Pricing and Revenue Optimization

This chapter describes the historical background of pricing and revenue optimization including the factors that have driven the growth of analytical approaches to pricing, such as the success of revenue management in the airlines, advances in information technology, the rise of e-commerce, and the success of machine learning. Pricing decisions have become exponentially more complex and dynamic to the extent that it is no longer possible to manage prices effectively using spreadsheets. The use of automated techniques to set and update prices dynamically has led to profitability improvements of 10% or more in many different industries.

This chapter introduces the basic concepts behind pricing and revenue optimization. It discusses common pricing challenges such as lack of consistent management, discipline, and analysis. I describe three purist approaches to pricing—cost-plus, market-based and value-based and explain the shortcomings of each. I define pricing and revenue optimization as a process for managing and updating pricing decisions across an organization in a way that most effectively meets corporate goals using mathematical analysis. I introduce the pricing and revenue optimization cube as a convenient way to think about pricing decisions across the organization and describe the steps in an effective pricing and revenue optimization process. I describe a closed-loop process for setting, evaluating and updating prices. Finally, I discuss the role of mathematical analysis and optimization in the pricing process and contrast explicit optimization with data-driven approaches.

This chapter introduces the price-response function, which describes how demand for a product changes as a function of price. The price-response function is a key component in pricing and revenue optimization. I show how the price-response function can be derived from the distribution of willingness to pay among potential customers and describe the properties that a proper price-response function should possess. I describe the most common measures of price sensitivity such as slope, elasticity, and hazard rate and extend these measures to the case in which a seller is offering multiple products that may compete with each other. I introduce the most common price-response functions including the linear, constant-elasticity, logit, and probit functions and describe their properties, as well as when they can be best used.

I show how a price-response function can be estimated from historical data about prices and demand. Ways in which historical data can be obtained include price tests, A/B tests, natural experiments, and regression discontinuity design. I show how regression can be used to estimate the parameters of different price-response functions including linear, exponential, and constant elasticity. I introduce measures of fit including root-mean-square error, mean absolute percentage error, and weighted mean absolute percentage error. I show how the availability of potential demand data can significantly improve estimation, and I introduce methods for estimating a price-response function when potential demand data are available. The estimation process is discussed, as well as challenges to estimation including collinearity and endogeneity and how they can be addressed. .

In this chapter I show how to calculate an optimal price. The first step is to determine an objective function to be maximized. Typically we assume that contribution is to be maximized, but in some cases, revenue may be an element in the objective function. I discuss how to calculate contribution. Given contribution and a price-response function, the optimal price must satisfy a set of conditions, such as marginal cost equaling marginal revenue and elasticity equaling inverse unit margin. I discuss the implications of these conditions for real-world prices and show how explicit optimization can be used to calculate an optimal price. I discuss how to address the case of multiple objective functions, when a seller might be interested in maximizing both profit and market share. Finally, I introduce a data-driven approach to finding an optimal price that does not require a price-response function.

Price differentiation is the practice of charging different prices to different customers for the same good or slightly different versions of the same good. In this chapter, I describe various techniques for using price differentiation to improve profitability including group pricing, channel pricing, regional pricing, and couponing. Some of the most effective tactics for price differentiation are inferior goods, superior goods, product lines, product versioning, and time-based differentiation. I show how to calculate optimal differentiated prices in the presence of arbitrage and cannibalization and discuss the implications of price differentiation for consumer welfare. One common approach to price differentiation is nonlinear pricing, in which purchasing multiple products together can be cheaper than purchasing them independently. I present models for two of the most common nonlinear pricing approaches: volume discounts and bundling.

Supply and capacity constraints are commonplace across many industries and can have a strong effect on optimal prices. I start by discussing the nature of supply constraints and the situations in which they occur. I then discuss how a seller can determine the optimal price to charge when faced with a supply constraint, and I introduce the important concept of opportunity cost. I extend the calculation of optimal prices to the case when a supplier has a segmented market and faces supply constraints. This leads to the tactic of variable pricing, which is used when a supplier has multiple units of constrained capacity and can change prices in order to balance supply and demand. I discuss examples of variable pricing from industries including ride-sharing, concerts, and sporting events.

Revenue management is a profit-maximizing tactic used by sellers with a fixed stock of perishable capacity. This chapter relates the history of revenue management and shows how revenue management is an application of price differentiation. I introduce revenue management tactics—the ways in which companies can manage their capacity to maximize return. The airlines and other travel-related industries were pioneers in revenue management. I show how computerized reservation systems and global distribution systems play major roles in the way that revenue management has been implemented in these industries. I discuss the role of ancillary revenue and incremental costs and how they influence revenue management in different industries. I describe how the effectiveness of a revenue management program can be measured and discuss the current status and future prospects of revenue management in different industries.

Capacity allocation is the problem of determining how many seats (or hotel rooms or rental cars) to allow low-fare customers to book when there is the possibility of future high-fare demand. I first analyze the two-class case in some detail. I then consider the multiclass problem, with an emphasis on the widely used expected marginal seat revenue (EMSR) heuristics. Next I discuss the dynamic multiclass problem. I then relax the independence assumption and discuss how booking limits can be set when demand in a fare class can depend on which other classes are currently open. I introduce a data-driven approach that does not depend on estimating parameters of a demand distribution. Finally, I discuss how the performance of a capacity allocation program can be measured and evaluated.

Network management is the problem of determining how to manage resource availability in the case when products can require multiple resources. Examples include hub-and-spoke airline networks as well as multiday hotel and rental car products. I introduce the network management problem, describe different types of networks, and discuss the industries in which network management is important. I show why the network management problem is complex and why a simple and intuitive greedy heuristic does not work well. I then present various approaches to the network management problem including linear programming, virtual nesting, and bid pricing. Finally, I discuss the issues involved in implementing network management.

Overbooking occurs whenever a seller with constrained supply sells more units than he has available to hedge against the possibility of no-shows or cancellations. The chapter begins with a short history of overbooking. I then characterize industries in which overbooking is used and introduce four different approaches to overbooking: a deterministic heuristic, risk-based policies, service-level policies, and hybrid policies. I show how booking limits can be determined under each policy in the case of a single price and an uncertain level of no-shows. I then present a data-driven approach to overbooking and discuss dynamic overbooking in the face of cancellations and multiple fare classes. Finally, I present extensions to the basic problem and discuss some alternatives to overbooking for managing cancellations and no-shows.

The goal of markdown management is to determine the timing and magnitude of price reductions that maximize revenue from a fixed stock of inventory. In this chapter I start by giving some background and show how, for certain goods and services, markdowns segment the market and provide a simple method by which retailers can profit from intertemporal price differentiation. I outline the markdown management process that retailers follow and some of the business issues that can constrain them. I formulate the markdown problem as a constrained optimization problem and outline the most common approaches to finding the optimal prices including explicit optimization and exhaustive search, or enumeration. I discuss the implications of strategic customers—those who anticipate future prices—on markdown policies. Finally, I discuss the use of markdown management systems and the experiences of companies using markdown optimization.

Customized pricing refers to the situation in which customers approach sellers with their desired product and the seller responds with a bid. In customized pricing, the seller can usually determine an individualized price for each customer and has access to information about failed bids as well as successful ones. I formulate the customized-pricing decision as an optimization problem and show how that problem can be solved to maximize the expected contribution margin from each bid. A key element in the customized-pricing problem is the bid-response function, which specifies the seller's expectation on how each customer will respond to his bid price. I show how bid-response functions can be estimated for different customers seeking to purchase different products. I then show how the customized-pricing model can deal with objectives other than maximizing expected contribution.

Classical approaches to pricing optimization assume that consumers are rational in that they choose among available alternatives in a way that maximizes the utility of the product purchased minus the price. However, both common experience and research show that this is not the case—customers are influenced by seemingly irrelevant factors such as how the price is presented and what prices are offered to other customers. In this chapter I describe the implications of customer irrationality for pricing in three categories: violations of the law of demand, price presentation and framing, and fairness. I discuss how these categories should be taken into consideration in pricing. Examples are drawn from Amazon, Coca-Cola, First National Bank of Chicago, and cruise lines, among other industries.