Showing papers on "Dynamic pricing published in 2014"

Decomposition by Partial Linearization: Parallel Optimization of Multi-Agent Systems

Abstract: We propose a novel decomposition framework for the distributed optimization of general nonconvex sum-utility functions arising naturally in the system design of wireless multi-user interfering systems. Our main contributions are i) the development of the first class of (inexact) Jacobi best-response algorithms with provable convergence, where all the users simultaneously and iteratively solve a suitably convexified version of the original sum-utility optimization problem; ii) the derivation of a general dynamic pricing mechanism that provides a unified view of existing pricing schemes that are based, instead, on heuristics; and iii) a framework that can be easily particularized to well-known applications, giving rise to very efficient practical (Jacobi or Gauss-Seidel) algorithms that outperform existing ad hoc methods proposed for very specific problems. Interestingly, our framework contains as special cases well-known gradient algorithms for nonconvex sum-utility problems, and many block-coordinate descent schemes for convex functions.

Dynamic Pricing with an Unknown Demand Model: Asymptotically Optimal Semi-Myopic Policies

Abstract: We consider a monopolist who sells a set of products over a time horizon of T periods. The seller initially does not know the parameters of the products' linear demand curve, but can estimate them based on demand observations. We first assume that the seller knows nothing about the parameters of the demand curve, and then consider the case where the seller knows the expected demand under an incumbent price. It is shown that the smallest achievable revenue loss in T periods, relative to a clairvoyant who knows the underlying demand model, is of order T in the former case and of order log T in the latter case. To derive pricing policies that are practically implementable, we take as our point of departure the widely used policy called greedy iterated least squares ILS, which combines sequential estimation and myopic price optimization. It is known that the greedy ILS policy itself suffers from incomplete learning, but we show that certain variants of greedy ILS achieve the minimum asymptotic loss rate. To highlight the essential features of well-performing pricing policies, we derive sufficient conditions for asymptotic optimality.

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, product attributes, and 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 solved 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 constraints 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 precommitted and contingent heuristic policies that are asymptotic equilibria for its stochastic counterpart, when demand and supply are sufficiently large. This paper was accepted by Yossi Aviv, operations management.

On the (Surprising) Sufficiency of Linear Models for Dynamic Pricing with Demand Learning

Abstract: We consider a multi-period single product pricing problem with an unknown demand curve. The seller's objective is to adjust prices in each period so as to maximize cumulative expected revenues over a given finite time horizon; in doing so, the seller needs to resolve the tension between learning the unknown demand curve and maximizing earned revenues. The main question that we investigate is the following: how large of a revenue loss is incurred if the seller uses a simple parametric model which differs significantly (i.e., is misspecified) relative to the underlying demand curve. This "price of misspecification'' is expected to be significant if the parametric model is overly restrictive. Somewhat surprisingly, we show (under reasonably general conditions) that this may not be the case.

A Mechanism Design Approach to Resource Procurement in Cloud Computing

Abstract: We present a cloud resource procurement approach which not only automates the selection of an appropriate cloud vendor but also implements dynamic pricing. Three possible mechanisms are suggested for cloud resource procurement: cloud-dominant strategy incentive compatible (C-DSIC), cloud-Bayesian incentive compatible (C-BIC), and cloud optimal (C-OPT). C-DSIC is dominant strategy incentive compatible, based on the VCG mechanism, and is a low-bid Vickrey auction. C-BIC is Bayesian incentive compatible, which achieves budget balance. C-BIC does not satisfy individual rationality. In C-DSIC and C-BIC, the cloud vendor who charges the lowest cost per unit QoS is declared the winner. In C-OPT, the cloud vendor with the least virtual cost is declared the winner. C-OPT overcomes the limitations of both C-DSIC and C-BIC. C-OPT is not only Bayesian incentive compatible, but also individually rational. Our experiments indicate that the resource procurement cost decreases with increase in number of cloud vendors irrespective of the mechanisms. We also propose a procurement module for a cloud broker which can implement C-DSIC, C-BIC, or C--OPT to perform resource procurement in a cloud computing context. A cloud broker with such a procurement module enables users to automate the choice of a cloud vendor among many with diverse offerings, and is also an essential first step toward implementing dynamic pricing in the cloud.

A Scalable Stochastic Model for the Electricity Demand of Electric and Plug-In Hybrid Vehicles

Abstract: In this paper we propose a stochastic model, based on queueing theory, for electric vehicle (EV) and plug-in hybrid electric vehicle (PHEV) charging demand. Compared to previous studies, our model can provide 1) more accurate forecasts of the load using real-time sub-metering data, along with the level of uncertainty that accompanies these forecasts; 2) a mathematical description of load, along with the level of demand flexibility that accompanies this load, at the wholesale level. This can be useful when designing demand response and dynamic pricing schemes. Our numerical experiments tune the proposed statistics on real PHEV charging data and demonstrate that the forecasting method we propose is more accurate than standard load prediction techniques.

A Survey on Green-Energy-Aware Power Management for Datacenters

Abstract: Megawatt-scale datacenters have emerged to meet the increasing demand for IT applications and services. The hunger for power brings large electricity bills to datacenter operators and causes significant impacts to the environment. To reduce costs and environmental impacts, modern datacenters, such as those of Google and Apple, are beginning to integrate renewable or green energy sources into their power supply. This article investigates the green-energy-aware power management problem for these datacenters and surveys and classifies works that explicitly consider renewable energy and/or carbon emission. Our aim is to give a full view of this problem. Hence, we first provide some basic knowledge on datacenters (including datacenter components, power infrastructure, power load estimation, and energy sources' operations), the electrical grid (including dynamic pricing, power outages, and emission factor), and the carbon market (including cap-and-trade and carbon tax). Then, we categorize existing research works according to their basic approaches used, including workload scheduling, virtual machine management, and energy capacity planning. Each category's discussion includes the description of the shared core idea, qualitative analysis, and quantitative analysis among works of this category.

Strategic pricing with reference effects in a competitive supply chain

Abstract: The reference-price effect refers to the demand deviation caused by consumers’ perceived losses or gains when the current market price of a product differs from a cognitive benchmark (known as a reference price) formed by the customers based on past prices. The impact of such a reference effect on the dynamic pricing policy of a monopolist has been widely studied in the literature. However, despite the importance of the topic due to the growing transparency of price information in the Internet era, its relevance in the context of a distribution channel has never been explored. In this study, we consider a supply chain consisting of a manufacturer and a retailer in a bilateral monopoly setting. The two channel members independently choose their pricing strategies to optimize their own benefits in the presence of consumers’ reference-price effects. Based on a deterministic demand function, we derive the equilibrium prices and analyze the resulting profit sensitivity with respect to various factors that crucially shape the reference effects. We conclude that both the centralized and decentralized channels should want consumers to have a higher initial reference price, be more sensitive to the reference-price effect, and be more loyal to their product.

Integrating Home Energy Simulation and Dynamic Electricity Price for Demand Response Study

Abstract: This paper studies how to develop and evaluate demand response strategies from the consumer's perspective through a computational experiment approach. The proposed approach includes a home energy consumption simulator, a demand response mechanism obtained through optimization, particle swam or heuristic method, and an integrative computing platform that combines the home energy simulator and MATLAB together for demand response development and evaluation. Several demand response strategies are developed and evaluated through the computational experiment technique. The paper investigates and compares characteristics of different demand response strategies and how they are affected by dynamic pricing tariffs, seasons, and weather. Case studies are conducted by considering home energy consumption, dynamic electricity pricing schemes, and demand response methods.

Dynamic pricing and profit maximization for the cloud with geo-distributed data centers

Abstract: Cloud providers often choose to operate datacenters over a large geographic span, in order that users may be served by resources in their proximity. Due to time and spatial diversities in utility prices and operational costs, different datacenters typically have disparate charges for the same services. Cloud users are free to choose the datacenters to run their jobs, based on a joint consideration of monetary charges and quality of service. A fundamental problem with significant economic implications is how the cloud should price its datacenter resources at different locations, such that its overall profit is maximized. The challenge escalates when dynamic resource pricing is allowed and long-term profit maximization is pursued. We design an efficient online algorithm for dynamic pricing of VM resources across datacenters in a geo-distributed cloud, together with job scheduling and server provisioning in each datacenter, to maximize the profit of the cloud provider over a long run. Theoretical analysis shows that our algorithm can schedule jobs within their respective deadlines, while achieving a time-average overall profit closely approaching the offline maximum, which is computed by assuming that perfect information on future job arrivals are freely available. Empirical studies further verify the efficacy of our online profit maximizing algorithm.

Cooperative game-based distributed resource allocation in horizontal dynamic cloud federation platform

Abstract: Distributed resource allocation is a very important and complex problem in emerging horizontal dynamic cloud federation (HDCF) platforms, where different cloud providers (CPs) collaborate dynamically to gain economies of scale and enlargements of their virtual machine (VM) infrastructure capabilities in order to meet consumer requirements HDCF platforms differ from the existing vertical supply chain federation (VSCF) models in terms of establishing federation and dynamic pricing There is a need to develop algorithms that can capture this complexity and easily solve distributed VM resource allocation problem in a HDCF platform In this paper, we propose a cooperative game-theoretic solution that is mutually beneficial to the CPs It is shown that in non-cooperative environment, the optimal aggregated benefit received by the CPs is not guaranteed We study two utility maximizing cooperative resource allocation games in a HDCF environment We use price-based resource allocation strategy and present both centralized and distributed algorithms to find optimal solutions to these games Various simulations were carried out to verify the proposed algorithms The simulation results demonstrate that the algorithms are effective, showing robust performance for resource allocation and requiring minimal computation time

Load Shaping Strategy Based on Energy Storage and Dynamic Pricing in Smart Grid

Abstract: Load shaping is one of important and challenging issues in power grid In this paper, we propose a novel load shaping strategy based on energy storage and dynamic pricing in smart grid In the proposed strategy, a consumer is encouraged to draw a certain amount of energy (ie, quota) from the grid When the actual energy demand is deviated from the quota, the consumer is faced with a higher electricity price With the help of energy storage, the consumer can draw less electricity from the grid at a lower price by discharging energy when the demand is higher than the quota and draw more electricity from the grid at a lower price by charging energy when the demand is lower than the quota As a result, the utility can implement load shaping and consumers can save energy cost simultaneously Moreover, the proposed strategy can be implemented with low complexity and in a distributed fashion, which offers scalability to large number of consumers Simulations results show the effectiveness of the proposed load shaping strategy

The Impact of Linear Optimization on Promotion Planning

Abstract: Sales promotions are important in the fast-moving consumer goods (FMCG) industry due to the significant spending on promotions and the fact that a large proportion of FMCG products are sold on promotion. This paper considers the problem of planning sales promotions for a FMCG product in a grocery retail setting. The category manager has to solve the promotion optimization problem (POP) for each product, i.e., how to select a posted price for each period in a finite horizon so as to maximize the retailer's profit. Through our collaboration with Oracle Retail, we developed an optimization formulation for the POP that can be used by category managers in a grocery environment. Our formulation incorporates business rules that are relevant in practice. We propose general classes of demand functions (including multiplicative and additive) which incorporate the post-promotion dip effect, and can be estimated from sales data. In general, the POP formulation has a nonlinear objective and is NP-hard. We then propose a linear integer programming (IP) approximation of the POP. We show that the IP has an integral feasible region and hence, can be solved efficiently as a linear program (LP). We develop performance guarantees for the profit of the LP solution relative to the optimal profit. Using sales data from a grocery retailer, we first show that our demand models can be estimated with high accuracy and then, demonstrate that using the LP promotion schedule could potentially increase the profit by 3%, with a potential profit increase of 5% if some business constraints were to be relaxed.

A Novel Model for Competition and Cooperation among Cloud Providers

Abstract: Having received significant attention in the industry, the cloud market is nowadays fiercely competitive with many cloud providers. On one hand, cloud providers compete against each other for both existing and new cloud users. To keep existing users and attract newcomers, it is crucial for each provider to offer an optimal price policy which maximizes the final revenue and improves the competitive advantage. The competition among providers leads to the evolution of the market and dynamic resource prices over time. On the other hand, cloud providers may cooperate with each other to improve their final revenue. Based on a service level agreement, a provider can outsource its users’ resource requests to its partner to reduce the operation cost and thereby improve the final revenue. This leads to the problem of determining the cooperating parties in a cooperative environment. This paper tackles these two issues of the current cloud market. First, we solve the problem of competition among providers and propose a dynamic price policy. We employ a discrete choice model to describe the user’s choice behavior based on his obtained benefit value. The choice model is used to derive the probability of a user choosing to be served by a certain provider. The competition among providers is formulated as a non-cooperative stochastic game where the players are providers who act by proposing the price policy simultaneously. The game is modelled as a Markov Decision Process whose solution is a Markov Perfect Equilibrium. Then, we address the cooperation among providers by presenting a novel algorithm for determining a cooperation strategy that tells providers whether to satisfy users’ resource requests locally or outsource them to a certain provider. The algorithm yields the optimal cooperation structure from which no provider unilaterally deviates to gain more revenue. Numerical simulations are carried out to evaluate the performance of the proposed models.

Economics of Free Under Perpetual Licensing: Implications for the Software Industry

Abstract: In this paper, we explore the economics of free under perpetual licensing. In particular, we focus on two emerging software business models that involve a free component: feature-limited freemiumFLF and uniform seedingS. Under FLF, the firm offers the basic software version for free, while charging for premium features. Under S, the firm gives away for free the full product to a percentage of the addressable market uniformly across consumer types. We benchmark their performance against a conventional business model under which software is sold as a bundle labeled as “charge for everything” or CE without free offers. In the context of consumer bounded rationality and information asymmetry, we develop a unified two-period consumer valuation learning framework that accounts for both word-of-mouth WOM effects and experience-based learning, and use it to compare and contrast the three business models. Under both constant and dynamic pricing, for moderate strength of WOM signals, we derive the equilibria for each model and identify optimality regions. In particular, S is optimal when consumers significantly underestimate the value of functionality and cross-module synergies are weak. When either cross-module synergies are stronger or initial priors are higher, the firm decides between CE and FLF. Furthermore, we identify nontrivial switching dynamics from one optimality region to another depending on the initial consumer beliefs about the value of the embedded functionality. For example, there are regions where, ceteris paribus, FLF is optimal when the prior on premium functionality is either relatively low or high, but not in between. We also demonstrate the robustness of our findings with respect to various parameterizations of cross-module synergies, strength of WOM effects, and number of periods. We find that stronger WOM effects or more periods lead to an expansion of the seeding optimality region in parallel with a decrease in the seeding ratio. Moreover, under CE and dynamic pricing, second period price may be decreasing in the initial consumer valuation beliefs when WOM effects are strong and the prior is relatively low. However, this is not the case under weak WOM effects. We also discuss regions where price skimming and penetration pricing are optimal. Our results provide key managerial insights that are useful to firms in their business model search and implementation.

Dynamic pricing vs. acquiring information on consumers’ heterogeneous sensitivity to product freshness

Abstract: We propose a model of an inventory system in which a perishable product is periodically replenished, and the retailer is unaware of consumer heterogeneity in consumers’ sensitivity to freshness of a perishable product with a fixed shelf life (though it exists). Using an analytical approach, we optimally solve the problem and evaluate the extent to which unawareness is likely to detract from a retailer’s profit and the extent to which it is likely to affect the price that consumers pay. In addition, we evaluate the conditions in which a dynamic pricing policy is beneficial either to the retailer or to the consumer, as compared with a static pricing policy. It is proven that the retailer should assign products a lower price at the early stages of their shelf life and then raise the price as the products approach expiration. A numerical illustration combined with sensitivity analysis demonstrates the applicability of the modelling approach. Key parameters such as volatility of consumer sensitivity to freshne...

A Distributed Demand-Side Management Framework for the Smart Grid

Abstract: This paper proposes a fully distributed Demand-Side Management system for Smart Grid infrastructures, especially tailored to reduce the peak demand of residential users. In particular, we use a dynamic pricing strategy, where energy tariffs are function of the overall power demand of customers. We consider two practical cases: (1) a fully distributed approach, where each appliance decides autonomously its own scheduling, and (2) a hybrid approach, where each user must schedule all his appliances. We analyze numerically these two approaches, showing that they are characterized practically by the same performance level in all the considered grid scenarios. We model the proposed system using a non-cooperative game theoretical approach, and demonstrate that our game is a generalized ordinal potential one under general conditions. Furthermore, we propose a simple yet effective best response strategy that is proved to converge in a few steps to a pure Nash Equilibrium, thus demonstrating the robustness of the power scheduling plan obtained without any central coordination of the operator or the customers. Numerical results, obtained using real load profiles and appliance models, show that the system-wide peak absorption achieved in a completely distributed fashion can be reduced up to 55%, thus decreasing the capital expenditure (CAPEX) necessary to meet the growing energy demand.

Learning-by-Doing in Solar Photovoltaic Installations

Abstract: The solar photovoltaic (PV) industry in the United States has been the recipient of billions of dollars of subsidies at the federal and state level, often motivated by environmental externalities and dynamic spillovers from learning-by-doing in the installation of the technology. This paper investigates cost reductions due to learning-bydoing (LBD) using comprehensive data on all solar PV installations in California from 2002 to 2012. We develop a model of installer firm pricing behavior that allows for economies of scale, market power, and dynamic pricing to quantify both appropriable and non-appropriable LBD. We find strong evidence for both, suggesting a role for solar PV subsidies to improve economic efficiency by addressing a non-appropriable LBD positive externality. However, our results suggest that the California Solar Initiative cannot be justified by non-appropriable LBD alone.

Reoptimization and Self-Adjusting Price Control for Network Revenue Management

Abstract: We consider a standard dynamic pricing problem with finite inventories, finite selling horizon, and stochastic demands, where the objective of the seller is to maximize total expected revenue. We introduce a simple improvement of the popular static price control known in the literature. The proposed heuristic only requires a single optimization at the beginning of the selling horizon and does not require any reoptimization at all. This provides an advantage over the potentially heavy computational burden of reoptimization, especially for very large applications with frequent price adjustments. In addition, our heuristic can be implemented in combination with a few reoptimizations to achieve a high-level revenue performance. This hybrid of real-time adjustment and reoptimization allows the seller to enjoy the benefit of reoptimization without overdoing it.

Dynamic Pricing and Inventory Management with Dual Suppliers of Different Lead Times and Disruption Risks

Abstract: It is common for a firm to make use of multiple suppliers of different delivery lead times, reliabilities, and costs. In this study, we are concerned with the joint pricing and inventory control problem for such a firm that has a quick-response supplier and a regular supplier that both suffer random disruptions, and faces price-sensitive random demands. We aim at characterizing the optimal ordering and pricing policies in each period over a planning horizon, and analyzing the impacts of supply source diversification. We show that, when both suppliers are unreliable, the optimal inventory policy in each period is a reorder point policy and the optimal price is decreasing in the starting inventory level in that period. In addition, we show that having supply source diversification or higher supplier reliability increases the firm's optimal profit and lowers the optimal selling price. We also demonstrate that, with the selling price as a decision, a supplier may receive even more orders from the firm after an additional supplier is introduced. For the special case where the quick-response supplier is perfectly reliable, we further show that the optimal inventory policy is of a base-stock type and the optimal pricing policy is a list-price policy with markdowns.

Optimal Pricing Strategy for Operators in Cognitive Femtocell Networks

Abstract: Cognitive femtocell has been envisioned as a promis- ing technology for covering indoor environment and assisting heavy-loaded macrocell network. Although lots of technical issues of cognitive femtocell network have been studied, e.g., spectrum sharing, interference mitigation, etc., the economic issues that are very important for practical femtocell deployment have not been well investigated in the literatures. In this paper, we focus on the pricing issues in the cognitive femtocell network and propose a two-tier pricing game theoretic framework with two models: static and dynamic pricing models. In the static pricing model, we derive the closed-form expressions for pricing and demand functions, as well as the Nash equilibrium pricing strategies for both macrocell and femtocell operators. In the dynamic pricing model, we first model the cognitive users' network access behavior as a two-dimensional Markov decision process and propose a modified value iteration algorithm to find the best strategy profiles for cognitive users. Based on the analysis of users' behavior, we further design an iterative gradient descent algorithm to find the Nash equilibrium pricing strategies for both macrocell and femto- cell operators. Simulation results verify our theoretic analysis and show that the proposed algorithm in the dynamic pricing model can quickly converge to the Nash equilibrium prices.