Shared mobility systems have become a frequently used inner-city mobility option. In particular, free-floating shared mobility systems are experiencing strong growth compared to station-based systems. For both, many approaches have been proposed to optimize operations, e.g., through pricing and vehicle relocation. To date, however, optimization models for free-floating shared mobility systems have simply adopted key assumptions from station-based models. This refers, in particular, to the models’ part that formalizes how rentals realize depending on available vehicles and arriving customers, i.e., how supply and demand match. However, this adoption results in simplifications that do not adequately account for the unique characteristics of free-floating systems, leading to overestimated rentals, suboptimal decisions, and lost profits.
In this paper, we address the issue of accurate optimization model formulation for free-floating systems. Thereby, we build on the state-of-the-art concept of considering a spatial discretization of the operating area into zones. We formally derive two novel analytical matching functions specifically suited for free-floating system optimization, incorporating additional parameters besides supply and demand, such as customers’ maximum walking distance and zone sizes. We investigate their properties, like their linearizability and integrability into existing optimization models. Our computational study shows that the two functions’ accuracy can be up to 20 times higher than the existing approach. In addition, in a pricing case study based on data of Share Now, Europe’s largest free-floating car sharing provider, we demonstrate that more profitable pricing decisions are made. Most importantly, our work enables the adaptation of station-based optimization models to free-floating systems.
Over the last decades, shared mobility systems have become an integral part of inner-city mobility. Modern systems allow one-way rentals, i.e. customers can drop off the vehicle at a different location to where they began their trip. A prominent example is car sharing. Indeed, this work was motivated by the insight we gained in collaborating closely with Europe's largest car sharing provider, Share Now. In car sharing, as well as in shared mobility systems in general, pricing optimization has turned out to be a promising means of increasing profit while challenged by limited vehicle supply and asymmetric demand across time and space. Thus, in practice, providers increasingly use minute pricing that is differentiated according to where a rental originates, i.e., considering its location and the time of day. In research, however, such approaches have not been considered yet. In this paper, we therefore introduce the corresponding origin-based differentiated, profit-maximizing pricing problem for shared mobility systems. The problem is to determine spatially and temporally differentiated minute prices, taking network effects on the supply side as well as several practice relevant aspects into account. Based on a deterministic network flow model, we formulate the problem as a mixed-integer linear program and prove that it is NP-hard. For its solution, we propose a temporal decomposition approach based on approximate dynamic programming. The approach integrates a value function approximation to incorporate future profits and account for network effects. Extensive computational experiments demonstrate the benefits of capturing such effects in pricing generally, as well as showing our value function approximation's ability to anticipate them precisely. Further, in a case study based on Share Now data from Florence in Italy, we observe profit increases of around 9% compared to constant uniform minute prices, which are still the de facto industry standard.
Most modern energy markets trade electricity in advance for technical reasons. Thus, market participants must commit to delivering or consuming a certain amount of energy before the actual delivery. In Germany, two markets with daily auctions coexist. In the day-ahead auction market, the energy is traded in 60-minute time slots, which are further partitioned into 15-minute time slots for the intraday auction market. Because of the slow ramp-ups of nuclear and fossil power plants, these price-makers trade mostly in the day-ahead market. Only the residual energy is traded in the intraday market, where the market prices fluctuate substantially more. These fluctuations as well as the expected price difference between these markets can be exploited by fast ramping energy storage systems. We address the decision problem of an owner of an energy storage who trades on both markets, taking ramping times into account. Because the state variable of our dynamic programming formulation includes all features of our high-dimensional electricity price forecast, this problem cannot be solved to optimality. Instead, we use approximate dynamic programming. In a numerical study based on real-world data, we benchmark the algorithm against an adapted state-of-the-art approach from literature and an expectation model with a receding horizon. Furthermore, we investigate the influence of the price forecast on expected profit and demonstrate that it is essential for the dynamic program to capture the high dimensionality of the price forecast to compete with the expectation model, which does not suffer from the curses of dimensionality.
On most modern energy markets, electricity is traded in advance and a power producer has to commit to deliver a certain amount of electricity some time before the actual delivery. This is especially difficult for power producers with renewable energy sources that are stochastic (like wind and solar). Thus, short term electricity storages like batteries are used to increase flexibility.
By contrast, long term storages allow to exploit price fluctuations over time, but have a comparably bad efficiency over short periods of time.
In this paper, we consider the decision problem of a power producer who sells electricity from wind turbines on the continuous intraday market and possesses two storage devices: a battery and a hydrogen based storage system. The problem is solved with a backwards approximate dynamic programming algorithm with optimal computing budget allocation. Numerical results show the algorithm’s high solution quality. Furthermore, tests on real-world data demonstrate the value of using both storage types and investigate the effect of the storage parameters on profit.
The intensive care unit (ICU) is one of the most crucial and expensive resources in a health care system. While high fixed costs usually lead to tight capacities, shortages have severe consequences. Thus, various challenging issues exist: When should an ICU admit or reject arriving patients in general? Should ICUs always be able to admit critical patients or rather focus on high utilization? On an operational level, both admission control of arriving patients and demand-driven early discharge of currently residing patients are decision variables and should be considered simultaneously. This paper discusses the trade-off between medical and monetary goals when managing intensive care units by modeling the problem as a Markov decision process. Intuitive, myopic rule mimicking decision-making in practice is applied as a benchmark. In a numerical study based on real-world data, we demonstrate that the medical results deteriorate dramatically when focusing on monetary goals only, and vice versa. Using our model, we illustrate the trade-off along an efficiency frontier that accounts for all combinations of medical and monetary goals. Coming from a solution that optimizes monetary costs, a significant reduction of expected mortality can be achieved at little additional monetary cost.
This paper revisits the impact of collection cost on a manufacturer’s optimal reverse channel choice. A manufacturer who remanufactures his own products has the choice between managing collection of used products himself, let the retailer manage collection or involve a third party company to manage collection. In particular, we consider a convex collection cost function depending on the collection rate. Contrary to previous literature, we show that the manufacturer always prefers retailer-managed collection, independent of collection cost. The retailer will always choose a positive collection rate. If collection cost is above a certain threshold, not all used products will be collected and the manufacturer (almost) collects all channel profits. Third party-managed collection is always dominated. In extensions, we also consider a restriction to equilibria and a minimum collection rate, which may be imposed by regulation. Both extensions may change the reverse channel choice to manufacturer-managed. Moreover, we see that it may be impossible for regulation to increase collection because the profit-maximizing collection rate may already be the highest economically viable one.
Today’s technology facilitates selling strategies that were unthinkable only a few years ago. One increasingly popular strategy uses incompletely specified products (ICSPs). The seller retains the right to specify some details of the product or service after the sale. The selling strategies’ main advantages are an additional dimension for market segmentation and operational flexibility due to supply-side substitution possibilities. Since the strategy became popular with Priceline and Hotwire in the travel industry about two decades ago, it has increasingly been adopted by other industries with stochastic demand and limited capacity as well. At the same time, it is actively researched from the perspectives of strategic operations management, empirics, and revenue management.
This paper first describes the application of ICSPs in practice. Then, we introduce the different research communities that are active in this field and relate the terminology they use. The main part is an exhaustive review of the literature on selling ICSPs from the different perspectives. Here, we complement a tabular overview with an introduction into the community and a detailed description of each paper. Finally, possible directions for future research are outlined.
We see that strategic operations management has described advantages of ICSPs over other strategies in a variety of settings, but also identified countervailing effects. Today, empirical research is confined to hotels and airlines and largely disconnected from the other perspectives. Operational papers are ample, but mostly concerned with the availability of ICSPs. Research on operational (dynamic) pricing is surprisingly scarce.
Many industries use dynamic pricing on an operational level to maximize revenue from selling a fixed capacity over a finite horizon. Classical risk-neutral approaches do not accommodate the risk aversion often encountered in practice. When risk aversion is considered, time-consistency becomes an important issue. In this paper, we use a dynamic coherent risk-measure to ensure that decisions are actually implemented and only depend on states that may realize in the future. In particular, we use the risk measure Conditional Value-at-Risk (CVaR), which recently became popular in areas like finance, energy or supply chain management.
A result is that the risk-averse dynamic pricing problem can be transformed to a classical, risk-neutral problem. To do so, a surprisingly simple modification of the selling probabilities suffices. Thus, all structural properties carry over. Moreover, we show that the risk-averse and the risk-neutral solution of the original problem are proportional under certain conditions, that is, their optimal decision variable and objective values are proportional, respectively. In a small numerical study, we evaluate the risk vs. revenue trade-off and compare the new approach with existing approaches from literature.
This has straightforward implications for practice. On the one hand, it shows that existing dynamic pricing algorithms and systems can be kept in place and easily incorporate risk aversion. On the other hand, our results help to understand many risk-averse decision makers who often use “conservative” estimates of selling probabilities or discount optimal prices.
Product-related and market-related uncertainties often cause users to defer from switching to new IT devices. There is a value of waiting (VoW) for users because waiting allows them to collect more information. At the same time, many IT switching decisions are increasingly complex due to increased connectivity and the resulting interdependencies between jointly used devices. Therefore, switching decisions for connected devices not only need to consider the new device in isolation, but must also account for the potential benefits from internally or externally connecting the device with other devices. Although crucial for users and providers alike, existing models cannot explain whether and when users switch in such connected
We focus on connected Smart Home Devices (SHDs) and simulate users’ actual switching timing based on a real options model which combines switching and deferral concepts in a context-specific setting. We examine how Smart Home Network (SHN) density influences switching and how providers can use incentives to accelerate switching to foster product diffusion. The findings show an accelerating effect of connectivity and a deferring effect of uncertainty on actual switching timing. We also learn that SHD providers should focus more on immediate than on delayed incentives to promote product diffusion, since the latter can also have undesired effects. Interestingly, external connectivity has almost no influence on decision timing in scenarios with highly dense SHNs, leading to further key implications for SHD providers.
Many industries use dynamic pricing on an operational level to maximize revenue from selling a fixed capacity over a finite horizon. Classical risk-neutral approaches do not accommodate the risk aversion often encountered in practice. We add to the scarce literature on risk aversion by considering the risk measure conditional value-at-risk (CVaR), which recently became popular in areas like finance, energy, or supply chain management. A key aspect of this paper is selling a single unit of capacity, which is highly relevant in, for example, the real estate market. We analytically derive the optimal policy and obtain structural results. The most important managerial implication is that the risk-averse optimal price is constant over large parts of the selling horizon, whereas the price continuously declines in the standard setting of risk-neutral dynamic pricing. This offers a completely new explanation for the price-setting behavior often observed in practice. For arbitrary capacity, we develop two algorithms to efficiently compute the value function and evaluate them in a numerical study. Our results show that applying a risk-averse policy, even a static one, often yields a higher CVaR than applying a dynamic, but risk-neutral, policy.
Revenue management Dynamic pricing Dynamic programming Risk management Service operations
Optimizing an airline schedule usually comprises multiple planning stages. These are the choice of flights to offer (schedule design), the assignment of fleets to flight legs (fleet assignment), and the construction of rotations under consideration of maintenance constraints (aircraft maintenance routing). Moreover, the airline must assign crews to all flights (crew scheduling). Traditionally, either these scheduling stages are considered sequentially or an existing schedule is modified to cope with the arising complexity issue. More recently, some authors have developed models that integrate adjacent stages. In this paper, outcomes of a research project with airline information technology provider Lufthansa Systems are presented. We consider the case of a small to medium-sized point-to-point airline with a homogeneous fleet. Hence, fleet assignment is omitted, which offers the possibility to solve schedule design and aircraft maintenance routing simultaneously. Our approach explicitly accounts for passengers’ return flight demand and for marginal revenues declining with increasing seat capacity, hence, anticipating the effects of capacity control in revenue management systems. To solve the arising integrated mixed-integer problem, a branch-and-price approach and a column generation-based heuristic have been developed. An extensive numerical study, using data from a major European airline provided by Lufthansa Systems, shows that the presented approaches yield high-quality solutions to real-world problem instances within a reasonable time.
In practice, human-decision makers often feel uncomfortable with the risk-neutral revenue management systems’ output. Reasons include a low number of repetitions of similar events, a critical impact of the achieved revenue for economic survival, or simply business constraints imposed by management. However, solving capacity control problems is a challenging task for many risk measures and the approaches are often not compatible with existing software systems. In this paper, we propose a flexible framework for risk-averse capacity control under customer choice behavior. Existing risk-neutral decision rules are augmented by the integration of adjustable parameters. Our key idea is the application of simulation-based optimization (SBO) to calibrate these parameters. This allows to easily tailor the resulting capacity control mechanism to almost every risk measure and customer choice behavior. In an extensive simulation study, we analyze the impact of our approach on expected utility, conditional value-at-risk (CVaR), and expected value. The results show a superior performance in comparison to risk-neutral approaches from the literature.
In deregulated markets, electricity is usually traded in advance, and the advance commitments have a time lag of several periods. For example, in the German intraday market, the seller commits to providing electricity 45 min before the 15-min interval in which delivery has to be made. We consider the problem of a producer that generates energy from stochastic, renewable sources, such as solar or wind and uses a storage device with conversion losses. We model the problem as a Markov Decision Process and consider lagged commitments for the first time in the literature. The problem is solved using an innovative approximate dynamic programming approach. Its key elements are the analytical derivation of the optimal action based on the value function approximation and a new combination of approximate policy iteration with classical backward induction. The new approach is quite general with regard to the stochastic processes describing the energy production and price evolution. We demonstrate the application of our approach by considering a wind farm/storage combination. A numerical study using real-world data shows the applicability and performance of the new approach and investigates how the storage device’s parameters influence profit.
Recently, the standard dynamic programming model of network revenue management has been extended for integrated upgrade decision-making. However, opposed to the original model, heuristically breaking the extended model down into a series of single-leg problems by dynamic programming decomposition in order to allow for real-world application is not possible. This is because the model’s state space does not incorporate resources but commitments reflecting already sold products and capacity consumption is only resolved at the end of the booking horizon, thereby considering upgrade options. In this paper, we consider arbitrary airline networks with upgrades being performed separately on each flight leg. We show that in this case, there are two reformulations of the extended model. First, we prove that an ad hoc formulation, in which upgrades are technically performed immediately after a sale, is completely equivalent. Second, we present another reformulation whose idea is adapted from linear programing-based production planning with alternative machine types. We prove that the resulting dynamic program is also equivalent. The advantage of both reformulations is that their state space is based on either real or virtual resources instead of commitments. Thus, dynamic programming decomposition techniques can again be applied. Despite the formal equivalence of both reformulations, applying decomposition techniques leads to different approximations and thus to potentially different results when applied in practice. Therefore, we finally numerically examine the approaches regarding revenue performance and discuss airline revenue management settings in which they differ.
Pokharel and Liang [2012. A model to evaluate acquisition price and quantity of used products for remanufacturing. Int. J. Prod. Econ. 138, 170–176] considered a consolidation center that buys used products of different quality levels and sells them together with spare parts to a remanufacturer. The consolidation center׳s decision problem is to determine the acquisition price to offer for used products and the quantities of spare parts to buy. In this paper, comments on their work are given. It is shown that following Pokharel and Liang׳s original assumptions, the problem has a trivial solution. We then consider an alternative assumption where supply is uniform and depends on the acquisition price. For this setting, an efficient solution algorithm and numerical examples are provided. In a second model, additional assumptions are relaxed, allowing the consolidation center more flexibility. As expected, this further decreases cost.
Many service industries use revenue management to balance demand and capacity. The assumption of risk-neutrality lies at the heart of the classical approaches, which aim at maximizing expected revenue. In this paper, we give a comprehensive overview of the existing approaches, most of which were only recently developed, and discuss the need to take risk-averse decision makers into account. We then present a heuristic that maximizes conditional value-at-risk (CVaR). Although CVaR has become increasingly popular in finance and actuarial science due to its beneficial properties, this risk measure has not yet been considered in the context of revenue management. We are able to efficiently solve the optimization problem inherent in CVaR by taking advantage of specific structural properties that allow us to reformulate this optimization problem as a continuous knapsack problem. In order to demonstrate the applicability and robustness of our approach, we conduct a simulation study that shows that the new approach can significantly improve the risk profile in various scenarios.
Product reclamation is a critical process in remanufacturing. It is generally assumed in the literature that customers simply want to get rid of their used products without expecting any compensation for them. Some authors have only recently started looking into firms that offer a posted (fixed) price for them. Following recent reports suggesting that customers are increasingly open to bargaining, we compare using a posted price and bargaining to obtain used products. In our analysis, we consider an original manufacturer acting as a monopolist as well as a manufacturer and an independent remanufacturer acting in a duopoly. We analytically show that bargaining is always beneficial to the monopoly manufacturer. In the duopoly case, we distinguish a Cournot competition and a market with the manufacturer as Stackelberg leader. The results of a numerical study show that both firms will use posted pricing in the Cournot competition, especially if bargaining is not costless. By contrast, the remanufacturer can significantly increase his profit by using negotiations if he is the Stackelberg follower.
A major benefit of flexible products is that they allow for supply-side substitution even after they have been sold. This helps improve capacity utilization and increase the overall revenue in a stochastic environment. As several authors have shown, flexible products can be incorporated into the well-known deterministic linear program (DLP) of revenue management׳s capacity control. In this paper, we show that flexible products have an additional “value of flexibility” due to their supply-side substitution possibilities, which can be captured monetarily. However, the DLP-based approaches proposed so far fail to capture this value and, thus, steadily undervalue flexible products, resulting in lower overall revenues. To take the full potential of flexible products into account, we propose a new approach that systematically increases the revenues of flexible products when solving the DLP and performing capacity control. A mathematical function of variables available during the booking horizon represents this artificial markup and adapts dynamically to the current situation. We determine the function׳s parameters using a standard simulation-based optimization method. Numerical experiments show that the benefits of the new approach are biggest when low value demand arrives early. Revenues are improved by up to 5% in many settings.
We consider the revenue management problem of capacity control with integrated upgrade decision-making. The dynamic programming formulation of this problem is hard to solve to optimality, even in the single-leg case, because multiple hierarchical resource types must be considered simultaneously. Therefore, in this paper, we propose a new heuristic approach that generalizes the idea behind the well-known single-leg EMSR-a procedure to multiple resource types. Similar to EMSR-a, our approach is based on the computation of protection levels, but additionally allows for the integrated consideration of upgrades. In addition, we derive control policies for typical demand arrival patterns. As an extension, we propose a generalization of our approach that allows for arbitrarily ordered prices with respect to the upgrade hierarchy. Furthermore, we perform a number of computational experiments to investigate the performance of the new approach compared to other capacity control methods that incorporate upgrades. We consider typical airlines′ single-leg scenarios with 10 (re)optimizations throughout the booking horizon. The results show that our approach can significantly outperform existing methods in terms of the total achieved revenue, including dynamic programming decomposition approaches that are proposed in literature, as well as successive planning approaches that are widely used in commercial revenue management systems.
This paper provides an overview of the literature on dynamic pricing with strategic customers. In the past, research on dynamic pricing was mostly concerned with optimally pricing products over time in a market with myopic customers. In recent years, the consideration of strategic customers, who can delay a purchase to take advantage of a future discount, has dramatically increased. This paper’s main contribution is the development of a comprehensive classification scheme to structure the field of research and, based upon this, a systematic overview of all relevant papers. We then present in detail the various aspects considered in the literature together with their motivation from industry and state the major findings of the most relevant papers. Further attention is given to important problem extensions proposed in the literature that have been considered in only a few papers and are usually motivated by specific practical applications. Finally, promising directions for future research are indicated.
Opaque products enable service providers to hide specific characteristics of their service fulfillment from the customer until after purchase. Prominent examples include internet-based service providers selling airline tickets without defining details, such as departure time or operating airline, until the booking has been made. Owing to the resulting flexibility in resource utilization, the traditional revenue management process needs to be modified. In this paper, we extend dynamic programming decomposition techniques widely used for traditional revenue management to develop an intuitive capacity control approach that allows for the incorporation of opaque products. In a simulation study, we show that the developed approach significantly outperforms other well-known capacity control approaches adapted to the opaque product setting. Based on the approach, we also provide computational examples of how the share of opaque products as well as the degree of opacity can influence the results.
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.
While flexible products have been popular for many years in practice, they have only recently gained attention in the academic literature on revenue management. When selling a flexible product, a firm retains the right to specify some of its details later. The relevant point in time is after the sale, but often before the provision of the product or service, depending on the customers’ need to know the exact specification in advance. The resulting flexibility can help to increase revenues if capacity is fixed and the demand to come difficult to forecast. We present several revenue management models and control mechanisms incorporating this kind of flexible products. An extensive numerical study shows how the different approaches can mitigate the negative impact of demand forecast errors.
Revenue management with flexible products has experienced a growing interest in the academic literature within the last few years. Flexible products allow supply-side substitution between resources and can therefore help to maximize overall revenue as well as capacity utilization in markets with highly uncertain demand. This paper addresses the question of how the mathematical models which have been developed for capacity control with flexible products should be used over time to exploit the substitution opportunities, while keeping practical applicability in mind. Several dynamic control mechanisms are proposed, each of which makes use of the flexibility to a different extent. A comprehensive computational study shows the potential of the different approaches by revealing their strengths and weaknesses.
Free-floating shared mobility systems offer customers the flexibility to pick up and drop off vehicles at any location within the business area and, thus, have become the most popular type of shared mobility system. However, this flexibility has the drawback that vehicles tend to accumulate at locations with low demand. To counter these imbalances, pricing has proven to be an effective and cost-efficient means. The fact that customers use mobile applications, combined with the fact that providers know the exact location of each vehicle in real-time, provides new opportunities for dynamic pricing.
In this context, we develop a pricing approach for the dynamic online problem of a provider who determines profit-maximizing prices whenever a customer opens the provider’s mobile application to rent a vehicle. Our pricing approach has three distinguishing features: First, it is customer-centric, i.e., it considers the customer’s location as well as disaggregated choice behavior to precisely capture the effect of price and walking distance to the available vehicles on the customer’s propensity to choose a vehicle. Second, our pricing approach is origin-based, i.e., prices are differentiated by location and time of rental start, which reflects the real-world situation where the rental destination is usually unknown. Third, our approach is anticipative and uses a stochastic dynamic program to anticipate the effect of current decisions on future vehicle locations, rentals, and profits. As solution method, we propose a non-parametric value function approximation, which offers several advantages for the application, e.g., historical data can readily be used and main parameters can be pre-computed such that the online pricing problem becomes tractable. Extensive numerical studies, including a case study based on Share Now data, demonstrate that our approach increases profits by up to 13% compared to existing approaches from the literature and other benchmarks.
Bike sharing has been introduced in many cities, often by municipalities and is nowadays an established alternative for other short-distance transport systems. However, in cities with high elevations, the usual bike-sharing systems face a severe problem. Resulting from an imbalance of demand, the number of bikes at stations at elevated locations decreases during the day, while it increases at stations at lower locations. This situation poses a challenge for the relocation process because high numbers of bicycles have to be transported to the stations at elevated locations in order to achieve a suitable starting point for the next period. With the usage of e-bike sharing-systems, this problem can be circumvented because e-bikes facilitate the mobility in elevated and steep terrains. This paper considers an e-bike sharing-system with removable batteries. In the first step, a deterministic Mixed-Integer Linear Program (MILP) calculates the optimal route for trucks and the optimal initial distribution of bikes. In the second step, a stochastic simulation should evaluate these results.