Dynamic Pricing Algorithm Research Articles

Modelling Passengers' Reaction to Dynamic Prices in Ride-on-demand Services

In emerging ride-on-demand (RoD) services such as Uber and Didi (in China), dynamic prices play an important role in regulating supply and demand, trying to improve the service quality for both drivers and passengers. In this paper, we take a new perspective to study RoD services besides the supply or demand, and focus on passengers' reaction to dynamic prices. Passengers' reaction can be regarded as a process of searching for the best price before getting on a car, and the searching process reflects passengers' demand elasticity -- “how eager they are requesting a ride”. We collect data of passengers' reaction from a real RoD service provider in China, and analyze the patterns of passengers' reaction. The analysis results show that both the dynamic prices and passengers' demand elasticity influence their reaction. We then adopt and extend a previous model for sequential search from a known distribution to understand passengers' reaction, and use our data to obtain the search costs under various circumstances, which could be interpreted as passengers' demand elasticity. Insights on the search cost and other relevant quantities are discussed. Our expectation is that the result of the study should be helpful not only for service providers in designing dynamic pricing algorithms, but also for passengers and policy makers in understanding the effects and implications of dynamic pricing.

Dynamic Pricing and Matching in Ride-Hailing Platforms

Ride-hailing platforms such as Uber, Lyft and DiDi have achieved explosive growth and reshaped urban transportation. The theory and technologies behind these platforms have become one of the most active research topics in the fields of economics, operations research, computer science, and transportation engineering. In particular, advanced matching and dynamic pricing algorithms -- the two key levers in ride-hailing -- have received tremendous attention from the research community and are continuously being designed and implemented at industrial scales by ride-hailing platforms. We provide a review of matching and dynamic pricing techniques in ride-hailing, and show that they are critical for providing an experience with low waiting time for both riders and drivers. Then we link the two levers together by studying a pool-matching mechanism called dynamic waiting that varies rider waiting and walking before dispatch, which is inspired by a recent carpooling product Express Pool from Uber. We show using data from Uber that by jointly optimizing dynamic pricing and dynamic waiting, price variability can be mitigated, while increasing capacity utilization, trip throughput, and welfare. We also highlight several key practical challenges and directions of future research from a practitioner's perspective.

Stabilization of Structure-Preserving Power Networks with Market Dynamics

This paper studies the problem of maximizing the social welfare while stabilizing both the physical power network as well as the market dynamics. For the physical power grid a third-order structure-preserving model is considered involving both frequency and voltage dynamics. By applying the primal-dual gradient method to the social welfare problem, a distributed dynamic pricing algorithm in port-Hamiltonian form is obtained. After interconnection with the physical system a closed-loop port-Hamiltonian system of differential-algebraic equations is obtained, whose properties are exploited to prove local asymptotic stability of the optimal point.

A dynamic pricing algorithm for a network of virtual resources

SummaryA service function chain (SFC) is an ordered combination of abstract network functions (eg, network address translation and a firewall) that together define a network service (eg, video on demand). In an SDN/NFV‐based architecture, SFCs are composed of virtual network functions that need to be mapped to physical network components. Because the mapping of an SFC may be possible by multiple competing infrastructure providers (InPs), price will be a key differentiating factor. The pricing algorithm is therefore essential towards revenue management, yet current static pricing approaches suffer from several limitations. Among others, they do not consider the characteristics of the requests or the current state of the physical network. Using historical data, market data, and the current state of the physical network we investigate whether it is possible to increase total revenue of an InP compared to traditional static pricing approaches. This paper proposes a dynamic pricing algorithm to determine (1) at which utilization level it is rewarding to charge a higher price for a particular resource and (2) the alternative price that should be charged.Our simulation results for 8 different setups show that the proposed heuristic outperforms a static pricing approach significantly (by 8‐85% points for the considered scenarios). As a consequence, the proposed approach can be considered as an alternative for static pricing approaches. Still, it is unclear how the total revenue of an InP is affected when multiple or all competitors use a dynamic pricing algorithm; this will therefore remain the focus of future work.

A Unifying Energy-Based Approach to Stability of Power Grids With Market Dynamics

In this paper, a unifying energy-based approach is provided to the modeling and stability analysis of power systems coupled with market dynamics. We consider a standard model of the power network with a third-order model for the synchronous generators involving voltage dynamics. By applying the primal-dual gradient method to a social welfare optimization, a distributed dynamic pricing algorithm is obtained, which can be naturally formulated in port-Hamiltonian form. By interconnection with the physical model a closed-loop port-Hamiltonian system is obtained, whose properties are exploited to prove asymptotic stability to the set of optimal points. This result is extended to the case that also general nodal power constraints are included into the social welfare problem. Additionally, the case of line congestion and power transmission costs in acyclic networks is covered. Finally, a dynamic pricing algorithm is proposed that does not require knowledge about the power supply and demand.

Dynamic Pricing and Energy Consumption Scheduling With Reinforcement Learning

In this paper, we study a dynamic pricing and energy consumption scheduling problem in the microgrid where the service provider acts as a broker between the utility company and customers by purchasing electric energy from the utility company and selling it to the customers. For the service provider, even though dynamic pricing is an efficient tool to manage the microgrid, the implementation of dynamic pricing is highly challenging due to the lack of the customer-side information and the various types of uncertainties in the microgrid. Similarly, the customers also face challenges in scheduling their energy consumption due to the uncertainty of the retail electricity price. In order to overcome the challenges of implementing dynamic pricing and energy consumption scheduling, we develop reinforcement learning algorithms that allow each of the service provider and the customers to learn its strategy without a priori information about the microgrid. Through numerical results, we show that the proposed reinforcement learning-based dynamic pricing algorithm can effectively work without a priori information about the system dynamics and the proposed energy consumption scheduling algorithm further reduces the system cost thanks to the learning capability of each customer.

A Real-Time Dynamic Pricing Algorithm for Smart Grid With Unstable Energy Providers and Malicious Users

In this paper, we consider a smart power model, where some subscribers share several energy providers and there are some malicious users in this power grid. The energy providers are managed by a power market scheduling center (PMSC), which broadcasts electricity price to subscribers and energy providers. The energy providers and subscribers update their capacities and energy consumption requirements, respectively, according to the electricity prices received. In order to identify the malicious users and the unstable energy providers, the mechanism of identification and processing (MIP) for the malicious users and unstable energy providers is proposed. By integrating the MIP, we proposed a heuristic algorithm called the dynamic pricing algorithm with malicious users and unstable energy providers (DPAMU) to get the optimal electricity price as well as the optimal power requirement and the load capacity. Finally, the simulation results show that the proposed DPAMU has good convergence performance and can shave and clip the peak load effectively.

Modelling revenue generation in a dynamically priced mobile telephony service

Dynamic pricing has been used extensively in specific markets for many years but recent years have seen an interest in the utilization of this approach for the deployment of novel and attractive tariff structures for mobile communication services. This paper describes the development and operation of an agent based model (ABM) for subscriber behavior in a dynamically priced mobile telephony network. The design of the ABM was based on an analysis of real call detail records recorded in a Uganda mobile telephony network in which dynamic pricing was deployed. The ABM includes components which simulate subscriber calling behavior, mobility within the network and social linkages. Using this model, this paper reports on an investigation of a number of alternative strategies for the dynamic pricing algorithm which indicate that the network operator will likely experience revenue losses ranging from a 5 %, when the pricing algorithm is based on offering high value subscriber cohort enhanced random discounts compared to a lower value subscriber cohort, to 30 %, when the priding algorithm results in the discount on offer in a cell being inversely proportional to the contemporary cell load. Additionally, the model appears to suggest that the use of optimization algorithms to control the level of discount offered in cells would likely result in discount simply converging to a no-discount scenario. Finally, commentary is offered on additional factors which need to be considered when interpreting the results of this work such as the impact of subscriber churn on the size of the subscriber base and the technical and marketing challenges of deploying the various dynamic pricing algorithms which have been investigated.

In-Depth Analysis of Pricing Problem Relaxations for the Capacitated Arc-Routing Problem

Recently, Bode and Irnich [Bode C, Irnich S (2012) Cut-first branch-and-price-second for the capacitated arc-routing problem. Oper. Res. 60(5):1167–1182] presented a cut-first branch-and-price-second algorithm for solving the capacitated arc-routing problem (CARP). The fundamental difference to other approaches for exactly solving the CARP is that the entire algorithm works directly on the typically sparse underlying graph representing the street network. This enables the use of highly efficient dynamic programming-based pricing algorithms to solve the column-generation subproblem also known as the pricing problem. The contribution of this paper is the in-depth analysis of the CARP pricing problem and its possible relaxations, including the construction of new labeling algorithms for their solution and comprehensive computational tests on standard benchmark problems. We show that a systematic variation of different relaxations provides a powerful approach to solve knowingly hard instances of the CARP to proven optimality.

Online Network Revenue Management Using Thompson Sampling

We consider a network revenue management problem where an online retailer aims to maximize revenue from multiple products with limited inventory constraints. As common in practice, the retailer does not know the consumer's purchase probability at each price and must learn the mean demand from sales data. We propose an efficient and effective dynamic pricing algorithm, which builds upon the Thompson sampling algorithm used for multi-armed bandit problems by incorporating inventory constraints into the model and algorithm. Our algorithm proves to have both strong theoretical performance guarantees as well as promising numerical performance results when compared to other algorithms developed for the same setting. More broadly, our paper contributes to the literature on the multi-armed bandit problem with resource constraints, since our algorithm applies directly to this setting when the inventory constraint is interpreted as general resource constraints.

Dynamic Scheduling and Pricing in Wireless Cloud Computing

In this paper, we consider a wireless cloud computing system in which the service provider operates a data center and provides cloud services to its subscribers at dynamic prices. We propose a joint optimization of scheduling and pricing decisions for delay-tolerant batch services to maximize the service provider's long-term profit. Unlike the existing research on jointly scheduling and pricing that focuses on static or asymptotic analysis, we focus on a dynamic setting and develop a provably-efficient Dynamic Scheduling and Pricing (Dyn-SP) algorithm which, without the necessity of predicting the future information, can be applied to an arbitrarily random environment that may follow an arbitrary trajectory overtime. We prove that, compared to the optimal offline algorithm with future information, Dyn-SP produces a close-to-optimal average profit while bounding the job queue length in the data center. We perform a trace-based simulation study to validate Dyn-SP. In particular, we show both analytically and numerically that a desired tradeoff between the profit and queueing delay can be obtained by appropriately tuning the control parameter. Our results also indicate that, compared to the existing algorithms which neglect demand-side management, cooling system energy consumption, and/or the queue length information, Dyn-SP achieves a higher average profit while incurring (almost) the same average queueing delay.

Model-Based Dynamic Pricing Algorithm for Managed Lanes

Managed lanes, or high-occupancy toll (HOT) lanes, have been implemented across the United States to improve the utility of existing road facilities. The pricing algorithm in managed lanes is the critical component in ensuring that the desired level of service metrics is met. Some pricing algorithms currently in use are static algorithms, and others adopt a dynamic strategy. Static pricing algorithms do not account for the changes in real-time traffic conditions. However, dynamic pricing algorithms are reactive in nature and do not account for the potential demand for actual future time intervals for which the toll is determined. The HOT-lane system is nonlinear and complex in nature; this complexity leads to high levels of instability in such a system. The complexity has been increasing because of the growth in demand as well as incorporation of other, noninteracting strategies that are implemented to address this demand. Therefore, more sophisticated designs of the pricing algorithm are needed for HOT-lane pricing control. A model-based pricing algorithm is proposed for determining the toll rate dynamically to maximize the throughput on the HOT lanes while maintaining a desired level of service. It consists of both proactive and reactive components to achieve fast response to real-time changes and maintain a steady, maximal traffic flow. The controller structure also incorporates active bottleneck management to maintain optimal traffic flow under stressed conditions. Implementation of this controller has shown high utilization of HOT lanes while ensuring the desired level of service.

Research on dynamic pricing of supply chain products based on channel advantages

PurposeThe purpose of this paper is to study the pricing problem of product transfer price under the channel advantages; determine the structure models of optimal transfer price expectation; and compare the differences in pricing of different pricing dominant parties.Design/methodology/approachUncertain factors are introduced into dynamic pricing mathematics models; production and storage models are combined; the method of functional analysis is used to solve transfer pricing question under different advantage conditions; and price matching models in supply chain integration are put forth.FindingsThere is a proportional relationship between the optimal transfer price expectation and price fluctuation. The party which has channel advantages will gain relatively more profit, but the maximum revenue can be obtained only in the supply chain integration.Research limitations/implicationsThere is no appropriate empirical data to verify the models.Practical implicationsThe paper provides pricing reference method to monopoly competitive enterprises on different stages. The matching pricing models based on E‐commerce can deal with the price deviation caused by goal difference and random factors automatically.Originality/valueThe paper considers production and inventory pricing, reflects the influence of the whole pricing factors under different channel advantages, and puts forth dynamic matching pricing models and algorithm under the E‐commerce circumstances.

Revenue Maximization in Time-Varying Multi-Hop Wireless Networks: A Dynamic Pricing Approach

In this paper, we study a wireless multi-hop network where multiple flows co-exist and share the network resource collectively. Each flow is associated with a user which has specific requirements on its tradeoff between cost and quality of service. To support heterogeneous transmissions efficiently, we propose a quality-aware dynamic pricing algorithm, namely, QADP, which provably maximizes the overall network revenue while maintaining the stability of the network. Our proposed scheme enjoys the merit of self-adaptability due to its online nature.

Dynamic Pricing and Queue Stability in Wireless Random Access Games

We study the interaction among users of contention-based wireless networks, where the performance of the network is highly correlated with user transmission probabilities. Considering the underlying user incentives, we make use of the conceptual framework of noncooperative game theory to obtain a distributed control mechanism to limit the contention among wireless nodes by taking into account queue stability and injecting linear pricing to punish greedy behavior. We present a comprehensive analysis of the game including existence and uniqueness of Nash equilibrium point, convergence dynamics, and robustness properties. Utilizing linear pricing enables us to move the equilibrium point of the game to a desirable region. We obtain conditions on linear prices necessary to achieve stability of user queues in the asymmetric and symmetric cases. In addition, we propose dynamic pricing algorithms, in which wireless users play the game without cooperation while the base station adjusts the linear price of each user. Under limited knowledge of game parameters, we present a dynamic equal pricing algorithm that moves the Nash equilibrium to the aggregate throughput maximizing solution. The theoretical results are verified, and the convergence and efficiency of the proposed game are illustrated via simulations.

A novel dynamic pricing scheme for contributing peers in the VoD system

In this paper we have proposed a dynamic pricing scheme for the contributing peers in the Video on Demand (VoD) system. The scheme provides an effective mechanism to maximize the profit through the residual resources of the contributing peers. A utilization function is executed for each contributing peer to estimate the utility factor based on the parameters such as initial setup cost, holding cost, chaining cost and salvage cost. In this paper, we urge an effective dynamic pricing algorithm that efficiently utilizes a range of parameters with a varying degree of complexity. The key findings of the algorithm are (i) each contributing peers are benefitted by the monetary based on its resource contributions to the VoD system and (ii) a high degree of social optimum is established by proficiently aggregating the contributing peer's resources with the overall resources of the VoD system. We validate our claim by simulating the proposed dynamic pricing scheme with other standard pricing schemes such as altruism, cost model and game theory perspective. The result of our dynamic pricing scheme shows the best utility factor than other standard pricing schemes.

Dynamic pricing model and algorithm for perishable products with fuzzy demand

AbstractThis paper studies the dynamic pricing problem of selling fixed stock of perishable items over a finite horizon, where the decision maker does not have the necessary historic data to estimate the distribution of uncertain demand, but has imprecise information about the quantity demand. We model this uncertainty using fuzzy variables. The dynamic pricing problem based on credibility theory is formulated using three fuzzy programming models, viz.: the fuzzy expected revenue maximization model, α‐optimistic revenue maximization model, and credibility maximization model. Fuzzy simulations for functions with fuzzy parameters are given and embedded into a genetic algorithm to design a hybrid intelligent algorithm to solve these three models. Finally, a real‐world example is presented to highlight the effectiveness of the developed model and algorithm. Copyright © 2009 John Wiley & Sons, Ltd.

Stackelberg-based dynamic incentive pricing algorithm in heterogeneous ubiquitous network

A challenge in the convergence of heterogeneous networks is how to combine the ubiquitous resources and provide the diversified individual services. This paper designs a market model for aggregating reconfiguration in heterogeneous networks based on the tradeoff between resource allocation and consumers’ requirement. To unify the benefits of operators and consumers, a novel Stackelberg-based dynamic incentive pricing algorithm is proposed. The results of the theoretical analysis and simulation demonstrate that the proposed strategy provides incentive for cooperation by means of appropriate resource allocation, and improves the utilization of network resources, thereby effectively realizing the optimization of the whole network performance.

Dynamic congestion-based pricing of bandwidth and buffer

We consider pricing of network resources in a reservation-based quality-of-service architecture. The pricing policy implements a distributed resource allocation to provide guaranteed bounds on packet loss and end-to-end delay for real-time applications. Distributed pricing roles are assigned to each user, each network node, and an arbitrager in between the user and the network. When delay constraints are not binding, we investigate two dynamic pricing algorithms using gradient projection and Newton's method to update prices, and prove their convergence. We analyze the performance of the dynamic pricing policies and show that the gradient algorithm using Newton's method converges more quickly and displays only a few small fluctuations. When delay constraints are binding, we investigate subgradient methods which can provide convergence to some range of the optimal allocation.

On pricing algorithms for batched content delivery systems

Businesses offering video-on-demand (VoD) and downloadable-CD sales are growing in the Internet. Batching of requests coupled with a one-to-many delivery mechanism such as multicast can increase scalability and efficiency. There is very little insight into pricing such services in a manner that utilizes network and system resources efficiently while also maximizing the expectation of revenue. In this paper, we investigate simple, yet effective mechanisms to price content in a batching context. We observe that if customer behavior is well understood and temporally invariant, a fixed pricing scheme can maximize expectation of revenue if there are infinite resources. However, with constrained resources and potentially unknown customer behavior, only a dynamic pricing algorithm can maximize expectation of revenue. We formulate the problem of pricing as a constrained optimization problem and show that maximizing the expectation of revenue can be intractable even when the customer behavior is well known. Since customer behavior is unlikely to be well known in an Internet setting, we develop a model to understand customer behavior online and a pricing algorithm based on this model. Using simulations, we characterize the performance of this algorithm and other simple and deployable pricing schemes under different customer behavior and system load profiles. Based on our work, we propose a pricing scheme that combines the best features of the different pricing schemes and analyze its performance.