Dynamic Pricing Policy Research Articles

Welfare Analysis of Dynamic Pricing

Dynamic pricing is designed to increase the revenues or profits of firms by adjusting prices in response to changes in the marginal value of capacity. We examine the impact of dynamic pricing on social welfare and consumers’ surplus. We present a dynamic pricing formulation designed to maximize welfare and show that the welfare-maximizing dynamic pricing policy has the same structural properties as the revenue-maximizing policy. For systems with scarce capacity, we show that the revenue-maximizing dynamic pricing policy and the market-clearing price are both asymptotically optimal for welfare. We also find in most cases that revenue-maximizing dynamic pricing improves consumers’ surplus compared to the revenue-maximizing static price. Our findings can potentially transform the public image of dynamic pricing and provide new managerial insights as well as policy implications: (1) in large-scale systems with scarce capacity, a central planner would essentially implement the same pricing policy as a firm with monopoly power; (2) the revenue-maximizing dynamic pricing policy can benefit customers when the demand elasticity is in a small bounded interval as is the case for several important demand functions.The online appendix is available at https://doi.org/10.1287/mnsc.2017.2943 .This paper was accepted by Serguei Netessine, operations management.

The Curse of Knowledge: Having Access to Customer Information Can Reduce Monopoly Profits

We demonstrate the curse of knowledge when a monopolist can recognize different consumer groups through their purchase histories, which are influenced by the firm's dynamic pricing policies. Under the Markov-perfect equilibrium, after each commitment period, the firm offers a new introductory price so as to attract new customers. More and more market segments are added gradually. Eventually, the whole market is covered. Shortening the commitment period will result in a fall in profit. In contrast, a full-commitment monopolist prefers to stick to uniform pricing, achieving higher profit. Hence, the firm is better off by refraining from collecting customer information.

Designing and Evaluating Dynamic Pricing Policies for Major League Baseball Tickets

Problem definition: We develop and estimate a demand model that can be used to evaluate and design dynamic pricing policies for single-game tickets by a sports team. Academic/practical relevance: Many firms have difficulty evaluating the impact of their pricing policy, which further inhibits their ability to design and implement dynamic pricing. We address this issue in the context of single-game ticket pricing for a Major League Baseball franchise. Methodology: We develop and estimate a comprehensive regression-based forecasting model that captures relevant aspects of the demand generation process such as ticket quantity and stadium seat section choice. The model is then used to evaluate the revenue associated with a specific pricing policy. Results: The demand model reveals factors that drive sports ticket revenue, such as the effect of home-team performance on overall price sensitivity and the relationship between customers’ arrival timing and product choice. These insights are incorporated into the optimization to improve the dynamic pricing policies. Managerial implications: We show that by leveraging the model insights and allowing sufficient pricing flexibility, the franchise can achieve a potential revenue improvement of 17.2% through daily price reoptimization. This improvement is comparable to the outcome of a clairvoyant policy in which the future evolution of demand is assumed to be known. The online supplement is available at https://doi.org/10.1287/msom.2018.0760 .

Availability-based dynamic pricing on a round-trip carsharing service: an explorative analysis using agent-based simulation

Carsharing companies aim to customize their service to increase fleet usage and revenues with different pricing schemes and offer types. Dynamic pricing policies can be designed to adjust and balance temporally and spatially cars availability but may pose some question on customers’ fairness. In this paper, we propose an explorative analysis of how an availability-based dynamic pricing scheme impacts the demand and the supply performance. The policy is simulated in MATSim and compared to a fixed pricing policy scheme. This simulation consists of analyzing the behavior of a synthetic population of car-sharing members for Berlin and the surrounding region in which is applied an availability-based dynamic pricing in which price depends on vehicle availability in booking stations. Results show that when the dynamic pricing is applied there is a light decrease in the number of bookings and people with low value of time tend to abandon the carsharing mode in favor of other modes of transportation.

E-Parking: Multi-agent Smart Parking Platform for Dynamic Pricing and Reservation Sharing Service

Parking is a key element of a sustainable urban mobility policy. It plays a fundamental role in travel planning and transport management, as the foremost vector of modal choice, but also as a potential means of freeing up public spaces. In this article we define the smart parking concept, as an application of smart mobility, present a historical analysis of the evolution of smart parking framework and show a statistical analysis of the published patent applications in this field around the world using the ORBIT database. Then, we propose a new smart parking architecture based on multi-agent features. Finally, we introduce the e-Parking system, platform to improve the driver experience of crowded cities. It provides real-time parking prices and offers a reservation and guidance services. In addition, the system assigns an optimal parking for a driver based on the user’s requirements that combine proximity to destination, parking cost and dwell time, while ensuring a fair sharing of public space among users and improves traffic conditions. Our approach is based on dynamic pricing policy. Our scheme is suitable for mixed-usage areas, as it considers the presence of reserved and not reserved driver in the same parking area.

Pricing policy selection for a platform providing vertically differentiated services with self-scheduling capacity

In this article, we study three pricing policies for a monopoly platform, such as Uber or Gett, who offers vertically differentiated services to customers via multiple types of self-scheduling providers. Ideally, the platform can employ a “dynamic pricing” policy, which pays providers wages and charges customers prices for the transactions of different services that both adjust based on prevailing demand conditions, to maximize its profit. However, since it is challenging for the platform to implement and for providers to understand this policy, the other two pricing policies are commonly adopted in practice, that is, “surge pricing” policy (adopted by Uber) which pays providers a fixed commission of its dynamic prices, and “static pricing” policy (applied by Gett) which pays providers a fixed commission of its fixed prices. By observing these phenomena, we propose to study and discuss the platform’s profit performance of these three pricing strategies. We show that the surge pricing policy does not always perform well, which can explain why some on-demand platforms would implement the static pricing policy in practice. Also, although the dynamic pricing policy will significantly improve the platform’s profit, we find that the profitability of the static (surge) pricing policy would approach that of the dynamic pricing policy if the platform can balance the number of different types of providers and/or reduce the commission rate.

A two-layer model for dynamic pricing of electricity and optimal charging of electric vehicles under price spikes

Pilot projects in power networks conducted across continents have established the benefits of dynamic pricing by inducing increased demand response. However, a key hurdle in the growth of demand response is the lack of widespread availability of advanced metering infrastructure, which has stymied the adoption of dynamic pricing. We believe that this hurdle will be partially addressed by the growth of electric vehicles (EVs), as smart and connected EV parking lots will be a provider of demand response. We develop a two-layer optimization model that simultaneously determines dynamic pricing policy for the system operator and demand response strategies for the EV parking lots. The model minimizes the cost to consumers, while ensuring the system operator's revenue neutral status and addressing real-time price uncertainties. A variant of the 5-bus PJM network is used to demonstrate model implementation. Numerical results show that for a low to moderate price spike scenario, dynamic pricing with demand response from EVs alone can lower the daily average consumer cost of 1.42% compared to the cost of flat pricing. A cost reduction of 6.5% is achieved when price spikes are relatively high. Computational challenges of implementing our model for real networks are discussed in the concluding remarks.

Dynamic pricing for inventories with reference price effects

Abstract This article presents a dynamic pricing model of a retailer selling an inventory, accounting for consumer behavior. The authors propose an optimal control model, maximizing the intertemporal profit with consumers sensitive to the selling price and to a reference price. The optimal dynamic pricing policy is solved with Pontryagin’s maximum principle with a structural (general) demand function. The authors obtain an original pricing rule, which explicitly accounts for the impact of price and inventory on future profits. The dynamics of price do not have to imitate the dynamics of the reference price. Instead, the dynamics of price are tied to opposing effects linked to this reference price. The authors also discuss managerial implications with regards to behavioral pricing policies.

Understanding undergraduate students’ perceptions of dynamic pricing policies: An exploratory study of two pilot deliberative pollings (DPs) in Guangzhou, China and Kyoto, Japan

Smart grids (SGs) are being deployed as a transformational technology in energy transitions. However, negative consumer responses to both smart meters and new pricing systems indicate that building public acceptance of these transitions is critically important. Deliberative Pollings (DPs) offer the potential to effectively integrate public perceptions into energy transition decision-making. Most deliberative governance studies focus on western countries and very few examine the Asian context. This paper presents an exploratory study of undergraduate students' perceptions of dynamic pricing options in two pilot DPs conducted in the cities of Guangzhou and Kyoto. The study indicates that deliberative processes yield mixed outcomes in changing participants' choice of pricing options. While many welcomed new pricing options, a significant number supported status quo options. Second, the normative mechanisms and outcomes of deliberative participation seem to apply in the Asian context. DP appears to enhance participants' acceptance of complex and sophisticated pricing options. Dialogic processes enhanced the participants’ ability to understand complex issues and weigh up trade-offs when comparing options. Third, national level contextual differences associated with public distrust and familiarity with market logic may explain the differences in responses between Chinese and Japanese participants. We argue that complex and controversial energy decision-making needs to be supported by deliberative participatory processes to enable citizens to make informed and considered choices.

Dynamic Pricing with Service Unbundling

In this study, we investigate unbundling when a firm dynamically prices a basic service, while separating the sale of a fixed‐price add‐on. We characterize the optimal dynamic unbundling pricing policy and investigate its structural properties. We find that the value function with unbundling increases in the degree of dependence between consumers’ reservation prices for basic service and add‐on. However, there are no similar monotonicity properties for the optimal price of the basic service. For several families of commonly used joint distributions, we show that the influence of the dependence parameter on the optimal price of the basic service depends on a threshold, which is a function of the dependence parameter. Moreover, the price of the bundled service is higher under unbundling when the add‐on price is high, and vice versa. Our model is then compared with the bundling model through a numerical experiment. Among most cases where unbundling outperforms, the degree of dependence is non‐negative. It is further revealed that given the non‐negativity of dependence, unbundling is worth practicing under the following situations: (i) the variance of the reservation price for the basic service (add‐on) is low (high); (ii) the mean of the reservation price for the basic service (add‐on) is high (low); (iii) the demand intensity is low; (iv) the capacity of the basic service is high; and (v) the incremental cost of the basic service (add‐on) is low (high). Finally, unbundling can improve the firm's expected profit and the consumers’ surplus at the same time.

Dynamic Pricing Mechanism in Smart Grid Communications Is Shaping Up

An efficient smart grid communication system is a key enabling technology for modernized utility that can adjust electricity usage to balance generation and demand in real time. However, the utility industry is not able to meet the power demand for the wholesale market during overloading or emergency situations. To mitigate power shortage pressures, utility providers need to employ a dynamic pricing policy to enforce higher pricing than pre-estimated statistic pricing to motivate consumers to reduce their power consumption. In this letter, the time of use (TOU) approach is proposed to regulate price variances considering desired power demand. In this mechanism, the consumers deliver their TOU electricity demands and subsequent control signals to utility providers through communication network infrastructure. The utility provider creates an hourly demand profile for each consumer by predicating individual requests over short- and long-time frames. The control signaling exchanged and prior arrangement of services enable utility providers to evaluate the status of wholesale market demand and assign prices considering dynamic changes in electricity demand. Numerical analysis study was carried out to validate the advantages of the proposed mechanism.

Strategic Timing and Pricing In On-Demand Platforms

This paper optimizes dynamic pricing and real-time resource allocation policies for a platform facing non- transferable capacity, stochastic demand-capacity imbalances, and strategic customers with heterogeneous price- and time-sensitivities. We characterize the optimal mechanism, which specifies a dynamic menu of prices and allocations. Service timing and pricing are used strategically to: (i) dynamically manage demand- capacity imbalances, and (ii) provide discriminated service levels. The balance between these two objectives depends on customer heterogeneity and customers’ time-sensitivities. The optimal policy may feature strategic idleness (deliberately rejecting incoming requests for discrimination), late service prioritization (clearing the queue of delayed customers) and deliberate late service rejection (focusing on incoming demand by rationing capacity for delayed customers). Surprisingly, the price charged to time-sensitive customers is not increasing with demand — high demand may trigger lower prices. By dynamically adjusting a menu of prices and service levels, the optimal mechanism increases profits significantly, as compared to dynamic pricing and static screening benchmarks. We also suggest a less information-intensive mechanism that is history-independent but fine-tunes the menu with incoming demand; this easier-to-implement mechanism yields close-to-optimal outcomes.

Stochastic Dynamic Pricing for EV Charging Stations With Renewable Integration and Energy Storage

This paper studies the problem of stochastic dynamic pricing and energy management policy for electric vehicle (EV) charging service providers. In the presence of renewable energy integration and energy storage system, EV charging service providers must deal with multiple uncertainties-charging demand volatility, inherent intermittency of renewable energy generation, and wholesale electricity price fluctuation. The motivation behind our work is to offer guidelines for charging service providers to determine proper charging prices and manage electricity to balance the competing objectives of improving profitability, enhancing customer satisfaction, and reducing impact on power grid in spite of these uncertainties. We propose a new metric to assess the impact on power grid without solving complete power flow equations. To protect service providers from severe financial losses, a safeguard of profit is incorporated in the model. Two algorithms-stochastic dynamic programming (SDP) algorithm and greedy algorithm (benchmark algorithm)-are applied to derive the pricing and electricity procurement policy. A Pareto front of the multi-objective optimization is derived. Simulation results show that using SDP algorithm can achieve up to 7% profit gain over using greedy algorithm. Additionally, we observe that the charging service provider is able to reshape spatial-temporal charging demands to reduce the impact on power grid via pricing signals.

A two-part dynamic pricing policy for household electricity consumption scheduling with minimized expenditure

In this paper we propose an optimization model for scheduling electrical appliances for an individual household. Here, customers are offered dynamic prices which are a function of that household’s planned consumption and forecasted grid load. We consider a grid connected system with a battery and an in-house renewable energy generator in the proposed scheduling model. This model minimizes the customer’s electricity bill subject to different constraints. We analyze our model with various pricing policies, price ranges and appliance operation windows. We find that the expenditure of the consumer decreases considerably in our model when shifting from flat prices to dynamic prices based on the forecasted grid load and the consumer’s individual planned consumption. Considerable expenditure reduction and individual load flattening is achieved with the use of a battery and an in-house renewable energy generator. Also, larger the price range, higher is the load flattening and lower is the expenditure. We show that our proposed pricing policy is beneficial to both consumers and suppliers.

Dynamic pricing, quality investment, and replenishment model for perishable items

AbstractThe deterioration of perishable items results not only in direct quantitative losses, but also in qualitative losses, which would reduce the customer acceptability. To maintain or improve the quality level, sellers usually invest in functionality, aesthetics, safety or any other attributes. In addition to quality, price also plays a critical role in influencing the purchase choice of consumers and the profit of a firm. Most inventory management models for perishables are restricted to physical quantity deterioration and do not address joint dynamic pricing and quality investment strategies. This paper studies an optimal replenishment model with dynamic pricing and quality investment for perishable products, where the quality and physical quantity deteriorate simultaneously. The demand rate is decreasing in sales price and increasing in quality level. A dynamic optimization model is proposed to maximize the total profit per unit time and solved on the basis of Pontryagin's maximum principle. The optimal joint dynamic pricing, quality investment, and replenishment policy is obtained. A numerical example and sensitivity analysis on the key system parameters are presented to illustrate the validity of the theoretical results. Some managerial implications for the pricing and quality investment for the perishables are provided.

Deep Koopman Controller Synthesis for Cyber-Resilient Market-Based Frequency Regulation

Abstract This paper investigates a data-driven countermeasure for price spoofing in the context of cyber security and market-based frequency regulation. Market-based control of transmission power networks relies on cyber-physical infrastructure, which raises questions of system vulnerability in relation to cyber-security. In this paper, we consider the challenge of engineering a robust data-driven controller in the presence of price spoofing, i.e. where hacking mechanisms adjust price signals in an ex-post market. We extend a recently developed algorithm called deep dynamic mode decomposition to learn Koopman operators of nonlinear systems with affine inputs. Based on the learned input-Koopman operator model, a design algorithm for nonlinear controller synthesis is devised to compute optimal dynamic pricing policies that restore the nominal frequency and recover economic efficiency in the presence of price spoofing. The efficacy of the proposed data-driven Koopman controller synthesis approach is validated through tests on a IEEE 39-bus benchmark.

Scenario-based system dynamics modeling for the cost recovery of new energy technology deployment: The case of smart metering roll-out

Abstract Smart meters are crucial technologies for enabling smart grid solutions and applications. Although smart metering deployment has been started at the national and regional levels, there is still the question that how should the costs of deployment be allocated among stakeholders. Cost-Benefit Analysis (CBA) is the common method for analyzing the economic feasibility of the deployment process. Starting from the CBA approach, this paper argues an efficient cost recovery scheme depends not only on the costs and benefits for each actor, but also on the interdependencies between the behavior of different actor groups. By taking a dynamic modeling approach and using System Dynamics models, this study examines the dynamics of interaction between different actors in the technology deployment process, and proposes scenarios for an efficient cost recovery. It is claimed that a dynamic view to the common Cost-Benefit Analysis approach has three advantages. First, the possibility of including actors benefiting from positive externalities or actors that can contribute to system efficiency is provided. Second, a balance can be found between the short term and long term consequences of system interventions; and finally, the development of innovative solutions, in the forms of business and policy scenarios is facilitated. The results may explain why reluctance to participate in the technology deployment process persists even after introducing dynamic pricing policies, and what factors are more critical in analyzing the cost and benefit structures of the technological system.

A model-based approximation of opportunity cost for dynamic pricing in attended home delivery

For online retailers with attended home delivery business models, the decisive factor for promising dynamic time slot pricing decisions is the quality of the opportunity cost approximation concerning incoming customer requests. For this purpose, we present a novel approximation approach based on mixed-integer linear programming that we integrate into the de facto standard dynamic pricing framework prevalent in the academic literature. Our approximation combines the most current information regarding the customers accepted to date with a forecast of expected customers to come that is adapted during the progress of the booking horizon. Thus, future customer requests demand management, i.e. the consequences of future pricing decisions, is anticipated. We approximate the retailer’s vehicle routes and thus delivery costs of expected customers by a dynamic seed-based scheme in which potential seeds’ locations as well as related distance approximations are dynamically adjusted under consideration of the locations of already accepted customers. In a computational study, we compare the approach to established pricing approaches in practice and to the state-of-the-art dynamic pricing policy. We show that our approach constantly yields the highest profit, specifically given a tight capacity level. We further provide implications for practical use. We show that, even for large-scale implementations in a real-time environment, our approach is applicable by using parallel computing and by only periodically recalculating opportunity cost. Even then, our approach leads to very good results.

CTS2M: concurrent task scheduling and storage management for residential energy consumers under dynamic energy pricing

Dynamic energy pricing policy introduces real-time power-consumption-reflective pricing in the smart grid in order to incentivise energy consumers to schedule electricity-consuming applications (tasks) more prudently to minimise electric bills. This has become a particularly interesting problem with the availability of photovoltaic (PV) power generation facilities and controllable energy storage systems. This study addresses the problem of concurrent task scheduling and storage management for residential energy consumers with PV and storage systems, in order to minimise the electric bill. A general type of dynamic pricing scenario is assumed where the energy price is both time-of-use and power dependent. Tasks are allowed to support suspend-now and resume-later operations. A negotiation-based iterative approach has been proposed. In each iteration, all tasks are ripped-up and rescheduled under a fixed storage charging/discharging scheme, and then the storage control scheme is derived based on the latest task scheduling. The concept of congestion is introduced to gradually adjust the schedule of each task, whereas dynamic programming is used to find the optimal schedule. A near-optimal storage control algorithm is effectively implemented. Experimental results demonstrate that the proposed algorithm can achieve up to 60.95% in the total energy cost reduction compared with various baseline methods.

Joint optimal inventory, dynamic pricing and advertisement policies for non-instantaneous deteriorating items

In this paper, a novel model for dynamic pricing and inventory control of non-instantaneously deteriorating items is proposed. To reflect the dynamic nature of the problem, the selling price is modeled as a time-dependent function of the initial selling price and the discount rate. To this end, the product is sold at the initial price value for a time period; then its price is exponentially discounted to boost customer demands. The demand rate is a function of dynamic price, advertisement and changes in price over time. The model seeks to maximize total profit of the system by determining the optimal replenishment cycle, initial price, discount rate, and frequency of advertisement. In order to characterize the optimal solution, some useful theoretical results are derived upon which an iterative solution algorithm is developed. To demonstrate validity of the proposed model and applicability of the developed algorithm, numerical results are provided that are accompanied by an efficient sensitivity analysis on the important parameters of the model.