Integrated revenue management approaches for capacity control with planned upgrades

Abstract

In many service industries, firms offer a portfolio of similar products based on different types of resources. Mismatches between demand and capacity can therefore often be managed by using product upgrades. Clearly, it is desirable to consider this possibility in the revenue management systems that are used to decide on the acceptance of requests. To incorporate upgrades, we build upon different dynamic programming formulations from the literature and gain several new structural insights that facilitate the control process under certain conditions. We then propose two dynamic programming decomposition approaches that extend the traditional decomposition for capacity control by simultaneously considering upgrades as well as capacity control decisions. While the first approach is specifically suited for the multi-day capacity control problem faced, for example, by hotels and car rental companies, the second one is more general and can be applied in arbitrary network revenue management settings that allow upgrading. Both approaches are formally derived and analytically related to each other. It is shown that they give tighter upper bounds on the optimal solution of the original dynamic program than the well-known deterministic linear program. Using data from a major car rental company, we perform computational experiments that show that the proposed approaches are tractable for real-world problem sizes and outperform those disaggregated, successive planning approaches that are used in revenue management practice today.

Introduction

Capacity control, which is considered to be the key component of modern revenue management, is concerned with the task of optimally selling a fixed perishable capacity within a given time horizon by controlling the availability of the products that make use of this capacity (see, e.g., Talluri and van Ryzin, 2004). However, traditional capacity control often ignores the fact that many firms in the service industry offer several products that are substitutable in the sense that the seller could fulfill a certain product request with a more desirable substitute from a prespecified set of alternative products. Examples include airlines selling economy, business, and first class seats and car rental companies offering many types of cars differing in size and features.

In this paper, we consider the situation when this substitution is provided at the original product’s price, which is called an upgrade. It is assumed that customers always accept upgrades to superior products if they are offered these at no extra cost. Conversely, if customers are urged to voluntarily buy a higher value product – in practice, this usually occurs at the time of fulfillment – this is termed an upsell. Upgrading and upselling can be beneficial if the selling firm faces a mismatch between supply and demand. This mismatch often occurs when capacity decisions have been determined for the long term, which is usual in traditional revenue management scenarios, while firms experience stochastic and seasonal demand. We assume that the capacity mismatch is relatively transient or not very pronounced; customers will therefore not strategically adapt to upgrades.

Two important aspects of upgrading are fairness and scope (see, e.g., Gallego and Stefanescu, 2009). Informally, upgrades are defined as fair if upgrade priority is given to customers who purchase higher quality products. Specifically, no customer should receive a higher quality upgrade than another who had originally bought a higher quality product. Regarding the scope of upgrades, two basic models can be distinguished: Full cascading, which allows upgrades to any higher quality product, and limited cascading, which is less flexible as upgrades are allowed only to the next higher quality product.

The research presented in this paper is motivated by an industry project conducted with a major car rental company. In fact, the car rental industry is one of the most important users of upgrades. As Geraghty and Johnson (1997) note, it is essential for car rental companies to undertake market segmentation by not only offering different products using the same resources but also by offering many different car types. This is especially important as some typical fencing conditions known from the airline industry, for example, advanced purchase restrictions, do not seem to work well in the car rental business (see, e.g., Carroll and Grimes, 1995). However, by offering many different car types, car rental companies cannot directly substitute one type for another but must consider a certain predefined upgrade hierarchy. The resulting supply-side substitution opportunities are inevitable as, although desirable, there still is no tight integration of fleet management and revenue management decisions in the car rental industry (see, e.g., Lieberman, 2007). Furthermore, as the differences in the cost are usually quite small, car rental firms have a common policy to acquire fewer economy cars than required and more compact or full-size cars. Through upgrading, the latter cars offer more flexibility if the demand situation changes.

Although the above examples illustrate an obvious need to explicitly incorporate upgrading opportunities in revenue management’s capacity control process, there is not much theoretical work on developing appropriate approaches. Practical implementations usually resort to rather simple heuristics, such as successive planning, which means that upgrade contingents on higher-valued resources are determined first and that, subsequently, the new virtual capacity is considered fixed for standard capacity control. Therefore, one of the contributions of this paper is the proposition of integrated dynamic programming decomposition approaches for capacity control with planned upgrades. Our approaches extend the well-known dynamic programming decomposition from traditional capacity control to additionally exploit the opportunities of planned upgrades. Furthermore, we show that the approaches are applicable to real-world scenarios in car rental revenue management and that they outperform common practice procedures, such as the successive planning of upgrade contingents and capacity control decisions.

The paper is structured as follows: Section 2 provides a brief review of related literature. In Section 3, we present two dynamic programming formulations for capacity control with planned upgrades that are adopted from the literature. Based on these formulations, as our first contribution, we theoretically derive new structural insights that facilitate the control process under certain conditions that often occur in practice, such as single-leg airline capacity control and daily car rental capacity control. Based upon these models and insights, we then propose two different dynamic programming decomposition approaches for capacity control with planned upgrades, which is the second contribution of the paper (Section 4). While the first approach is specifically suited for multi-day revenue management problems that occur, for example, in the hotel and car rental businesses, the second approach is more general and can be applied in arbitrary network revenue management settings. In Section 5, we discuss the computational results from a simulation study based on real-world data obtained from our car rental industry partner. These results demonstrate the decomposition approaches’ practical applicability and their relative performance compared to other common control procedures, such as successive planning. We conclude with a summary of the key results (Section 6). The proofs of all propositions as well as complementary tables with additional information on the simulation study are provided in the Online Appendix.