributed to the Cambridge economist Arthur Pigou, who, following the famous Marshallian analysis of supply and demand curves and consumers’ and producers’ surpluses, presented three forms, or degrees, of price discrimination (see the fourth edition of The Economics of Welfare: Pigou (1932)). First-degree price discrimination is the one that a fully clairvoyant monopolist could implement, having direct access to the willingness to pay of its customers. This was for Pigou a theoretical construct. However, as we will see below, in the context of online marketplaces, either in retail or when using auctions for online advertising, the theoretical construct comes close to reality. Third-degree price discrimination in Pigou covers the segmentation performed by the firm, as when a firm sets some discount for seniors, explicitly creating groups. The most important case for the history of RMP is second-degree price discrimination, where the firm sets different terms of trade, different contracts, in order to force customers to self-select, revealing the differences in willingness to pay amongst the population of customers; as in the business practices mentioned above, implemented by Gillette or IBM.
Economists were also well aware of the power of auctions in getting buyers to reveal the value they attach to a good or service, or their reservation price. An early theoretical result is the sealed-bid second-price auction analyzed by Vickrey (1961); the Nobel Memorial Prize in Economic Sciences was awarded to Vickrey in 1996. In a Vickrey auction, the price paid is not the highest (“first-price”), but rather the second highest price, or more generally, the price of the highest unsuccessful bid. Under simple, plausible assumptions, Vickrey showed that the optimal bid for the buyers is to bid their true value or reservation price, therefore eliciting their valuations of the good or service to the sellers, thanks to the auction mechanism. For instance, Lucking-Reiley (2000) reports evidence that Vickrey-style auctions were used in the stamp collecting market since 1878. Starting in 1992, the U.S. Treasury started to sell some U.S. Treasury Bills (T-Bills) in essentially a Vickrey auction (see Garbade and Ingber (2005)). For a particular offering, each prospective buyer submits a sealed bid for how many T-Bills they wish to buy and the highest price they are willing to pay. There is a single clearing price charged to every successful bidder, equal to the lowest successful bid. When there are lots of bidders for a large quantity, there is only a small difference between the lowest successful bid and the highest unsuccessful bid. The eBay online auction site has used Vickrey type bidding starting as early as 1998. They called it proxy bidding. A problem with a Vickrey auction is that it is open to auctioneer cheating. The auctioneer can submit fake bids, so the second highest bid is just slightly less than the highest winning bid price. Moldovanu and Tietzel (1998) describe how the German author Goethe, when selling the rights to one of his works in 1797 in a Vickrey style auction, was a victim of such cheating. Auction theory therefore provides insights into what revenue management aims at. Indeed, auction theory in economics starts by acknowledging that both the seller’s minimum acceptable price and the buyers’ maximum price are private information. The seller and the buyers have no immediate interest in revealing that information. Auction theory speculates about the optimal mechanisms for discovering prices which clear the market given the acknowledgment of the private character of that information. Most RMP approaches use posted prices, as opposed to auctions, yet auctions theory illuminates what RMP tries to achieve, even with posted prices: the firm which posts a price can be considered as asking who is ready to buy at that price, as in a form of auction.
Interestingly, there was an early direct connection (as opposed to a parallel theoretical development) between auction theory in economics and the practice of revenue management. Vickrey himself considered using auctions in relation with airline pricing, and rejected it, on practical grounds (Vickrey (1955), cited in Beckmann (1958)). Aware of Vickrey’s work, Rothstein’s team at American Airlines also considered the use of auctions to solve the overbooking problem in the 1960s: in case of overselling, an auction would be held at the airport, paying the lowest bidder not to fly. Here again the solution was firmly discarded on practical grounds (Rothstein (1971)). Auction theory was therefore in the mind of airline operations research teams when deregulation hit. But, as in Vickrey’s 1961 paper, auction mechanisms were considered by operations researchers as theoretical constructs, i.e., speculative mechanisms to be explored in order to understand what the optimal solution to allocation problems would be, and more generally in order to understand pricing. Auctions have become a central component of RMP only later, in the 2000s, in particular in the online advertising context. Google sold ad space on its website using a Vickrey style auction as early as 2002, for various reasons Google switched to a first-price auction in 2019, as we will see below.
At the same – theoretical and explanatory – level, economists knew well before deregulation hit the airline industry that there could be another motivation than price discrimination for charging different prices to different users for the same product. In a context of limited capacity and uncertain demand, as when bookings are piling up for a scheduled flight, charging different prices could be a way to screen the demand in order to attract the more certain segments of it. Lower valuation customers are shifted off-peak, ultimately reducing the cost of capacity for all customers. This is a different motivation than price discrimination. As mentioned above, for economists, there is price discrimination when there is no change in costs. Furthermore, in economic theory price discrimination requires some market power. In the alternative model to price discrimination, the pricing policy is not motivated by the extraction of consumers’ surplus, the pricing policy is motivated by reduction in the cost of capacity. Therefore, in this alternative model, there could be price dispersion in highly competitive markets, i.e., without market power. This alternative model is called peak-load pricing, a pricing policy aiming at shifting off-peak the demand willing to do so (with lower valuation for the good or service provided), in order to reduce capacity costs. The first peak-load pricing model was developed by Marcel Boiteux, an economist working after the Second World War on pricing for the French public-owned monopoly for electricity generation and distribution, Électricité de France (Boiteux 1949, see Boiteux 1960 for an English translation). Air travel, with its fixed capacity, perishable product and uncertain demand, could be a good fit for the peak-load pricing model.
When People Express entered the market in the early 1980s and threatened American Airlines, there were therefore a wealth of business practices engaging in value-based pricing and market segmentation in many other industries. In parallell, economists described in sophisticated models the reasons to engage in price discrimination when there is market power, the ability of specific auction mechanisms to optimally reveal customers’ valuations, or, in the absence of market power, the practice of peak-load pricing, shifting demand off-peak in order to reduce capacity costs. These ideas all shed some light on why revenue management emerged – as opposed to how pricing decisions are made (for a very clear illustration of this distinction, see van Ryzin (2000) and van Ryzin (2016), and below).
Even though Robert Crandall did not explicitly put it that way, the business idea he came up with was what economists call second-degree price discrimination. Crandall acknowledged that American Airlines was operating at zero marginal cost on most of its flights. Indeed, most flights departed with empty seats. The cost of an additional passenger in that case is almost zero. Additional fuel costs are negligible, the number of crew members is fixed and independent of the number of passengers as it is set by safety regulations, and the cost of a free drink is negligible. Under the threat of low costs carriers like People Express, Crandall considered these seats as “surplus seats” for potential “surplus passengers”. These seats could be considered similar to those on a flight operated by People Express, and therefore could be priced as such.
Crandall’s segmentation idea was that People Express was tapping into a market, the leisure travelers, that did not exist in the regulated regime, when flying used to be a luxury product and airlines were content with their business customers. The leisure travelers were a new thing: they book early, are willing to stay over for the weekend, are price sensitive. These are families on holiday, couples getting away for the weekend, college students visiting home. American Airlines was familiar with business travelers: they book later, want to be back on Friday night with their families, have little flexibility, value schedule convenience the most, and are much less price sensitive because they are travelling with company money. Crandall proposed to reflect this observation in a sharp segmentation. American created a new fare (the super-saver fare), with a lower price, but available only for those who booked early (30 days in advance) and were willing to stay over for the weekend. These restrictions were entirely artificial, they had nothing to do with the cost of the ticket. The aim was the self-selection of the customers to avoid cross-cannibalization between the two segments as business customers would presumably not abide to the conditions associated with the low fare, thus creating fences.
Crandall’s new business vision shortly predated deregulation and the challenge raised by People Express. American’s first super-saver discounted fare was first introduced in 1977. This matters not just for the historical record, but also because it shows that deeper changes in market circumstances were at play before deregulation. In line with the steady rise in income per capita in the U.S. since the 1960s (Lamoreaux, Raff and Temin (2003)), a new, more heterogeneous and diverse demand for flying was developing in the 1970s. Crandall’s price discrimination idea was a response to this.
American Airlines’ Revenue Management System
However, when deregulation hit, discounted fares could not be offered on an ad hoc, “manual”, “on-and-off” basis on low demand flights departing empty. The pressure exerted by People Express was too great. For American, the risk of bankruptcy was real. Discounted fares could not be a peripheral practice anymore. The new thickness and heterogeneity of the market required more than a few discretionary discounted fares. But this raised a difficult question for American Airlines, namely the systematic identification of the “surplus seats” on each flight. American’s problem was to avoid cabins filled with leisure customers, therefore displacing high-paying business travelers. Thomas Cook, head of the operations research department at American, and Barry Smith and his team (at American Airlines Decision Technologies, the company that American Airlines created to sell the SABRE system and other decision support tools externally), are credited with the development of the first revenue management (or yield management, as it was called at the time) system; see Smith, Leimkuhler and Darrow (1992). They made a key breakthrough, because they narrowed down the problem posed by the success of People Express, which in the early 1980s was threatening to push American Airlines out of business, to an optimization problem: how many seats need to be protected for business customers in the SABRE system for each scheduled flight?
This framing of the problem cleverly exploited the technological affordances offered by the SABRE system. Two independent streams of demand could be isolated within the SABRE system and forecasted for each scheduled flight. Actually, only knowledge of the booking pattern of business customers was needed. This was the forecasting component, used to attach probabilities to numbers of business bookings on each flight. Then, there was a capacity allocation problem, or more technically in the language of operations research, an inventory control problem: how many seats to allocate to each fare class? The model developed at the time was static, the allocation was decided in advance, for a single scheduled flight. It was inspired by Littlewood’s work for British Airways (Littlewood 1972). The rule (the algorithm) was as follows: the number of seats in the cabin to be allocated to the low fare was determined by the marginal value of the inventory. One more seat can be added to the low-fare class, as long as the revenue of selling one more seat at the low fare was higher than the expected revenue of selling this seat at the higher fare. The optimization was a clever use of the technical affordances offered by the SABRE system. The control was a number of seats associated to each of the two fare classes, a quantity allocation, which means that for each booking request logged into SABRE by travel agents, the revenue management system, nested inside SABRE, would just provide an accept or reject response (the decision), based on the seats remaining in each fare class. The initial setup for RMP was shaped by a specific technological environment (the SABRE system) and underpinned by a specific business model (Crandall’s price discrimination idea).
The two-fare class seat allocation optimization was introduced in 1982, and the whole DINAMO system (for dynamic inventory and maintenance optimizer) was fully implemented in 1988. DINAMO was a true technological innovation. This was the first instance of the use of a large database and automated decisions to perform an economic function (pricing, and more broadly matching demand with supply). More practically, it also put People Express out of business in 1987.
The Expected Marginal Seat Revenue (EMSR) Heuristics: The Late 1980s
The EMSR methodology was introduced in the late 1980s by Peter Belobaba (see his PhD dissertation at the Flight Transportation Laboratory at MIT, Belobaba (1987), and the later publication of the methodology in Belobaba (1989)). These heuristics are based on the newsvendor idea and extend Littlewood’s rule, to manage more than two fare classes on a single flight. The EMSR approach had a tremendous effect on industry, where they are still in use. Belobaba was working for Delta Airlines and participated in the implementation of their revenue management system around 1987. His model involves a more sophisticated probabilistic approach, accounting for uncertainty in demand forecasting. Furthermore, Belobaba’s model uses nested booking control, not just booking limits. While the American Airlines model created two completely distinct inventories for the low-fare class and the high-fare class, Belobaba’s model retains the booking limit on low fares, but became ‘transparent from above’ (i.e., from the high-fare class): the high-fare class has access to all the inventory. Lastly, Belobaba’s model is more dynamic and allowed revisions of the allocation while the cabin was filing up. Overall, the model moved from the Littlewood two-fare class model to an n-fare class model. As a result, in the late 1980s, airlines could optimize for bookings made up to 365 days in advance, opening and closing up to 26 fare classes.
The Growth of Revenue Management and Pricing: The 1990s and 2000s
In the late 1980s, Belobaba’s EMSR heuristics, and more broadly the understanding of airline revenue management systems as a successful application of the newsvendor problem, attracted the attention of the operations research scholarly community. Yet, academic work remained scant. RMP truly became a large and clearly identified subfield of operations research in the 1990s. From the early 1990s to the late 2000s (when RMP started to expand into various online marketplace settings, transforming RMP as an academic field), RMP grew around three topics: dynamic pricing (where price, and not quantity allocation, is the control), network revenue management (where the firm sells products that are bundles of resources), and choice modelling (improving the forecasting component through a better appraisal of the customers’ behavior, in particular their response to price), the latter topic being connected to assortment optimization (the optimization of the subset of products offered to customers, a third form of control, alongside quantity-based revenue management and price-based revenue management).
A New Framework, Price-Based Revenue Management: The Early 1990s
An important contribution for the expansion of the field was a paper by Guillermo Gallego and Garrett van Ryzin published in 1994 (Gallego and van Ryzin (1994)). The paper mattered on two different levels: as the first foray into retail, and maybe more importantly, as a new intellectual framework, a new way to think about revenue management, in relation to pricing.
The paper first addressed a problem in retail. The paper was motivated by research done for Federated Department Stores (a large conglomerate that included Macy’s). This is historically significant, as business historians tell us that the new diversity of individual tastes was a challenge for department stores in the U.S. since the late 1970s (Lamoreaux, Raff, and Temin, (2003); on Sears, Roebuck as a case in point, see Raff and Temin (1999)). Facing a new heterogeneous demand, much less interested in the standard white shirts and white bed sheets, the large department stores buyers made more mistakes, with inventories piling up. The department stores were also facing the competition of new businesses like The Gap and The Limited, two companies mentioned in the introduction of the van Ryzin and Gallego paper, which responded to these new market conditions with a new business model: garments required eight months to be assembled overseas, but the sales horizon was nine weeks. This short sale season was the new rule in the fashion industry in the 1990s. In this new business model, shorter lead time and offshore production were coupled with technologies leveraging data on what was selling (style, color, size), in every time period and every location, in order to better know the demand and adjust orders and assortment accordingly, but also to manage prices, markdowns, and therefore inventories much more flexibly. Retail was facing a problem surprisingly similar to the airlines.
Gallego and van Ryzin show that this new business model created a fixed inventory (no adjustments of supply were possible), a finite time horizon, and a perishable product. As this new way of producing and selling fashion items became the norm in large segments of the industry, pricing, and more specifically, markdowns could and, according to the two authors, needed, to be optimized, by leveraging the data generated over repeated short selling seasons. The two authors sought to go beyond a crude trade-off: slashing the prices when one comes closer to the end of the season, in order to get rid of the inventory left, but when making sales as time goes on, the product becomes scarce, and there is an incentive to raise the price.
Gallego and van Ryzin here used intensity control theory and applied it to the price-demand relationship. The general framework was dynamic programming, with its distinctive recursive approach, and this was new. Dynamic programming comes from Bellman’s work in the 1950s at the RAND Corporation (Bellman first described the problem in a RAND report released in 1951, a first presentation of the theory of dynamic programming is in Bellman (1954)). What was new was thinking about pricing as a dynamic programming problem. The authors modelled demand as the rate of arrival of customers in the store, a Poisson process. Events (the arrival of customers) are unrelated to each other and independent of each other, they are random, but the average time between the events can be known. This rate of arrival (or intensity of demand) was modelled as a function of price. The paper then develops a closed form solution, providing the entire pattern of prices for a rate of arrival that is an exponential function. The model determined the intensity of demand that maximized revenue, as a function of the level of the inventory and the time left. The price decreases slightly with time, but a new sale (which decreases inventory) may slightly raise the price.
The Gallego and van Ryzin model assumes that the retailer has granular and real-time data available about inventory and the customers’ rate of arrival. The model also assumes that the retailer has full price flexibility and can change prices continuously in real time. These assumptions were ahead of what existing information systems in brick-and-mortar retail could handle in the early 1990s (but markdown optimization eventually became a cornerstone of online retailing; see Friend and Walker (2001), showing that markdown optimization was still a new practice in brick-and-mortar retail in the early 2000s). The authors were well aware of this, and therefore the Gallego and van Ryzin paper has a second aim, broader than the paper’s technical contribution per se. It shows that airline revenue management can be considered as an idiosyncratic form of dynamic pricing, with limited price flexibility. In the airline setup, fare classes are discrete, with prices set in advance, and the revenue management system makes decisions on when to close a fare class, which can be conceptualized as a price increase. Viewed in this light, the restrictions (Saturday-night stay, advance-purchase), the fences, the segmentation, choke the demand curve. Instead of using quantity rationing to control demand (the allocation of seats to different fare classes), the paper suggests it is more profitable to directly use prices to match demand with the existing supply. More broadly, it demonstrates that a new class of pricing problems (fixed inventory and perishable assets), common to airline revenue management and retail markdown optimization, can be approached using a dynamic programming framework.
The message of the paper was not that airlines should adopt dynamic pricing hic et nunc. The authors were aware that even if, from a theoretical point of view, the use of pure pricing as control is more profitable, airlines did not have much of a choice in the matter, because of the technological and market environment described above. The contribution was a new way of framing the problem and thinking about it, hence the importance of the paper for RMP as a scientific field. The paper is considered as a building block of RMP science because it showed that capacity allocation decisions in airline revenue management and pricing decisions were inextricably linked. To put it differently, it subsumed capacity allocation under a broader class of pricing problems, ready for a new approach rooted in operations research. Operations research on the supply-side was a well-developed academic field, but the coordination of supply-side decisions with demand-side decisions was new, and the Gallego and van Ryzin paper provided a framework to approach it scientifically. Operations researchers could go to the market, so to speak, and add to supply-chain optimization questions (exogeneous demand, price fixed, decisions within the firm), demand and market management questions. The tactical and granular matching of supply and demand could be tackled with the operations research toolkit.
Tackling the Network Effect: The Early 1990s
The second major topic for RMP science in the 1990s was the network problem. Here again, a new business strategy opened up a new problem for RMP science. After deregulation, large airlines in the U.S. developed their hub-and-spoke structure. Long before deregulation, one of the Icelandair’s predecessors, Loftleiðir – known as Icelandic Airlines internationally - pioneered the hub-and-spoke system in 1953. It had flights from about a half dozen cities in the U.S., connecting at the hub at Keflavik airport in Iceland, and then connecting to about a half dozen cities in Europe, thus providing low-cost service to about 36 different origin-destination markets. After deregulation, the hub-and-spoke structure enabled the major U.S. airlines to serve more destinations domestically and internationally with a relatively low number of flights. There might not be many people who would like to fly from Fargo to Charlotte, but there are many people who would like to fly out of Fargo to somewhere else. For major U.S. airlines the hub-and-spoke structure became a crucial competitive advantage against carriers like People Express, which operated only point-to-point flights on routes in high demand to keep operations simple and costs low.
The post-deregulation growth of the hub-and-spoke structure greatly complicated the revenue management problem, or, more positively, opened up new opportunities for incremental revenue. The first revenue management systems were leg based. But depending on demand and fares, it might be more profitable, in many cases, to accept a booking for a low fare which consume two resources (i.e., two flight legs), than to accept a high fare booking request for flying only one of these legs. Accepting too many of the latter could displace the former, and incur a loss of revenue. The leg-based optimization, as in the Littlewood-inspired original framework, could therefore be suboptimal, because it does not factor in the network effect.
Airlines quickly developed practical solutions to the problem. Barry Smith and his team are credited with implementing the first approach, called virtual nesting, at American Airlines (the story is told in Smith, Leimkuhler and Darrow (1992); the first mention of virtual nesting was in an American Airlines technical report, Smith (1986), quoted in Vinod (2021)). Virtual nesting was a form of control which tackled the network problem within the existing system, i.e., the leg-based accept/reject decisions using the EMSR heuristics. The idea was to map origin-destination fares into each leg (“backward”, so to speak), a process called indexing. On each leg, there were now what was called “buckets” containing a range of fare values, including various origin-destination fares of similar values. The EMSR heuristics could be applied to these buckets, in order to determine booking limits for each bucket. For each origin-destination fare booking request, the booking system checked availability on each leg: an origin-destination fare could for instance have access to all capacity on one leg, but only some of the total capacity on the other leg.
How did the indexing work? How to compute the value of an origin-destination fare on each of the legs it consumed, in order to be able to assign the origin-destination fare to a bucket in each leg? This could be done using linear programming. Solving a linear program provides the opportunity costs of the other resources used by the origin-destination fare. The value of an origin-destination fare on one leg was the total value of the fare minus the opportunity costs of the resource on the other leg. This set a value for each origin-destination fare on each leg, and put it in a bucket on each leg. Then, as already mentioned, the EMSR heuristics (inspired by the Littlewood two-fare classes model) can be used, based on a forecast of the total demand for each bucket. The virtual nesting approach implied very limited change to the technological system. That was its main justification, showing here again the importance of technology, both as an affordance and a legacy, in shaping the problems and the solutions in RMP.
RMP science soon proposed a new approach to the network problem. It was first developed in Elizabeth Williamson’s PhD dissertation, based on research done at the MIT Flight Transportation Laboratory (Williamson (1992)). Elizabeth Williamson presented her work at the 28th annual symposium of the Airline Group of the International Federation of Operational Research Societies - AGIFORS - in New Seabury, Massachusetts, where Barry Smith presented a similar approach (Smith and Penn (1988)). Robert Simpson, who was with Peter Belobaba in Elizabeth Williamson’s PhD dissertation committee, was also working on similar approaches at the time (Simpson (1989)). Williamson proposed to use bid-price controls, a particularly elegant and economical form of control. A booking request for a product (an origin-destination fare) is accepted if the fare is higher than the sum of the bid prices for each of the resources (the flight legs) the product uses.
The problem that followed was how to calculate the bid prices? Williamson framed the network problem as one of allocating different resources (seats in a flight leg) to competing uses (origin-destination fares), in order to maximize revenue. Bid prices can, therefore, be calculated using a linear programming approach. In the linear program, the resources are mapped into the origin-destination products which use them. Williamson’s approach was deterministic, using mean demand as if demand for each origin-destination fare was known with certainty, which provides a set of inequalities. The other set of inequalities was provided by each flight capacity. The number of seats allocated to each fare class should be less than demand and/or capacity. The objective function was to maximize revenue (the prices for each origin-destination fare class being set in advance) given these two constraints (demand and capacity), by finding the number of seats to allocate to each fare class. Solving the linear program generates an allocation of seats to each origin-destination fare class, but it also gives the shadow prices, the marginal cost of capacity, the cost of parting with one unit of capacity, the break-even point for the airline in a way. These can be used as bid-price control, giving to this form of control a sound economic interpretation.
Williamson’s bid-price controls computed by solving a deterministic linear program had a tremendous effect on practice. Hotels were the first to implement the new approach. Before Williamson’s work on the deterministic linear program, hotels had understood how beneficial the revenue management tactics used in the airlines could be for them. The hotels setup is very similar to the airlines’: fixed inventory (the number of rooms), perishable product (an unoccupied room for one night is a net loss in revenue), variable and uncertain demand. Yet the airlines original framework, the two-fare classes quantity control model, did not work in hotels. In hotels, the length of stay is as important as optimizing revenue on each single night. Folklore says that this recognition came in the late 1980s, when Bill Marriott, CEO of Marriott International, after a lunch with Robert Crandall, tasked Richard Hanks and his team with implementing revenue management at Marriott. Hanks and consultants from Aeronomics had identified the length-of-stay issue in the context of Munich Oktoberfest (the story is told in Cross (1997), pp. 139-142; and in Hanks, Cross, Noland (1992)). Selling all the rooms to high-rate demand in mid-week at peak-load would displace low-rate customers with longer lengths of stay (the ones who would like to check-in before the fest and/or check out a few days after), customers who would fill the hotel in off-peak periods when demand is low. Optimizing revenue for each night would incur a loss of revenue, when the whole week is considered. Controlling for the length of stay was, therefore, central in hotel revenue management. Marriott first developed some ad hoc rules, but from there, the hotel problem could be conceptualized as a network revenue management problem. Hotels sell more products than an airline, each product being a length of stay starting on a specific day at a specific rate, making systematic virtual nesting cumbersome. Hence hotels were the first to use the economical bid-price control with the deterministic linear programming computation (Holiday Inn in 1992, Club Med in 1993, with SABRE: Vinod (2021), p. 170). Decision Focus Incorporated developed the first system for Scandinavian Airlines in 1992, after implementing it for Hertz car rentals (Phillips (2021), p. 265), and American Airlines moved from virtual nesting to bid-price controls in 1998. Virtual nesting based on EMSR heuristics is still in use today in airlines, and the transition to bid-price control continues.
Approximations for the Network Problem: The Mid-1990s
Starting in the mid-1990s, RMP scholars approached network revenue management from a dynamic programming perspective, derived and translated from the Gallego and van Ryzin dynamic pricing framework (see Gallego and van Ryzin (1997) for this extension).
The dynamic programming approach was interesting because it relaxed the worst-case scenario assumption embedded in the original approach, which assumed that all the low-fare demand arrives before the high-fare demand. Dynamic programming also helped to easily factor in the model cancellations and overbooking. But the dimension of the dynamic programming network problem was mind-blowing. A major airline in the mid-1990s could manage 4000 flight legs (the resources) and 500,000 origin-destination fares (the products), with 200 seats in each cabin. This so-called “curse of dimensionality” made it impossible to use dynamic programming in practice.
Yet the dynamic programming approach provided grist for the RMP research mill. RMP researchers used dynamic programming to study the structure of the optimal solution to the network problem and develop a theoretical backbone for the already existing approximations, like Williamson’s approach. The dynamic programming framework also fostered, in the 1990s and up to today, new approximation methods. A landmark result was presented in a paper by Talluri and van Ryzin (1998). They showed the optimality of bid-price controls computed by solving a deterministic linear program.
This large scientific production (for a review of the large body of work on approximation methods for network revenue management produced by RMP science in the 1990s, see McGill and van Ryzin (1999)), which built on the use of dynamic programming as a theoretical framework, participated in changing the way the inventory control problem was considered in the airlines, relaxing the assumptions on demand arrivals, and accompanying the move towards bid-price controls computed by solving a deterministic linear program. There was, indeed, a heated debate in the 1990s between the proponents of virtual nesting and those of bid-price controls (see Boyd and Bilegan (2003)). The former accused bid-price controls of being “unsafe” in practice, the latter showed that bid-price control, with bid-prices computed by solving a deterministic linear program, were a near-optimal approximation. This knowledge of the structure of the optimal solution was particularly valuable to guide the development of implementable systems, towards bid-price control.
Choice Modelling and Assortment Optimization: The 2000s
The increasing density, over the course of the 1990s, of the networks operated by global airlines made one of the basic assumptions of airline revenue management, independent demands, increasingly weak. When there were only two very different fares, as in the Littlewood-inspired original American Airlines revenue management model of the 1980s, the fences worked well. The business customers could not abide by the restrictions on the low fares. The fences segmented the market by creating two streams of demand, two separate markets. With the development of hub-and-spoke networks, the assumption of independent streams of demand, deeply embedded in revenue management systems, was becoming less accurate. Customers in the 1990s were obviously buying up (there is no leisure fare left, but I really need to go so I will buy a business fare) and buying down (my company cut my expenses and the ticket is now way too expensive, I will stay over for the weekend and buy the leisure fare). Customers could also consider different routes, non-stop flights and connecting flights, or consider leaving earlier or later (in the mid-1990s American had eight flights a day from New York to Tampa, plus connecting flights options).
RMP scholars, working on the increasingly dense airlines networks in the 1990s, understood the extent to which customers’ behavior had changed. The demand recapture (within a flight, when a fare class is closed) and the demand spill (to a different flight, earlier or later for instance) were becoming too important not to have an impact on revenue. Yet these behaviors were not captured in existing systems. Starting in the late 1990s, RMP scholars introduced discrete choice models in their revenue management models, in order to capture this behavior.
An AGIFORS presentation seems to have been the starting point of this body of literature (van Ryzin et al. (1999)). The first model, general and for a single resource, was proposed by Talluri and van Ryzin (Talluri and van Ryzin (2004)). The model was then applied to a network (Liu and van Ryzin (2008)). From there, a whole new topic of research, revenue management with dependent demand, emerged (a non-technical account of the importance and challenges of the shift to dependent demand models is provided in van Ryzin (2005)).
Revenue management models with dependent demand rested on the axioms of choice formulated by Duncan Luce. Duncan Luce was a mathematician by training, who aimed in the 1950s to introduce up-to-date mathematical methods into psychology (Luce (1959a), (1959b)). A second source of inspiration for the new revenue management models was the work of Daniel McFadden. McFadden was an econometrician, who developed measurement methods rooted in Luce’s axioms. McFadden’s logit model had computational simplicity and bridged the gap between theory and measurement of choice behavior (McFadden (1974); (1978)). McFadden’s methods inspired a large body of literature in travel demand modelling. More specifically, a book by Ben-Akiva and Lerman (1985), an extensive text about the methods and applications in choice modelling for travel demand, was a crucial inspiration for RMP scholars. These methods had long been used by airlines for flight scheduling, but not for revenue management.
Choice modelling was introduced in revenue management along the following lines. The first step was to redefine the unit of demand. It was not a customer who wants a certain flight at a certain price anymore. The aim became to model the customer’s choice at a specific point in time. In the second step, this choice was represented as a choice between a discrete set of alternatives. To each alternative, a utility can be attached, which was a function of the attributes of each alternative. It was a regression model, with utility being a function of price, of some ‘measures of convenience’ (hours of deviation from the requested departure time), with some dummy variables (whether or not the flight is non-stop), and a noise term (to account for unobserved attributes). Third step, given the utility attached to each attribute, choice probabilities could be calculated. If multiplied by the number of customers making the choice, one has an estimate of demand.
However, implementing choice-based revenue management in practice required a complete overhaul of the revenue management systems in use by the airlines or hotels in the late 1990s and early 2000s. At the most fundamental level, the forecasting component of the existing systems needed to be completely transformed. Choice-based revenue management models required changing the focus of data collection. To estimate the choice models, historical booking data for each fare class were useless, because they were focused on estimating demand for a product (an origin-destination fare). For choice modelling, one needed to have access to data about choice outcomes: what alternatives the customers were presented with and which choice they made. RMP scholars developed statistical techniques to recover the demand function, the so-called “uncensored demand”, from historical sales data (there is a whole literature on demand untruncation, for instance). RMP scholars also had in mind loyalty programs to track customers’ behavior over time. Third parties also sold more and more panel data. But in the scientific literature, from the early 2000s, the proper data source for estimating choice models was web clickstreams, which fulfilled all the requirements listed above.
Moreover, customer choice modelling led RMP scholars to rethink optimization. Choice-based revenue management became the springboard for a vast literature in assortment optimization (a review of this body work, which shows the link between choice-based revenue management and assortment optimization, can be found in Strauss et al. (2018)). In assortment optimization, the decision space changes. Based on the knowledge of customers’ choice behavior, and the profit contribution of each product (the marginal value of capacity), the assortment optimizer makes decisions on the set of products shown to the customers and dynamically manages this offer set in time. Assortment optimization is a new way of controlling demand, not quantity-based, not price-based, but steering customers using the set of products offered. Choice modelling and assortment optimization were a conceptual change, reframing the revenue management problem. The problem was not anymore to respond to the probability of a number of customers showing up to request a certain product. The problem was to respond to the probabilities attached to individual choices between products, and to structure the offer set dynamically, while bookings are piling up in the network.
Choice modelling and assortment optimization approaches are much more granular than the previous quantity-based framework, which was based on a stable segmentation by fences. With these new methods, the RMP research community was starting, in the 2000s, to show how the potentialities of a new technological environment for e-commerce, the Internet, could be leveraged in revenue management systems. The magnitude of the changes required in the systems already in place explains why airlines did not immediately implement choice-based approaches, and kept using the independent demand framework.
This changed in the late 2000s. The 2000s saw the rise of ultra low-cost carriers, like EasyJet or Ryanair in Europe (Vinod (2021), Chapter 5). Ultra low-cost carriers did not sell restricted fares, because they wanted to implement and manage a simpler, less costly, revenue management system. This meant that, close to departure, an unrestricted low fare could be available to anyone. These low-cost carriers also started, in the mid-2000s, to sell tickets online on their own website, bypassing the global distribution systems and the travel agents, to directly reach out to customers. Around the same time, online aggregators and metasearch engines (like Expedia and Travelocity) became widely used. The availability of the low fares became transparent to virtually anyone. Suddenly, for major global airlines, integrating choice-modelling into their revenue management systems was essential. With lightly restricted, or restriction-free fares, demand was only dependent on the fare being offered. Demand recapture (within the same flight) and demand spill (to other flights), both happening when a fare was closed, needed to be estimated, forecasted and optimized. This was what choice-based revenue management was all about.
From Demand Management to Marketplace Engineering: The 2010s
The growth of choice modelling and assortment optimization shows that the RMP literature was ready to leverage the new affordances offered by the nascent internet-based e-commerce infrastructure. It should, therefore, not be a surprise that, in the 2010s, RMP research invaded the new problem space opened by online marketplaces. This movement was not a straightforward application of the RMP methods presented above, which were developed mostly with the airlines, hotels and brick-and-mortar retail in mind. The rise of online marketplaces offered a new, thriving playground for RMP science. In particular, sophisticated pricing mechanisms blossomed in three completely new industries, and transformed RMP, from the science of demand management to the science of market management. The RMP science literature on these three industries is huge, and constantly expanding. The main areas of research are briefly listed below to illustrate how RMP has morphed into a science for marketplace engineering.
The first industry is online retailing. Online retailing provides a conducive environment for the dynamic pricing approach. Online retail makes the full use of price flexibility, to manage demand and inventory in real time, much easier than in brick-and-mortar retail. Online retail also offers a natural playground for assortment optimization approaches. In online retail, the structure of the set of products presented to customers, given what the e-retailer knows about the customer and state of the inventory, matters a lot for revenue. Yet moving to this online retail setup pushed RMP science beyond the choice modelling approaches developed in the 2000s, towards online learning. Recent work focusses on introducing online experimentation, such as induced price fluctuations to learn about demand, into the assortment optimization framework of the 2000s. Research done at companies like Amazon is a case in point.
The second industry is online advertising. The online environment enabled the development of advertising exchanges. In an ad exchange (like the one run by Google), each impression (the right to show an ad to a specific viewer on a webpage) is sold by publishers (for instance the New York Times website) to advertisers through an auction run in real time (i.e., in the second it takes to the viewer’s browser to load the webpage). In this context, there is a finite inventory (the number of impressions) - although uncertain, which is new for RMP - a perishable product (if no ad is shown to the viewer, the slot is lost), and a real-time dimension (the fraction of second for the page to load). These features make ad exchanges a relevant area for RMP. Ad exchanges also have an important specificity. The whole point of online advertising is that it offers new possibilities for targeted advertising. Therefore, the value of an impression for the advertiser depends on the information about the viewer and about the context (the webpage) sent to the advertiser. As a consequence, the publisher, or the intermediary (the ad exchange), can hardly know the value of the impression in advance. In this setup, demand valuations are utterly unpredictable, unlike for an airline that has been operating the same route for decades. This is why auctions are used in ad exchanges: auctions are great for eliciting value. The design of the auction mechanism by the ad exchange has become a rich new problem set for RMP. The control is not the price, but the optimization of the rules of the auction mechanism. Hence the fruitful connection between RMP and mechanism design in economics (for a non-technical presentation of the main research questions for RMP, see Korula, Mirrokni and Nazerzadeh (2016)).
The third industry is ride-sharing, with the emergence in the mid-2010s of businesses like Uber and Lyft. Here too, it is easy to see why RMP would invade this new space. Demand estimation techniques, choice modelling, the mix of price and allocation controls, all these 2000s approaches seemed useful for ride-sharing platforms. It is almost as if ride-sharing has been invented to apply RMP science. When a rider opens up the application, capacity (the number of drivers on the road) is fixed. At first sight, a straightforward application of dynamic pricing would be enough. Prices would be used to control demand and maximize revenue. The interesting new features of ride-sharing for RMP that prevents a straightforward application of a dynamic pricing approach are the following. First, ride-sharing platforms, when they first emerged, had less trouble dampening demand in cases of shortages, than attracting drivers on the road, where and when they were needed. The use of surge pricing is as much about controlling demand as it is about managing supply. Supply is less fixed than in the airline context, drivers are not directly controlled by the platform. Both prices and pick-up times can be used here as control (Yan, Zhu and Woodard (2020)). Second, for ride-sharing firms the aim is more complex than maximizing revenue hic et nunc. Growth is important for the service to be efficient (Lian and van Ryzin (2021)). This makes the objective of the optimization more complex. Third, the pricing problem in ride-sharing has an interesting spatial dimension. The pricing mechanism can be used to shape the directional flows, factoring in the cost of relocating the resources (the drivers) on the network (see Balseiro, Brown, Chen (2021)). RMP has truly become the science for the optimization of marketplace management: the tactical, fine-grained, real-time matching of supply and demand, for the pursuit of complex profit-making strategies, in the context of firms run as marketplaces.
Acknowledgements
The author thanks Linus Schrage, who provided references, ideas, suggestions and editorial assistance, and three anonymous reviewers. The author also would like to express his gratitude to the revenue management researchers and practitioners who have been incredibly generous with their time and shared their insights with the author on the history of the field: Prashant Balepur, David Brown, Guillermo Gallego, Philip Kaminsky, Sherri Kimes, Tara Mardan, Preston McAfee, Robert Phillips, Richard Ratliff, Dave Roberts, Kalyan Talluri, Huseyin Topaloglu, Garrett van Ryzin, Gustavo Vulcano, and Dawn Woodard. The views expressed here reflect only the author’s interpretation. The author welcomes any corrections and comments. Furthermore, the author, a historian of science and technology, is currently working on a comprehensive history of revenue management and pricing, as a business practice and a scientific field. The author is conducting interviews with researchers and practitioners, who have been active in revenue management and pricing, from the origins to today. Researchers and practitioners who would like to share any information, material or memories are most welcome to reach out.
Written by: Guillaume Yon; Center for the History of Political Economy, Duke University; contact: [email protected]. Edited by Linus Schrage.
Links and References
References
Arrow K., Harris T. and Marschak J. (1951). Optimal Inventory Policy. Econometrica 19(3), 250-272.
Beckmann J. (1958). Decision and Team Problems in Airline Reservations. Econometrica 26(1), 134-145.
Balseiro S., Brown D. and Chen C. (2021). Dynamic Pricing of Relocating Resources in Large Networks. Management Science 67 (7), 4075–4094.
Bellman R. (1954). The Theory of Dynamic Programming. Bulletin of the American Mathematical Society 60(6), 503-515.
Belobaba P. (1987). Air Travel Demand and Airline Seat Inventory Management. PhD Dissertation: Massachusetts Institute of Technology.
Belobaba P. (1989). Application of a Probabilistic Decision Model to Airline Seat Inventory Control. Operations Research 37(2), 183-197.
Ben-Akiva M. and Lerman S. (1985). Discrete Choice Analysis: Theory and Application to Travel Demand. Cambridge, MA: MIT Press.
Boiteux, M. (1949). La tarification des demandes en pointe. Revue générale de l’électricité (58), 321–40.
Boiteux, M. (1960). Peak-Load Pricing. Journal of Business 33(2), 157–79.
Boyd A. (2007). The Future of Pricing: How Airline Ticket Pricing Has Inspired a Revolution, New York: Palgrave.
Boyd A. and Bilegan I. (2003). Revenue Management and E-Commerce. Management Science 49(10),1363-1386.
Cross R. (1997). Revenue Management: Hard-Core Tactics for Market Domination, New York: Broadway Books.
Dupuit J. (1844). De la mesure de l'utilité des travaux publics. Annales des Ponts et Chaussées 8(2), 332-375.
Edgeworth F. (1888). The Mathematical Theory of Banking. Journal of the Royal Statistical Society 51(1), 113-127.
Friend S. and Walker P. (2001). Welcome to the New World of Merchandising. Harvard Business Review 79(10), 133-139.
Gallego, G. and Topaloglu, H. (2019) Revenue Management and Pricing Analytics, New York: Springer.
Gallego G. and van Ryzin G. (1994). Optimal Dynamic Pricing of Inventories with Stochastic Demand over Finite Horizons, Management Science, 40(8), 999-1020.
Gallego G. and Van Ryzin G. (1997). A Multiproduct Dynamic Pricing Problem and its Applications to Network Yield Management. Operations Research 45(1), 24-41.
Garbade K. and Ingber J. (2005). The Treasury Auction Process: Objectives, Structure, and Recent Adaptations, Current Issues in Economics and Finance, Federal Reserve Bank of New York 11(2), 1-11.
Haan M., Heijnen P., Schoonbeek L. and Toolsema L. (2012). Sound Taxation? On the Use of Self-Declared Value. European Economic Review 56 (2), 205–215.
Hanks R., Cross R. and Noland. P. (1992). Discounting in the Hotel Industry: A New Approach. Cornell Hotel and Restaurant Administration Quarterly 33 (1): 15-23.
Harberger, A. C. (1965). Issues of Tax Reform for Latin America. In Fiscal Policy for Economic Growth in Latin America: Papers and Proceedings of a Conference Held in Santiago, Chile, December, 1962. Baltimore, MD: Johns Hopkins University Press.
Korula N., Mirrokni V. and Nazerzadeh H. (2016). Optimizing Display Advertising Markets: Challenges and Directions. IEEE Internet Computing 20(1), 28-35.
Kosten, L. (1960) Een mathematisch model voor een reserveringsprobleem. Statistisca Neerlandica 14 (1), 85-94.
Lamoreaux N., Raff D. and Temin P. (2003). Beyond Markets and Hierarchies: Toward a New Synthesis of American Business History. American Historical Review 108(2), 404-433.
Lian Z. and van Ryzin G. (2021). Optimal Growth in Two-sided Markets. Management Science, 67(11), 6862-6879.
Littlewood, K. (2005) [1972]. Forecasting and Control of Passenger Bookings. Journal of Revenue and Pricing Management 4(2), 111-123.
Liu Q. and van Ryzin G. (2008). On the Choice-based Linear Programming Model for Network Revenue Management. Manufacturing and Service Operations Management 10(2), 288-310.
Lobel I. (2021). Revenue Management and the Rise of the Algorithmic Economy. Management Science 67(9), 5389-5398.
Luce D. (1959a). On the Possible Psychophysical Laws. Psychological Review, 66(2), 81-95.
Luce D. (1959b). Individual Choice Behavior: A Theoretical Analysis. New York: Wiley.
Lucking-Reiley D. (2000). Vickrey Auctions in Practice: From Nineteenth-Century Philately to Twenty-First-Century E-Commerce. Journal of Economic Perspectives 14(3), 183-192.
McFadden D. (1974). Conditional Logit Analysis of Qualitative Choice Behavior. In Zarembka P. ed. Frontiers in Econometrics. New York: Academic Press, 105–142.
McFadden D. (1978). Modelling the Choice of Residential Location. In Karlquist A. ed. Spatial Interaction Theory and Planning Models. Amsterdam: North Holland, 75–96.
McGill J. and van Ryzin G. (1999). Revenue Management: Research Overview and Prospects. Transportation Science 33(2), 233-256.
Moldovanu B. and Tietzel M. (1998). Goethe's Second‐Price Auction. Journal of Political Economy 106(4), 854-859.
Morse P. and Kimball G. (1951). Methods of Operations Research. New York: Wiley.
Phillips R. (2021). Pricing and Revenue Optimization. Second Edition. Stanford: Stanford University Press.
Pigou A. (1932). The Economics of Welfare. Fourth Edition. London: Macmillan.
Raff D. and Temin P. (1999). Sears, Roebuck in the Twentieth Century: Competition, Complementarities, and the Problem of Wasting Assets. In Lamoreaux N. ed. Learning by Doing in Markets, Firms, and Countries. Chicago: University of Chicago Press, 219-252.
Rothstein M. (1971) Airline Overbooking: The State of the Art. Journal of Transport Economics and Policy 5(1), 96-99.
Rothstein M. (1985). OR and the Airline Overbooking Problem. Operations Research 33(2), 237-248.
Simpson R. (1989). Using Network Flow Techniques for Origin-Destination Seat Inventory Control. Memorandum M89-1, Flight Transportation Laboratory: MIT.
Smith, B. (1986). O&D Control with Virtual Nesting. Internal Technical Report: American Airlines.
Smith B. and Penn C. (1988). Analysis of Alternate Origin-Destination Control Strategies. In Proceedings of the 28th AGIFORS Symposium, New Seabury, Massachusetts.
Smith B., Leimkuhler J. and Darrow R. (1992). Yield Management at American Airlines. Franz Edelman Award Paper. Interfaces 22 (1), 8-31.
Strauss A., Klein R. and Steinhardt C. (2018). A Review of Choice-Based Revenue Management: Theory and Methods. European Journal of Operational Research 271(2), 375-387.
Talluri K. and van Ryzin G. (1998). An Analysis of Bid-Price Controls for Network Revenue Management. Management Science, 44(11-part-1), 1577-1593.
Talluri K. and van Ryzin G. (2004a). The Theory and Practice of Revenue Management. Boston: Kluwer.
Talluri K. and van Ryzin G. (2004b). Revenue Management under a General Discrete Choice Model of Demand. Management Science 50(1), 15–33.
van Ryzin, G. (2000). The Brave New World of Pricing. Financial Times October 16, 2000.
van Ryzin, G. (2005). Future of Revenue Management: Models of Demand. Journal of Revenue and Pricing Management 4 (2), 204–210.
van Ryzin, G. (2016). Marketplace Engineering. Presentation at Cornell Tech September 2016.
van Ryzin G., Talluri K. and Mahajan S. (1999). Why We Need Discrete Choice Theory in Revenue Management. Presentation at the 39th AGIFORS Symposium, New Orleans.
Vickrey W. (1955). Some Implications of Marginal Cost Pricing for Public Utilities. Paper Presented at the 67th Annual Meeting of the American Economic Association, Detroit.
Vickrey W. (1961). Counterspeculation, Auctions, and Competitive Sealed Tenders. The Journal of Finance 16 (1): 8–37.
Vinod B. (2021). The Evolution of Yield Management in the Airline Industry. Origins to the Last Frontier. Cham: Springer.
Williamson E. (1992). Airline Network Seat Inventory Control: Methodologies and Revenue Impacts. PhD Dissertation: MIT.
Yan C., Zhu H., Korolko N. and Woodard D. (2020). Dynamic Pricing and Matching in Ride‐hailing Platforms. Naval Research Logistics 67(8), 705-724.