Showing papers on "Dynamic pricing published in 2011"

Optimal demand response based on utility maximization in power networks

Abstract: Demand side management will be a key component of future smart grid that can help reduce peak load and adapt elastic demand to fluctuating generations. In this paper, we consider households that operate different appliances including PHEVs and batteries and propose a demand response approach based on utility maximization. Each appliance provides a certain benefit depending on the pattern or volume of power it consumes. Each household wishes to optimally schedule its power consumption so as to maximize its individual net benefit subject to various consumption and power flow constraints. We show that there exist time-varying prices that can align individual optimality with social optimality, i.e., under such prices, when the households selfishly optimize their own benefits, they automatically also maximize the social welfare. The utility company can thus use dynamic pricing to coordinate demand responses to the benefit of the overall system. We propose a distributed algorithm for the utility company and the customers to jointly compute this optimal prices and demand schedules. Finally, we present simulation results that illustrate several interesting properties of the proposed scheme.

Do Residential Customers Respond to Hourly Prices? Evidence from a Dynamic Pricing Experiment

Abstract: This paper uses the results of a dynamic pricing experiment for households in the District of Columbia to determine whether the reduction in demand associated with an hourly price signal is economically different from the demand reduction associated with an equivalent price signal that is four times longer in duration. For both regular and all-electric customers, the percentage demand reduction associated with a given percentage increase in the hourly price is approximately equal to the percentage demand reduction associated with the same percentage price increase of a much longer duration.

Analysis of Residential Demand Response and double-auction markets

Abstract: Demand response and dynamic pricing programs are expected to play increasing roles in the modern smart grid environment. While direct load control of end-use loads has existed for decades, price driven response programs are only beginning to be explored at the distribution level. These programs utilize a price signal as a means to control demand. Active markets allow customers to respond to fluctuations in wholesale electrical costs, but may not allow the utility to control demand. Transactive markets, utilizing distributed controllers and a centralized auction, can be used to create an interactive system which can limit demand at key times on a distribution system, decreasing congestion. With the current proliferation of computing and communication resources, the ability now exists to create transactive demand response programs at the residential level. With the combination of automated bidding and response strategies, coupled with education programs and customer response, emerging demand response programs have the ability to reduce utility demand and congestion in a more controlled manner. This paper will explore the effects of a residential double-auction market, utilizing transactive controllers, on the operation of an electric power distribution system.

Joint Dynamic Pricing of Multiple Perishable Products Under Consumer Choice

Abstract: In response to competitive pressures, firms are increasingly adopting revenue management opportunities afforded by advances in information and communication technologies. Motivated by these revenue management initiatives in industry, we consider a dynamic pricing problem facing a firm that sells given initial inventories of multiple substitutable and perishable products over a finite selling horizon. Because the products are substitutable, individual product demands are linked through consumer choice processes. Hence, the seller must formulate a joint dynamic pricing strategy while explicitly incorporating consumer behavior. For an integrative model of consumer choice based on linear random consumer utilities, we model this multiproduct dynamic pricing problem as a stochastic dynamic program and analyze its optimal prices. The consumer choice model allows us to capture the linkage between product differentiation and consumer choice, and readily specializes to the cases of verticallyand horizontallydif ferentiated assortments. When products are vertically differentiated, our results show monotonicity properties (with respect to quality, inventory, and time) of the optimal prices and reveal that the optimal price of a product depends on higher qualitypr oduct inventories only through their aggregate inventory rather than individual availabilities. Furthermore, we show that the price of a product can be decomposed into the price of its adjacent lower qualitypr oduct and a markup over this price, with the markup depending solely on the aggregate inventory. We exploit these properties to develop a polynomial-time, exact algorithm for determining the optimal prices and the profit. For a horizontally differentiated assortment, we show that the profit function is unimodal in prices. We also show that individual, rather than aggregate, product inventory availability drives pricing. However, we find that monotonicity properties observed in vertically differentiated assortments do not hold.

Dynamic Pricing with Loss-Averse Consumers and Peak-End Anchoring

Abstract: We study the dynamic pricing implications of a new, behaviorally motivated reference price mechanism based on the peak-end memory mode. This model suggests that consumers anchor on a reference price that is a weighted average of the lowest and most recent prices. Loss-averse consumers are more sensitive to perceived losses than gains relative to this reference price. We find that a range of constant pricing policies is optimal for the corresponding dynamic pricing problem. This range is wider the more consumers anchor on lowest prices, and it persists when buyers are loss neutral, in contrast with previous literature. In a transient regime, the optimal pricing policy is monotone and converges to a steady-state price, which is lower the more extreme and salient the low-price anchor is. Our results suggest that behavioral regularities, such as peak-end anchoring and loss aversion, limit the benefits of varying prices, and caution that the adverse effects of deep discounts on the firm's optimal prices and profits might be more enduring than previous models predict.

Price Discrimination in E-Commerce? An Examination of Dynamic Pricing in Name-Your-Own-Price Markets Management Information Systems Quarterly (MISQ)

Abstract: The enhanced abilities of online retailers to learn about their customers' shopping behaviors have increased fears of dynamic pricing, a practice in which a seller sets prices based on the estimated buyer's willingness-to-pay. However, among online retailers, a deviation from a one-price-for-all policy is the exception. When price discrimination is observed, it is often in the context of customer outrage about unfair pricing. One setting where pricing varies is the name-your-own-price (NYOP) mechanism. In contrast to a typical retail setting, in NYOP markets, it is the buyer who places an initial offer. This offer is accepted if it is above some threshold price set by the seller. If the initial offer is rejected, the buyer can update her offer in subsequent rounds. By design, the final purchase price is opaque to the public; the price paid depends on the individual buyer's willingness-to-pay and offer strategy. Further, most forms of NYOP employ a fixed threshold price policy. In this paper, we compare a fixed threshold price setting with an adaptive threshold price setting. A seller who considers an adaptive threshold price has to weigh potentially greater profits against customer objections about the perceived fairness of such a policy. We first derive the optimal strategy for the seller. We analyze the effectiveness of an adaptive threshold price vis-a-vis a fixed threshold price on seller profit and customer satisfaction. Further, we evaluate the moderating effect of revealing the threshold price policy (adaptive versus fixed) to buyers. We test our model in a series of laboratory experiments and in a large field experiment at a prominent NYOP seller involving real purchases. Our results show that revealing the usage of an adaptive mechanism yields higher profits and more transactions than not revealing this information. In the field experiment, we find that applying a revealed adaptive threshold price can increase profits by over 20 percent without lowering customer satisfaction.

Does AMD Spur Intel to Innovate More

Abstract: We estimate an equilibrium model of dynamic oligopoly with durable goods and endogenous innovation to examine the effect of competition on innovation in the personal computer microprocessor industry. Firms make dynamic pricing and investment decisions while consumers make dynamic upgrade decisions, anticipating product improvements and price declines. Consistent with Schumpeter, we find that the rate of innovation in product quality would be 4.2 percent higher without AMD present, though higher prices would reduce consumer surplus by $12 billion per year. Comparative statics illustrate the role of product durability and provide implications of the model for other industries.

Dynamic placement of virtual machines for cost optimization in multi-cloud environments

Abstract: The number of providers in the cloud computing market is increasing at rapid pace. At the same time, we are observing a fragmentation of the market in terms of pricing schemes, virtual machine offers and value-add features. In the early phase of cloud adoption, the price model was dominated by fixed prices. However, cloud market trend shows that dynamic pricing schemes utilization is being increased. In this plan, prices change according to demand in each cloud provider. In general, it is difficult for users to search cloud prices and decide where to put their resources. In this paper, we propose a scheduling model for optimizing virtual cluster placements across available cloud offers. This scheduler uses some variables such as average prices or cloud prices trends for suggesting an optimal deployment. Also, this scheduler is part of a cloud broker which automates actions and makes them transparent for users. The performance of our model is evaluated in a real-world cloud environment and the results show that user's investment decreases when part of the virtual infrastructure is dynamically distributed among clouds instead of maintaining it in a fixed one.

Short-Term Load Forecasting with Neural Network Ensembles: A Comparative Study [Application Notes]

Abstract: Load Forecasting plays a critical role in the management, scheduling and dispatching operations in power systems, and it concerns the prediction of energy demand in different time spans. In future electric grids, to achieve a greater control and flexibility than in actual electric grids, a reliable forecasting of load demand could help to avoid dispatch problems given by unexpected loads, and give vital information to make decisions on energy generation and purchase, especially market-based dynamic pricing strategies. Furthermore, accurate prediction would have a significant impact on operation management, e.g. preventing overloading and allowing an efficient energy storage.

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 freemium (FLF) and uniform seeding (S). 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 with Limited Supply

Abstract: We consider the problem of dynamic pricing with limited supply. A seller has $k$ identical items for sale and is facing $n$ potential buyers ("agents") that are arriving sequentially. Each agent is interested in buying one item. Each agent's value for an item is an IID sample from some fixed distribution with support $[0,1]$. The seller offers a take-it-or-leave-it price to each arriving agent (possibly different for different agents), and aims to maximize his expected revenue. We focus on "prior-independent" mechanisms -- ones that do not use any information about the distribution. They are desirable because knowing the distribution is unrealistic in many practical scenarios. We study how the revenue of such mechanisms compares to the revenue of the optimal offline mechanism that knows the distribution ("offline benchmark"). We present a prior-independent dynamic pricing mechanism whose revenue is at most $O((k \log n)^{2/3})$ less than the offline benchmark, for every distribution that is regular. In fact, this guarantee holds without *any* assumptions if the benchmark is relaxed to fixed-price mechanisms. Further, we prove a matching lower bound. The performance guarantee for the same mechanism can be improved to $O(\sqrt{k} \log n)$, with a distribution-dependent constant, if $k/n$ is sufficiently small. We show that, in the worst case over all demand distributions, this is essentially the best rate that can be obtained with a distribution-specific constant. On a technical level, we exploit the connection to multi-armed bandits (MAB). While dynamic pricing with unlimited supply can easily be seen as an MAB problem, the intuition behind MAB approaches breaks when applied to the setting with limited supply. Our high-level conceptual contribution is that even the limited supply setting can be fruitfully treated as a bandit problem.

Optimal Service Pricing for a Cloud Cache

Abstract: Cloud applications that offer data management services are emerging. Such clouds support caching of data in order to provide quality query services. The users can query the cloud data, paying the price for the infrastructure they use. Cloud management necessitates an economy that manages the service of multiple users in an efficient, but also, resource-economic way that allows for cloud profit. Naturally, the maximization of cloud profit given some guarantees for user satisfaction presumes an appropriate price-demand model that enables optimal pricing of query services. The model should be plausible in that it reflects the correlation of cache structures involved in the queries. Optimal pricing is achieved based on a dynamic pricing scheme that adapts to time changes. This paper proposes a novel price-demand model designed for a cloud cache and a dynamic pricing scheme for queries executed in the cloud cache. The pricing solution employs a novel method that estimates the correlations of the cache services in an time-efficient manner. The experimental study shows the efficiency of the solution.

Energy management for buildings and microgrids

Abstract: Intelligent consumer energy management systems will become important elements at the delivery points of the smart grid inside homes, buildings, and industrial plants The end users will be able to better monitor and manage their energy consumption, while utilities will gain more flexible mechanisms for management of peak demands that will extend beyond demand response initiatives as they are implemented today With a broader use of distributed generation many buildings and campuses will become microgrids interconnecting multiple generation, storage, and consumption devices of one or several end users We discuss how energy management and control for such facilities can be viewed as a large-scale optimization problem Specific supply-side and demand-side aspects include on-site renewable generation, storage technologies, electric cars, dynamic pricing, and load management Technical challenges related to the optimization formulation are noted - in general, mixed-integer, nonlinear, constrained optimization is needed We also describe an implementation of optimization-based energy management solution for a hospital in the Netherlands, providing economic details and an analysis of the savings achieved

Optimal dynamic pricing strategies for high-occupancy/toll lanes

Abstract: This paper proposes a self-learning approach to determine optimal pricing strategies for high-occupancy/toll lane operations. The approach learns recursively motorists’ willingness to pay by mining the loop detector data, and then specifies toll rates to maximize the freeway’s throughput while ensuring a superior travel service to the users of the toll lanes. In determination of the tolls, a multi-lane hybrid traffic flow model is used to explicitly consider the impacts of the lane-changing behaviors before the entry points of the toll lanes on throughput and travel time. Simulation experiments are conducted to demonstrate and validate the proposed approach, and provide insights on when to convert high-occupancy lanes to toll lanes.

Blind Network Revenue Management

Abstract: We consider a general class of network revenue management problems, where mean demand at each point in time is determined by a vector of prices, and the objective is to dynamically adjust these prices so as to maximize expected revenues over a finite sales horizon. A salient feature of our problem is that the decision maker can only observe realized demand over time but does not know the underlying demand function that maps prices into instantaneous demand rate. We introduce a family of “blind” pricing policies that are designed to balance trade-offs between exploration (demand learning) and exploitation (pricing to optimize revenues). We derive bounds on the revenue loss incurred by said policies in comparison to the optimal dynamic pricing policy that knows the demand function a priori, and we prove that asymptotically, as the volume of sales increases, this gap shrinks to zero.

TECHNICAL NOTE---Optimal Product Acquisition, Pricing, and Inventory Management for Systems with Remanufacturing

Abstract: Acquisition of used products (cores) is central to the success of remanufacturing programs for companies. At the same time, dynamic pricing strategies have been adopted in various industries to better balance supply and customer demand. In this paper, we study the integration of these two aspects of operations together with inventory management for a production/remanufacturing firm. We develop a periodic-review single-product inventory system with price-dependent customer demand. The product return in each period is random but can be actively controlled by the firm's acquisition effort. The firm aims to maximize its total discounted profit over a finite planning horizon by implementing optimal production, remanufacturing, product acquisition, and pricing strategies. We first show that with an exogenous selling price, the optimal production-remanufacturing-disposal policy is simple and characterized by three state-independent parameters. The optimal acquisition effort is decreasing in the aggregate inventory level of serviceable product and cores. Nevertheless, when pricing is an endogenous decision, we find that the optimal policy becomes much more complicated, and its control parameters are state dependent. The optimal selling price is decreasing, whereas the optimal acquisition effort is increasing in the serviceable product inventory level, and both decisions decrease with the aggregate inventory level.

Forecasting the usage of household appliances through power meter sensors for demand management in the smart grid

Abstract: Electricity demand management mechanisms are expected to play a key role in smart grid infrastructures to reduce buildings power demand at peak hours, by means of dynamic pricing strategies. Unfortunately these kinds of mechanisms require the users to manually set a lot of configuration parameters, thereby reducing the usability of these solutions. In this paper we propose a system, developed within the BEE Project, for predicting the usage of household appliances in order to automatically provide inputs to electricity management mechanism, exactly in the same way a user could do. In our architecture we use a wireless power meter sensor network to monitor home appliances consumption. Data provided by sensors are then processed every 24 hours to forecast which devices will be used on the next day, at what time and for how long. This information represents just the input parameters required by load demand management systems, hence avoiding complex manual settings by the user.

Examining uncertainty in demand response baseline models and variability in automated responses to dynamic pricing

Abstract: Controlling electric loads to deliver power system services presents a number of interesting challenges. For example, changes in electricity consumption of Commercial and Industrial (CI however, a number of facilities exhibit real DR parameter variability. In some cases, the aggregate population of C&I facilities exhibits real DR parameter variability, resulting in implications for the system operator with respect to both resource planning and system stability.

Social Learning and Dynamic Pricing of Durable Goods

Abstract: We analyze the impacts of social learning (SL) on the dynamic pricing and consumer adoption of durable goods in a two-period monopoly. Consumers can make either early, uninformed purchases or late but potentially informed purchases as a result of social learning. Several results are derived. First, we identify the market conditions under which ex ante homogeneous consumers may choose to purchase at different times. Second, equilibrium adoption may demonstrate inertia (where all adopt late) or frenzy (where all adopt early). In particular, adoption inertia appears when SL intensity is reasonably high but may vanish when SL intensity exceeds a certain threshold. Third, firm profits and social welfare first weakly decrease in SL intensity and may then jump up by a lump-sum amount at the threshold SL intensity level mentioned above. Last, we show that the firm potentially benefits from informative advertising or investing to cultivate more social learning.

Dynamic Pricing Strategies for Multiproduct Revenue Management Problems

Abstract: This chapter reviews multi-product dynamic pricing models for a revenue maximizing monopolist flrm. The baseline model studied in this chapter is of a seller that owns a flxed capacity of a resource that is consumed in the production or delivery of some type of product. The seller selects a dynamic pricing strategy for the ofiered product so as to maximize its total expected revenues over a flnite time horizon. We then review how this model can be extended to settings where the flrm is selling multiple products that consume this flrm’s capacity, and flnally highlight a connection between these dynamic pricing models and the closely related model where prices are flxed, and the seller dynamically controls how to allocate capacity to requests for the difierent products. Methodologically, this chapter reviews the dynamic programming formulations of the above problems, as well as their associated deterministic (∞uid) analogues. It highlights some of the key insights and pricing heuristics that are known for these problems, and brie∞y mentions possible extensions and areas of current interest.

Dynamic pricing, product and process innovation

Abstract: The question of simultaneous dynamic pricing, product and process investment policies is crucial for manufacturing and high-tech industries. This paper models these policies in an optimal control setting. On the supply side, the firm sets prices, product and process investment levels over time. On the demand side, current demand depends on price and quality. Under an additive separable demand function, dynamic pricing increases with quality and cost. Therefore, both product innovation and process innovation impact the pricing policy. Under a multiplicative separable demand function, dynamic pricing policy follows the dynamic of production cost and is independent of the evolution of product quality. Thus, process innovation is the main determinant of a firm’s pricing policy over time and product innovation has no impact.

Optimal Control of Residential Energy Storage Under Price Fluctuations

Abstract: An increasing number of retail energy markets exhibit price fluctuations and provide home users the oppor- tunity to buy energy at lower than average prices. However, such cost savings are hard to realize in practice because they require human users to observe the price fluctuations and shi ft their electricity demand to low price periods. We propose to temporarily store energy of low price periods in a home battery and use it later to satisfy user demand when energy prices are high. This enables home users to save on their electricity bill by exploiting price variability without changing their consumption habits. We formulate the problem of minimizing the cost of energy storage purchases subject to both user demands and prices as a Markov Decision Process and show that the optimal policy has a threshold structure. We also use a numerical example to show that this policy can lead to significant cost savings, an d we offer various directions for future research. Index Terms—Battery storage, dynamic pricing, dynamic pro- gramming, energy storage, threshold policy.

Dynamic pricing of electricity in the mid-Atlantic region: econometric results from the Baltimore gas and electric company experiment

Abstract: The Baltimore Gas and Electric Company (BGE) undertook a dynamic pricing experiment to test customer price responsiveness to different dynamic pricing options. The pilot ran during the summers of 2008 and 2009 and was called the Smart Energy Pricing (SEP) Pilot. In 2008, it tested two types of dynamic pricing tariffs: critical peak pricing (CPP) and peak time rebate (PTR) tariffs. About a thousand customers were randomly placed on these tariffs and some of them were paired with one of two enabling technologies, a device known as the Energy Orb and a switch for cycling central air conditioners. The usage of a randomly chosen control group of customers was also monitored during the same time period. In 2009, BGE repeated the pilot program with the same customers who participated in the 2008 pilot, but this time it only tested the PTR tariff. In this paper, we estimate a constant elasticity of substitution (CES) model on the SEP pilot’s hourly consumption, pricing and weather data. We derive substitution and daily price elasticities and predictive equations for estimating the magnitude of demand response under a variety of dynamic prices. We also test for the persistence of impacts across the two summers. In addition, we report average peak demand reduction for each of the treatment cells in the SEP pilot and compare the findings with those reported from earlier pilots. These results show conclusively that it is possible to incentivize customers to reduce their peak period loads using price signals. More importantly, these reductions do not wear off when the pricing plans are implemented over two consecutive summers. Our analyses reveal that SEP participants reduced their peak usages in the range of 18 to 33% in the first summer of the SEP pilot and continued these reductions in the second summer.

Dynamic Pricing of Limited Inventories When Customers Negotiate

Abstract: Although take-it-or-leave-it pricing is the main mode of operation for many retailers, a number of retailers discreetly allow price negotiation when some haggle-prone customers ask for a bargain. At these retailers, the posted price, which itself is subject to dynamic adjustments in response to the pace of sales during the selling season, serves two important roles: (i) it is the take-it-or-leave-it price to many customers who do not bargain, and (ii) it is the price from which haggle-prone customers negotiate down. To effectively measure the benefit of dynamic pricing and negotiation in such a retail environment, one must take into account the interactions among inventory, dynamic pricing, and negotiation. The outcome of the negotiation (and the final price a customer pays) depends on the inventory level, the remaining selling season, the retailer's bargaining power, and the posted price. We model the retailer's dynamic pricing problem as a dynamic program, where the revenues from both negotiation and posted pricing are embedded in each period. We characterize the optimal posted price and the resulting negotiation outcome as a function of inventory and time. We also show that negotiation is an effective tool to achieve price discrimination, particularly when the inventory level is high and/or the remaining selling season is short, even when implementing negotiation is costly.

Insulated Platform Competition y

Abstract: The externalities that operating system users receive from software developers are among the leading features of those ‘platform’ industries but are rarely incorporated into applied models of imperfect competition. We argue this omission arises from the di culty of collapsing the dynamic pricing characterizing such industries into a static policy analysis model. Given the role these pricing strategies play in coordinating consumer behavior, a theory ignoring them quickly becomes intractable and indeterminate. Postulating that platforms identify and then robustly implement best response allocations, we show platforms play an Insulated Equilibrium that eliminates the need for consumers to coordinate their behavior. This facilitates the analysis of an oligopoly model without unrealistic restrictions imposed for tractability. We use this to illustrate the additional distortion, analogous to that identified by Spence’s (1975) study of a quality-choosing monopolist, arising when platforms determine both their prices and their (externality-driven) level of quality.

Dynamic pricing for demand-side management in the smart grid

Abstract: Intermittent renewable energy sources and the use of smart meters introduce a significant challenge for the reliability of the smart grid. Real-time pricing is an important demand-side management mechanism for improving smart grid reliability through dynamically changing or shifting the electricity consumption of users. Presently, the dynamic real-time pricing research in the smart grid mainly focuses on the interactions between a single utility company/retailer and its users. In this paper, we consider electricity liberalization, where more than one electricity retailer can co-exist in each region, and the retailers compete or cooperate with each other to achieve the highest individual or combined revenue. Two types of electricity users are considered in this paper: traditional electricity users who pay a fixed price and opportunistic electricity users who may change the electricity demand or even turn to another electricity retailer. Two game formulations are described for the proposed real-time pricing scheme. One formulation is proposed for a totally competitive environment. Another game formulation is proposed for a cooperative environment. Some simulation results are presented to show the effectiveness of the proposed real-time pricing scheme.

Optimal sizing of energy storage for efficient integration of renewable energy

Abstract: In this paper, we study the optimal storage investment problem faced by an owner of renewable generator the purpose of which is to support a portion of a local demand. The goal is to minimize the long-term average cost of electric bills in the presence of dynamic pricing as well as investment in storage, if any. Examples of this setting include homeowners, industries, hospitals or utilities that own wind turbines or solar panels and have their own demand that they prefer to support with renewable generation. We formulate the optimal storage investment problem and propose a simple balancing control for operating storage. We show that this policy is optimal for constant prices and some special cases of price structures that restrict to at most two levels. Under this policy, we provide structural results that help in evaluating the optimal storage investment uniquely and efficiently. We then characterize how the cost and efficiency of storage, dynamic pricing and parameters that characterize the uncertainty in generation and demand impact the size of optimal storage and its gain. One surprising result we prove is that for storage to be profitable under the balancing policy the ratio amortized cost of storage to the peak price of energy should be less than 1 over 4