Showing papers on "Dynamic pricing published in 2013"

Dynamic pricing and learning: Historical origins, current research, and new directions

Abstract: The topic of dynamic pricing and learning has received a considerable amount of attention in recent years, from different scientific communities. We survey these literature streams: we provide a brief introduction to the historical origins of quantitative research on pricing and demand estimation, point to different subfields in the area of dynamic pricing, and provide an in-depth overview of the available literature on dynamic pricing and learning. Our focus is on the operations research and management science literature, but we also discuss relevant contributions from marketing, economics, econometrics, and computer science. We discuss relations with methodologically related research areas, and identify directions for future research.

Bandits with Knapsacks

Abstract: Multi-armed bandit problems are the predominant theoretical model of exploration-exploitation tradeoffs in learning, and they have countless applications ranging from medical trials, to communication networks, to Web search and advertising. In many of these application domains the learner may be constrained by one or more supply (or budget) limits, in addition to the customary limitation on the time horizon. The literature lacks a general model encompassing these sorts of problems. We introduce such a model, called "bandits with knapsacks", that combines aspects of stochastic integer programming with online learning. A distinctive feature of our problem, in comparison to the existing regret-minimization literature, is that the optimal policy for a given latent distribution may significantly outperform the policy that plays the optimal fixed arm. Consequently, achieving sub linear regret in the bandits-with-knapsacks problem is significantly more challenging than in conventional bandit problems. We present two algorithms whose reward is close to the information-theoretic optimum: one is based on a novel "balanced exploration" paradigm, while the other is a primal-dual algorithm that uses multiplicative updates. Further, we prove that the regret achieved by both algorithms is optimal up to polylogarithmic factors. We illustrate the generality of the problem by presenting applications in a number of different domains including electronic commerce, routing, and scheduling. As one example of a concrete application, we consider the problem of dynamic posted pricing with limited supply and obtain the first algorithm whose regret, with respect to the optimal dynamic policy, is sub linear in the supply.

Dynamic Cloud Pricing for Revenue Maximization

Abstract: In cloud computing, a provider leases its computing resources in the form of virtual machines to users, and a price is charged for the period they are used. Though static pricing is the dominant pricing strategy in today's market, intuitively price ought to be dynamically updated to improve revenue. The fundamental challenge is to design an optimal dynamic pricing policy, with the presence of stochastic demand and perishable resources, so that the expected long-term revenue is maximized. In this paper, we make three contributions in addressing this question. First, we conduct an empirical study of the spot price history of Amazon, and find that surprisingly, the spot price is unlikely to be set according to market demand. This has important implications on understanding the current market, and motivates us to develop and analyze market-driven dynamic pricing mechanisms. Second, we adopt a revenue management framework from economics, and formulate the revenue maximization problem with dynamic pricing as a stochastic dynamic program. We characterize its optimality conditions, and prove important structural results. Finally, we extend to consider a nonhomogeneous demand model.

Dynamic Pricing Competition with Strategic Customers Under Vertical Product Differentiation

Abstract: We consider dynamic pricing competition between two firms offering vertically differentiated products to strategic customers who are intertemporal utility maximizers. We show that price skimming arises as the unique pure-strategy Markov perfect equilibrium in the game under a simple condition. Our results highlight the asymmetric effect of strategic customer behavior on quality-differentiated firms. Even though the profit of either firm decreases as customers become more strategic, the low-quality firm suffers substantially more than the high-quality firm. Furthermore, we show that unilateral commitment to static pricing by either firm generally improves profits of both firms. Interestingly, both firms enjoy higher profit lifts when the high-quality firm commits rather than when the low-quality firm commits. This paper was accepted by Yossi Aviv, operations management.

UDP: Usage-Based Dynamic Pricing With Privacy Preservation for Smart Grid

Abstract: Smart sensing and wireless communication technologies enable the electric power grid system to deliver electricity more efficiently through the dynamic analysis of the electricity demand and supply. The current solution is to extend the traditional static electricity pricing strategy to a time-based one where peak-time prices are defined to influence electricity usage behavior of customers. However, the time-based pricing strategy is not truly dynamic and the electricity resource cannot be optimally utilized in real time. In this paper, we propose a usage-based dynamic pricing (UDP) scheme for smart grid in a community environment, which enables the electricity price to correspond to the electricity usage in real time. In the UDP scheme, to simplify price management and reduce communication overhead, we introduce distributed community gateways as proxies of the utility company to timely respond to the price enquiries from the community customers. We consider both community-wide electricity usage and individual electricity usage as factors into price management: a customer gets higher electricity unit price if its own electricity usage becomes larger under certain conditions of the community-wide collective electricity usage. Additionally, we protect the privacy of the customers by restricting the disclosure of the individual electricity usage to the community gateways. Lastly, we provide privacy and performance analysis to demonstrate that the UDP scheme supports real-time dynamic pricing in an efficient and privacy-preserving manner.

Decentralized Participation of Flexible Demand in Electricity Markets—Part II: Application With Electric Vehicles and Heat Pump Systems

Abstract: Realizing the significant demand flexibility potential in deregulated power systems requires its suitable integration in electricity markets. Part I of this work has presented the theoretical, algorithmic and implementation aspects of a novel pool market mechanism achieving this goal by combining the advantages of centralized mechanisms and dynamic pricing schemes, based on Lagrangian relaxation (LR) principles. Part II demonstrates the applicability of the mechanism, considering two reschedulable demand technologies with significant potential, namely electric vehicles with flexible charging capability and electric heat pump systems accompanied by heat storage for space heating. The price response sub-problems of these technologies are formulated, including detailed models of their operational properties. Suitable case studies on a model of the U.K. system are examined in order to validate the properties of the proposed mechanism and illustrate and analyze the benefits associated with the market participation of the considered technologies.

Decentralized Participation of Flexible Demand in Electricity Markets—Part I: Market Mechanism

Abstract: In the deregulated power systems setting, the realization of the significant demand flexibility potential should be coupled with its integration in electricity markets. Centralized market mechanisms raise communication, computational and privacy issues while existing dynamic pricing schemes fail to realize the actual value of demand flexibility. In this two-part paper, a novel day-ahead pool market mechanism is proposed, combining the solution optimality of centralized mechanisms with the decentralized demand participation structure of dynamic pricing schemes and based on Lagrangian relaxation (LR) principles. Part I presents the theoretical background, algorithmic approaches and suitable examples to address challenges associated with the application of the mechanism and provides an implementation framework. Non-convexities in reschedulable demand participants' price response and their impacts on the ability of the basic LR structure to reach feasible market clearing solutions are identified and a simple yet effective LR heuristic method is developed to produce both feasible and high quality solutions by limiting the concentrated shift of reschedulable demand to the same low-priced time periods.

Scalable and Robust Demand Response With Mixed-Integer Constraints

Abstract: A demand response (DR) problem is considered entailing a set of devices/subscribers, whose operating conditions are modeled using mixed-integer constraints. Device operational periods and power consumption levels are optimized in response to dynamic pricing information to balance user satisfaction and energy cost. Renewable energy resources and energy storage systems are also incorporated. Since DR becomes more effective as the number of participants grows, scalability is ensured through a parallel distributed algorithm, in which a DR coordinator and DR subscribers solve individual subproblems, guided by certain coordination signals. As the problem scales, the recovered solution becomes near-optimal. Robustness to random variations in electricity price and renewable generation is effected through robust optimization techniques. Real-time extension is also discussed. Numerical tests validate the proposed approach.

Effects of price framing on consumers’ perceptions of online dynamic pricing practices

Abstract: The viability of online dynamic pricing, or differential pricing for the same product from the same seller, is still debatable given the contradictory findings reported in both modeling and behavioral price research. This paper examines tactical ways for online merchants to mitigate consumers’ negative reactions when adopting dynamic pricing strategies. In three experiments, we show that using various price-framing tactics, compared to no framing, can induce price-disadvantaged consumers to perceive their ostensibly similar transactions differently relative to their comparative other parties. As the degree of perceived transaction dissimilarity increases, price-disadvantaged consumers’ perceived price fairness, trust, and repurchase intentions are enhanced. We further compare different price framing tactics and demonstrate that they have different effects on consumers across different product price levels, customer segments, and framing formats. The paper concludes with theoretical and managerial implications of the research.

Smart parking solutions for urban areas

Abstract: Finding a parking place in a busy city centre is often a frustrating task for many drivers; time and fuel are wasted in the quest for a vacant spot and traffic in the area increases due to the slow moving vehicles circling around. In this paper, we present the results of a survey on the needs of drivers from parking infrastructures from a smart services perspective. As smart parking systems are becoming a necessity in today's urban areas, we discuss the latest trends in parking availability monitoring, parking reservation and dynamic pricing schemes. We also examine how these schemes can be integrated forming technologically advanced parking infrastructures whose aim is to benefit both the drivers and the parking operators alike.

Integrating dynamic pricing of electricity into energy aware scheduling for HPC systems

Abstract: The research literature to date mainly aimed at reducing energy consumption in HPC environments. In this paper we propose a job power aware scheduling mechanism to reduce HPC's electricity bill without degrading the system utilization. The novelty of our job scheduling mechanism is its ability to take the variation of electricity price into consideration as a means to make better decisions of the timing of scheduling jobs with diverse power profiles. We verified the effectiveness of our design by conducting trace-based experiments on an IBM Blue Gene/P and a cluster system as well as a case study on Argonne's 48-rack IBM Blue Gene/Q system. Our preliminary results show that our power aware algorithm can reduce electricity bill of HPC systems as much as 23%.

Chasing Demand: Learning and Earning in a Changing Environment

Abstract: We consider a dynamic pricing problem in which a seller faces an unknown demand model that can change over time. We measure the amount of change over a time horizon of T periods using a quadratic variation metric, and allow a finite "budget" for such changes. We first derive a lower bound on the expected performance gap between any pricing policy and a clairvoyant who knows a priori the temporal evolution of the underlying demand model, and then design families of near-optimal pricing policies, the revenue performance of which asymptotically matches said lower bound. We also show that the seller can achieve a substantially better revenue performance in demand environments that change in "bursts" than it would in a demand environment that changes "smoothly." Finally, we extend our analysis to the case of rapidly changing demand settings, and obtain a range of results that quantify the net effect of the volatility in the demand environment on the seller’s revenue performance.

Simple Policies for Dynamic Pricing with Imperfect Forecasts

Abstract: We consider the “classical” single-product dynamic pricing problem allowing the “scale” of demand intensity to be modulated by an exogenous “market size” stochastic process. This is a natural model of dynamically changing market conditions. We show that for a broad family of Gaussian market-size processes, simple dynamic pricing rules that are essentially agnostic to the specification of this market-size process perform provably well. The pricing policies we develop are shown to compensate for forecast imperfections (or a lack of forecast information altogether) by frequent reoptimization and reestimation of the “instantaneous” market size.

Dynamic pricing and learning with finite inventories

Abstract: We study a dynamic pricing problem with finite inventory and parametric uncertainty on the demand distribution. Products are sold during selling seasons of finite length, and inventory that is unsold at the end of a selling season, perishes. The goal of the seller is to determine a pricing strategy that maximizes the expected revenue. Inference on the unknown parameters is made by maximum likelihood estimation. We propose a pricing strategy for this problem, and show that the Regret - which is the expected revenue loss due to not using the optimal prices - after T selling seasons is O(log2(T)). Apart from a small modification, our pricing strategy is a certainty equivalent pricing strategy, which means that at each moment, the price is chosen that is optimal w.r.t. the current parameter estimates. The good performance of our strategy is caused by an endogenous-learning property: using a pricing policy that is optimal w.r.t. a certain parameter sufficiently close to the optimal one, leads to a.s. convergence of the parameter estimates to the true, unknown parameter. We also show an instance in which the regret for all pricing policies grows as log(T). This shows that ourupper bound on the growth rate of the regret is close to the best achievable growth rate.

Conspicuous Consumption and Dynamic Pricing

Abstract: How do firms develop marketing strategy when consumers seek to satisfy both quality and status-related considerations? We develop an analytical model to study this issue, examining both pricing and product management decisions in markets for conspicuous durable goods. Our analysis yields many interesting and nontrivial insights. First, we demonstrate that high intrinsic quality indirectly generates exclusivity via pricing effects; in turn, this exclusivity generates considerable social payoffs where consumers value status. This insight reverses the direction of causality in the existing literature, wherein only status considerations matter and mere price increases may enhance consumer utility. Second, our dynamic model indicates that where consumers prioritize status benefits, producers incur substantial price depreciation in equilibrium. Third, we examine the product management strategies used by firms to preserve early adopter exclusivity. Finally, we discuss the boundary conditions of our results as well as our results' implications for managerial and policy issues.

Dynamic pricing for hotel revenue management using price multipliers

Abstract: In this article we propose a new dynamic pricing approach for the hotel revenue management problem. The proposed approach is based on having ‘price multipliers’ that vary around ‘1’ and provide a varying discount/premium over some seasonal reference price. The price multipliers are a function of certain influencing variables (for example, hotel occupancy, time until arrival). We apply an optimization algorithm for determining the parameters of these multipliers, the goal being to maximize the revenue, taking into account current demand, and the demand-price sensitivity of the hotel's guest. The optimization algorithm makes use of a Monte Carlo simulator that simulates all the hotel's processes, such as reservations arrivals, cancellations, duration of stay, no shows, group reservations, seasonality and trend, as faithfully as possible. We have tested the proposed approach by successfully applying it to the revenue management problem of Plaza Hotel, Alexandria, Egypt, as a case study.

Demand response through smart home energy management using thermal inertia

Abstract: In this paper, the value of thermal inertia in demand response to benefit customers is determined through a Mixed Integer Linear Programming (MILP) algorithm. Thermal models with different sophistications for a smart house are investigated. The energy consumption for cooling a smart house is optimized to minimize the expenditure of cooling load. One parameter and two-parameter thermal models are integrated into the optimization. The optimization of thermal load for maintaining the smart house within thermal comfort level is formulated as a MILP algorithm under the dynamic pricing policy. It is observed that the utilization of thermal inertia could potentially benefit both smart house owners and grid operators in the context of smart grid.

Arcturus: International Evidence on Dynamic Pricing

Abstract: This paper introduces Arcturus, an international database of dynamic pricing and time-of-use pricing studies. It contains the demand response impacts of 163 pricing treatments that were offered on an experimental or full-scale basis in 34 projects in seven countries located in four continents. The treatments included various types of dynamic pricing rates and simple time-of-use rates, some of which were offered with enabling technologies such as smart thermostats. The demand response impacts of these treatments vary widely, from 0% to more than 50%, and this discrepancy has led some observers to conclude that we still don’t know whether customers respond to dynamic pricing. We find that much of the discrepancy in the results goes away when demand response is expressed as a function of the peak to off-peak price ratio. We then observe that customers respond to rising prices by lowering their peak demand in a fairly consistency fashion across the studies. The response curve is nonlinear and is shaped in the form of an arc: as the price incentive to reduce peak use is raised, customers respond by lowering peak use, but at a decreasing rate. We also find that the use of enabling technologies boosts the amount of demand response. Overall, we find a significant amount of consistency in the experimental results, especially when the results are disaggregated into two categories of rates: time-of-use rates and dynamic pricing rates. This consistency evokes the consistency that was found in earlier analysis of time-of-use pricing studies that was carried out by EPRI in the early 1980s. Our analysis supports the case for the rollout of dynamic pricing wherever advanced metering infrastructure is in place.

Online Algorithm for Optimal Real-Time Energy Distribution in the Smart Grid

Abstract: The two-way energy and information flows in a smart grid, together with the smart devices, bring new perspectives to energy management and demand response. This paper investigates an online algorithm for electricity energy distribution in a smart grid environment. We first present a formulation that captures the key design factors such as user's utility and cost, grid load smoothing, dynamic pricing, and energy provisioning cost. The problem is shown to be convex and can be solved with an offline algorithm if future user and grid related information are known a priori. We then develop an online algorithm that only requires past and present information about users and the grid, and prove that the online solution is asymptotically optimal. The proposed energy distribution framework and the online algorithm are quite general, suitable for a wide range of utility, cost, and pricing functions. It is evaluated with trace-driven simulations and shown to outperform a benchmark scheme.

Dynamic pricing, heterogeneous users and perception error: Probit-based bi-criterion dynamic stochastic user equilibrium assignment

Abstract: A probit-based bi-criterion dynamic stochastic user equilibrium (BDSUE) model is presented to capture path choice behavior of heterogeneous users with distinct values of time (VOT) and different perception of travel costs in response to pricing and congestion in a transportation network. Across the population of travelers, the VOT is represented by a continuously distributed random variable, and path travel cost perception errors are multivariate normally distributed. The BDSUE problem is formulated as a fixed point problem in the infinite dimensional space, and solved by a column generation framework which embeds (i) a parametric analysis method (PAM) to transform the continuous problem to the finite dimensional space by finding breakpoints that partition the entire range of VOT into subintervals and define a multi-class dynamic stochastic user equilibrium (MDSUE) problem; (ii) a column generation algorithm to augment a feasible path set for each user class; (iii) a probit-based stochastic path flow updating scheme to solve a restricted MDSUE problem defined by the set of feasible paths using an averaging method; and (iv) dynamic network loading using a particle-based traffic simulator to capture traffic dynamics and determine experienced travel times for a given path flow pattern. Numerical experiments on a medium size network are conducted to explore convergence of the solution algorithm and to illustrate heterogeneous user responses to dynamic tolls.

Advance Selling in the Presence of Speculators and Forward-Looking Consumers

Abstract: This article examines the pricing policy of a monopolist seller who may sell in advance of consumption in a market that comprises of myopic consumers, forward-looking consumers, and speculators. The latter group has no consumption value for the goods and is in the market with the sole objective of making a profit by reselling the purchased goods shortly after. Consumers, although homogeneous in terms of their valuations, are different with respect to their perspectives. We show that in an “upward” market where the expected valuation increases over time, the optimal pricing policy is an ex ante “static” one where the seller “prices into the future” and prices the myopic consumers out of the advance market. However, in a “downward” market where the expected valuation decreases over time, the seller adopts a dynamic pricing strategy except for the case when higher initial sales can trigger more demand subsequently and when the downward trend is not too high. In this case, the seller prefers an ex ante “static” pricing strategy and deliberately prices lower initially to sell to speculators. We identify the conditions under which the seller benefits from the existence of speculators in the market. Moreover, although the presence of entry costs is ineffective as an entry deterrence, we determine the conditions under which exit costs can rein in speculative purchase.

A comparison of fixed and dynamic pricing policies in revenue management

Abstract: We consider the problem of selling a fixed capacity or inventory of items over a finite selling period. Earlier research has shown that using a properly set fixed price during the selling period is asymptotically optimal as the demand potential and capacity grow large and that dynamic pricing has only a secondary effect on revenues. However, additional revenue improvements through dynamic pricing can be important in practice and need to be further explored. We suggest two simple dynamic heuristics that continuously update prices based on remaining inventory and time in the selling period. The first heuristic is based on approximating the optimal expected revenue function and the second heuristic is based on the solution of the deterministic version of the problem. We show through a numerical study that the revenue impact of using these dynamic pricing heuristics rather than fixed pricing may be substantial. In particular, the first heuristic has a consistent and remarkable performance leading to at most 0.2% gap compared to optimal dynamic pricing. We also show that the benefits of these dynamic pricing heuristics persist under a periodic setting. This is especially true for the first heuristic for which the performance is monotone in the frequency of price changes. We conclude that dynamic pricing should be considered as a more favorable option in practice.

Dynamic Pricing of Perishable Assets under Competition

Abstract: We study dynamic price competition in an oligopolistic market with a mix of substitutable and complementary perishable assets. Each firm has a fixed initial stock of items and competes in setting prices to sell them over a finite sales horizon. Customers sequentially arrive at the market, make a purchase choice and then leave immediately with some likelihood of no-purchase. The purchase likelihood depends on the time of purchase, the product attributes and the current prices. The demand structure includes time-variant linear and MultiNomial Logit demand models as special cases. Assuming deterministic customer arrival rates, we show that any equilibrium strategy has a simple structure, involving a finite set of shadow prices measuring capacity externalities that firms exert on each other: equilibrium prices can be resolved from a one-shot price competition game under the current-time demand structure, taking into account capacity externalities through the time-invariant shadow prices. The former reflects the transient demand side at every moment and the latter captures the aggregate supply constraint over the sales horizon. This simple structure sheds light on dynamic revenue management problems under competition, which helps capture the essence of the problems under demand uncertainty. We show that the equilibrium solutions from the deterministic game provide pre-committed and contingent heuristic policies that are asymptotic equilibria for its stochastic counterpart, when demand and supply are sufficiently large.

When the price is right: enabling time-dependent pricing of broadband data

Abstract: In an era of 108% annual growth in demand for mobile data and $10/GB overage fees, Internet Service Providers (ISPs) are experiencing severe congestion and in turn are hurting consumers with aggressive pricing measures. But smarter practices, such as time-dependent pricing (TDP), reward users for shifting their non-critical demand to off-peak hours and can potentially benefit both users and ISPs. Although dynamic TDP ideas have existed for many years, dynamic pricing for mobile data is only now gaining interest among ISPs. Yet TDP plans require not only systems engineering but also an understanding of economic incentives, user behavior and interface design. In particular, the HCI aspects of communicating price feedback signals from the network and the response of mobile data users need to be studied in the real world. But investigating these issues by deploying a virtual TDP data plan for real ISP customers is challenging and rarely explored. To this end, we carried out the first TDP trial for mobile data in the US with 10 families. We describe the insights gained from the trial, which can help the HCI community as well as ISPs, app developers and designers create tools that empower users to better control their usage and save on their monthly bills, while also alleviating network congestion.