Optimal Dynamic Pricing Strategy Research Articles

Optimal capacity configuration and dynamic pricing strategy of a shared hybrid hydrogen energy storage system for integrated energy system alliance: A bi-level programming approach

The shared energy storage system is recognized as a promising business model for the coordinated operation of integrated energy systems (IES) to improve the utilization of energy storage and the consumption of renewable energy. As the hydrogen energy gradually receives more attention, this paper constructs the structure of a hybrid hydrogen energy storage system shared by an IES alliance in a dynamic pricing mode. A bi-level optimization model for the shared hybrid hydrogen energy storage system (SHHESS) is proposed to optimize the capacity configuration decisions and the pricing strategy jointly. The upper level determines the capacity and dynamic price of SHHESS with maximum profits and the lower level obtains the optimal operation of the IES alliance minimizing the total operation costs. The proposed model is solved by an improved PSO-GA algorithm and CPLEX solver. Finally, numerical tests are conducted in different scenarios. The results show that the hybrid energy storage system improves the daily profits of SHHESS by 70.3% and 5.44%, and reduces the renewable energy curtailment by 80.93% and 48.92% respectively compared to the battery-only and hydrogen-only systems. Additionally, the daily operation cost of the IES alliance is 35.2% lower than the individual operation scenario. The proposed model confirms the feasibility and superiority of the hybrid hydrogen energy storage system in a sharing business mode.

Dynamic pricing strategy for content products considering consumer fairness concerns and strategic behavior

PurposeThe development of the digital age has made data and information more transparent, enhancing the strategic perspectives of both buyers (strategic waiting) and sellers (price fluctuations) in their decision-making. This research investigates the optimal dynamic pricing strategy of the content product developer in relation to their consideration of consumer fairness concerns to elucidate the impact of consumer fairness concerns on the dynamic pricing strategy of the developer.Design/methodology/approachThis paper assumes that monopolistic content developers implement a dynamic pricing strategy for the content product. Through constructing a two-period dynamic pricing game model, this research investigates the optimal decisions of the content developer, contingent upon their consideration or disregard of consumer fairness concerns. In the extension section, the authors additionally account for the influence of myopic consumers on these optimal decisions.FindingsOur findings reveal that the degree of consumer fairness concerns significantly influences the developer’s optimal dynamic pricing decision. When a developer offers content products with lower depth, there is a propensity for the developer to refrain from incorporating consumer fairness concerns into a dynamic pricing strategy. Conversely, in cases where the developer offers a high-depth content product, consumer fairness concerns benefit the developer. Furthermore, our analysis reveals a consistent benefit for the developer from the inclusion of myopic consumers.Originality/valueFew studies have delved into the conjoined influence of consumer fairness concerns and strategic behavior on dynamic pricing strategy. Our findings indicate that consumer fairness concerns can enhance the efficiency of the value chain for content products under specific conditions. This paper not only enriches the existing literature on dynamic pricing by incorporating consumer fairness concerns theoretically but also offers practical insights. The outcomes of this research can guide content product developers in devising optimal dynamic pricing strategies.

Pricing for the Stars: Dynamic Pricing in the Presence of Rating Systems

Maintaining good ratings increases the profits of sellers on online platforms. We analyze the role of strategic pricing for ratings management in a setting where a monopolist sells a good of unknown quality. Higher prices reduce the value for money, which on average worsens reviews. However, higher prices also induce only those consumers with a strong taste for the product to purchase, which on average improves reviews. Our model flexibly parametrizes the two effects. This parametrization can rationalize the observed heterogeneity in the relationship between reviews and prices. Based on an analytic characterization of the optimal dynamic pricing strategy, we study a platform’s choice of the sensitivity of its rating system to incoming reviews. The optimal sensitivity depends on the effect of prices on reviews and on how the platform weighs consumers and sellers in its objective. Although sellers always benefit from more sensitivity, consumers may suffer from higher prices and from slower learning from reviews due to endogenously emerging price and rating cycles. This paper was accepted by Kartik Hosanagar, information systems. Funding: This work was supported by the Deutsche Forschungsgemeinschaft [CRC TR 224, Project C3]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2023.4771 .

Joint dynamic pricing and freshness-keeping effort strategy for perishable products with price-, freshness-, and stock-dependent demand

In this paper, we formulate a joint dynamic pricing and freshness-keeping effort strategy for perishable products in a finite horizon. Based on the perishable nature of perishable products, this paper considers the product demand influenced by selling price, product freshness and stock level. Since the freshness level decreases with time, we assume that the freshness deteriorates exponentially. Besides, a freshness-keeping effort is introduced to reduce the deterioration rate of freshness. Our purpose is to determine the optimal joint dynamic pricing and freshness-keeping effort strategy to maximize profits. To solve the problem, the Pontryagin's maximum principle is applied. We present a numerical example in support to the theoretical results and propose the sensitivity analysis of the main parameters. In the end, some managerial guidelines are also provided. When the cost of freshness-keeping effort is high or the effect of freshness-keeping effort is low, not to adopt freshness-keeping effort is the optimal decision. However, if the cost of freshness-keeping effort is small or the effect of freshness-keeping effort is significant, adopting freshness-keeping effort is the best. In addition, managers can gain more profits by expanding market size and restraining inventory decay rate and freshness deterioration rate.

Dynamic Pricing Strategy for Two-Generation Products under Different Trade-in Subsidy Strategies

Trade-in is one of the most widely used recycling methods in practice. A key problem in the trade-in process is the dynamic pricing strategy under different trade-in subsidy strategies. Consumers are divided into myopic and strategic consumers. Considering three situations, namely, (1) no trade-in subsidy strategy, (2) the firm’s trade-in subsidy strategy, and (3) the government’s trade-in subsidy strategy, the dynamic game equilibrium between firms and consumers is analyzed. The optimal dynamic pricing strategy is obtained by constructing a two-stage dynamic game model. The results show that (1) the number of consumers who purchase next-generation new products is not impacted by the trade-in subsidy strategy. However, the number of consumers who engage in trade-ins is impacted by the trade-in subsidy strategy. (2) The number of consumers who engage in trade-ins with the trade-in subsidy strategy is larger than that without the trade-in subsidy strategy. (3) Compared with the government’s trade-in subsidy strategy, the firm’s trade-in subsidy strategy can more effectively motivate consumers to engage in trade-in activity.

Providing Data Samples for Free

We consider the problem of a seller of data who sells information to a buyer regarding an unknown (to both parties) state of the world. Traditionally, the literature explores one-round strategies for selling information because of the seller’s holdup problem: once a portion of the data set is released, the buyer’s estimate improves, and as a result, the value of the remaining data set drops. In this paper, we show that this intuition is true when the buyer’s objective is to improve the precision of the estimate. On the other hand, we establish that when the buyer’s objective is to improve downstream operational decisions (e.g., better pricing decisions in a market with unknown elasticity) and when the buyer’s initial estimate is misspecified, one-round strategies are outperformed by selling strategies that initially provide free samples. In particular, we provide conditions under which such free-sample strategies generate strictly higher revenues than static strategies and illustrate the benefit of providing data samples for free through a series of examples. Furthermore, we characterize the optimal dynamic pricing strategy within the class of strategies that provide samples over time (at a constant rate), charging a flow price until some time when the rest of the data set is released at a lump-sum amount. This paper was accepted by Itai Ashlagi, revenue management and market analytics. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2022.4534 .

Selective and optimal dynamic pricing strategy for residential electricity consumers based on genetic algorithms

The continuous increase in residential population implies an increase in electricity demand. The demand prediction performed by the utility company (UC) to schedule and plan the next energy purchase from the market may not be efficient since the actual demand consistently exceeds the supply. To use the energy production infrastructure efficiently and decrease the grid system's overload, the UC seeks to match the demand with the supply. Dynamic pricing is a simple yet effective way to influence consumption as price-sensitive consumers may reschedule the operation of some of the appliances. This paper presents a novel, consumption data-driven, selective and dynamic Time-of-Use (ToU) electricity pricing strategy applicable by the UC for residential electricity consumers. The method consists of clustering real consumption data using the k-means clustering technique and heuristically categorizing clusters based only on their consumption data to simplify the design of the ToU tariffs and limit the number of different tariffs in the same population. The method includes a heuristic determination of the time period for the ToU tariff changes for each category. The ToU tariff parameters are determined by minimizing a single cost function using genetic algorithms and considering all consumer clusters such that the consumer behavior model is based on price elasticity. The optimal ToU tariffs result in decreasing the demand in power peaks by targeting the overconsumer categories in the latter. Implementing the ToU tariff results in a profit margin distributed among the UC and the consumer. Moreover, the optimal prices guarantee positive gains for both of them with the presence of a wide range of parameter uncertainties. The proposed pricing strategy necessitates the presence of consumption data only, which implies the conservation of the consumers' privacy. Real consumption data obtained for two towns in Hungary over three years is used to show the efficiency of the proposed pricing strategy.

Data-driven optimal dynamic pricing strategy for reducing perishable food waste at retailers

Approximately forty per cent of fresh products are wasted in low and middle-income countries before reaching consumers. Perishable foods have only a certain shelf-life and they need to be sold for consumption before a specific date. When a product is priced incorrectly, it is often disposed of directly or redistributed. Redistribution of surplus food also has an economic impact on food prices. Therefore, setting an optimal pricing strategy is crucial to reduce inventory and surplus food in an environment with volatile demands. In this context, big data analytics can help managers forecast customer behaviour and determine pricing strategies throughout the retail industry. This study focuses on food waste at the retailer stage of food supply chain (FSC). We present a dynamic pricing model that uses real-time Internet of Things (IoT) sensor data as a novel contribution to decide pricing at different stages of a sales season for retailers. The food waste problem at the retail stage of a FSC is investigated in a pilot project for bulk apple sales to address the research question. This study proposes a four-stage data-driven optimal dynamic pricing strategy for bulk produce to reduce food waste for retailers in low and middle-income countries. A multi-stage dynamic programming method is used to decide on a pricing strategy for bulk produce, with real-time IoT sensor data being retrieved to analyse and determine the length of freshness scores. The effect of the sale price, replenishment amount, discount rate, and freshness score on profit and food waste are evaluated. All these analyses assist managers in taking the best possible actions and remedies. Appropriate interventions boost sales, increase profits by reducing waste and determining competitive sales price, while improving customer loyalty and satisfaction by striking the right balance between food quality and price. Our results show the huge potential of using hyperspectral imaging sensors in the FSC of a retailer. The model is demonstrated empirically to test its practicability.

Selective and Optimal Dynamic Pricing Strategy for Residential Electricity Consumers

Selective and Optimal Dynamic Pricing Strategy for Residential Electricity Consumers

Optimal Dynamic Mechanism under Customer Search

This paper investigates the seller's revenue maximizing mechanism in face of a customer who searches for alternatives over a finite horizon. The seller, without observing the customer's valuation to her product nor any realization of the search outcomes, can propose a contract to the customer before he begins any searches. We show that it is optimal for the seller to offer a menu of American options comprising of a menu of deposits and strike prices, wherein the customer is screened based on the valuation for the seller's product. Under the optimal mechanism, low valuation customer searches for outside alternatives without engaging with the seller while high valuation customer exercises the option immediately---effectively making the option an exploding offer. Customer with intermediate valuation will always hold the option till the end of the planning horizon. In the special case when all outside alternatives have zero value to the customer, then the customer's sequential search problem reduces to the one in which he strategically times his purchases of the seller's product. Our optimal mechanism in this case reduces to making a single exploding offer with monopoly price and hence recovering the classic result in Stokey (1979). We also characterize the optimal constant and dynamic pricing strategies under specific conditions and numerically compare their performances with the optimal mechanism. The profit can be improved by as much as 50.7% and 14.4% from using an optimal mechanism compared with the optimal constant and dynamic pricing strategies, respectively.

Optimal pricing of crowdsourcing logistics services with social delivery capacity

Based on the sharing economy, crowdsourcing logistics services share social delivery freelancers instead of traditional full-time delivery employees. The optimal dynamic pricing model of crowdsourcing logistics services, which could be applied to adjust the social delivery capacity supply to meet the stochastic demand especially during the peak period, is established based on optimal control theory. We study optimal pricing strategies under both conditions when the supply and the demand is balanced and accumulated delivery orders are minimized. Moreover, the impact of delivery riders’ wage ratio on pricing and platforms’ expected revenue are analyzed. It is verified by numerical simulation results that optimal dynamic pricing strategies of crowdsourcing logistics services could effectively balance supply and demand, further maximize the expected revenue of platforms. The growth rate of optimal pricing of crowdsourcing logistics services is increasing with respect to the delivery riders’ wage ratio. However, the expected revenue of crowdsourcing logistics platforms declines as the wage ratio increases.

Gacha Game: Selling a Unit Good to a Prospect Theory Consumer

This paper considers the design problem of selling a unit good to a prospect theory buyer, with non-negative constraints on the realized price. When the value is private and the reservation value is 0, it is optimal for the seller to use a post binary random price mechanism, where he charges a large price that may exceed the buyer's actual value and gives a full refund with some probability. When the reservation value is positive, the seller may provide infinite menus to different types of buyers. Each menu consists of a binary random price and a (potentially) interior probability of getting the good. If the buyer is naive about her dynamic inconsistent preference caused by probability weighting, the seller can potentially gain more profit from a dynamic pricing process. When the buyer's value is public, the generically unique optimal dynamic pricing strategy is to sell a ``lucky chest'' that delivers the good with some constant probability in each period. Until she finally gets the good, the buyer always naively believes she will try her luck just one last time.

Dynamic Pricing and Optimal Control for a Stochastic Inventory System with Non-Instantaneous Deteriorating Items and Partial Backlogging

In this paper, we consider a problem of the dynamic pricing and inventory control for non-instantaneous deteriorating items with uncertain demand, in which the demand is price-sensitive and governed by a diffusion process. Shortages and remains are permitted, and the backlogging rate is variable and dependent on the waiting time for the next replenishment. In order to maximize the expected total profit, the problem of dynamic pricing and inventory control is described as a stochastic optimal control problem. Based on the dynamic programming principle, the stochastic control model is transformed into a Hamilton-Jacobi-Bellman (HJB) equation. Then, an exact expression for the optimal dynamic pricing strategy is obtained via solving the HJB equation. Moreover, the optimal initial inventory level, the optimal selling pricing, the optimal replenishment cycle and the optimal expected total profit are achieved when the replenishment cycle starts at time 0. Finally, some numerical simulations are presented to demonstrate the analytical results, and the sensitivities analysis on system parameters are carried out to provide some suggestions for managers.

Existence and characterization of optimal dynamic pricing strategies with reference-price effects

In this paper, we revisit the problem of existence of an optimal dynamic pricing strategy when the demand depends on a reference price. Using alternative assumptions and technique to those typically used in the literature, we show the existence of a unique pricing policy parametrized in the initial value of the reference price. Our main results are as follows: if this value is low enough, then the best option is to implement a penetration pricing. If it is high enough, then price skimming is optimal. If the initial reference price has an intermediate value, then constant pricing throughout the planning horizon is optimal.

A Dynamic Pricing Strategy for Vehicle Assisted Mobile Edge Computing Systems

The idle computing resources of parked vehicles could be utilized to improve performance by assisting task executions in mobile edge computing (MEC) systems. As a result, the owner of a vehicle could be compensated, resulting in a win-win situation. A dynamic pricing strategy is proposed to minimize the average cost of the MEC system under the constraints on quality of service by adjusting the price constantly based on the current system state. To do so, a cost minimization problem is solved to obtain the optimal dynamic pricing strategy efficiently. Finally, the optimization results are validated with extensive simulations.

Intertemporal Price Discrimination with Complementary Products: E-Books and E-Readers

This paper studies intertemporal price discrimination (IPD) with complementary products in the context of e-readers and e-books. Using individual-level data (2008–2012), I estimate a dynamic demand model for e-reader adoption and subsequent book quantity, reading format, and retailer choices in several book genres. I use the estimates to simulate a monopolist’s optimal dynamic pricing strategies when facing forward-looking consumers. The results illustrate how skimming/penetration pricing incentives for e-readers and harvesting/investing incentives for e-books interact in this novel setting. The optimal joint IPD strategy is skimming for e-readers and investing for e-books. Counterfactual results suggest that combining IPD with complementary product pricing improves firm profitability because it attenuates the limitations of each pricing approach. In a single-product IPD setting, firms’ pricing power is limited when consumers anticipate future price changes and delay purchases. Adding complementary products offers firms two pricing instruments; opposite price trajectories provide conflicting incentives for consumers, limiting intertemporal arbitrage. In a static complementary product setting, firms’ pricing power is limited when the relative elasticity between the two products is heterogeneous and conflicting among consumers. Adding IPD sorts heterogeneous consumers into different periods and reduces the need to balance across consumer types. This paper was accepted by Matthew Shum, marketing.

Optimal Policies for the Pricing and Replenishment of Fashion Apparel considering the Effect of Fashion Level

Fashion apparel, with short product lifecycles and highly volatile demand, requires careful attention during both the initial ordering periods before the selling season and during the selling season, with its decisions regarding price and replenishment. Using Pontryagin’s maximum principle method, this study investigates the problem of the dynamic pricing strategy and replenishment cycle for fashion apparel by considering the effect of fashion level on demand. First, we provide a framework for fashion apparel by formulating a model that includes both price and demand at different fashion levels. We then provide an algorithm to derive the optimal dynamic pricing strategy and replenishment cycle. Numerical examples and sensitivity analyses of the main system parameters are provided to demonstrate the obtained results, which form the basis for managerial insights. It is shown that the apparel retailer has three types of optimal dynamic pricing strategies and that the optimal strategy is independent of the replenishment cycle. The apparel retailer is able to realize the profit advantage of a continuously variable price policy by adjusting the sales price periodically.

A joint dynamic pricing and production model with asymmetric reference price effect

Reference price plays a significant role in influencing purchase decisions of customers. Due to loss aversion, the asymmetric reference price effect on market demand should be taken into account. This paper develops a joint dynamic pricing and production model with asymmetric reference price effect. In a finite planning horizon, the demand rate is time-varying and depends on price as well as reference price. The decision-making problem with the asymmetric reference price effect turns to be a nonsmooth optimal control problem, which cannot be solved by standard optimal control method. As a special case, we first obtain the joint optimal dynamic pricing and production strategy with symmetric reference price effect by solving the corresponding standard optimal control problem based on Maximum principle. For the case of asymmetric reference price effect, we propose a systematical method on basis of optimality principle to solve the nonsmooth optimal control problem, and obtain the joint strategy. Numerical examples are employed to illustrate the effectiveness of the proposed method. In addition, we assess the sensitivity analysis of system parameters to examine the impacts of asymmetric reference price on optimal pricing and production strategies and total profits.

Optimal dynamic pricing for perishable foods with quality and quantity deteriorating simultaneously under reference price effects

ABSTRACTEmpirical evidences demonstrate that food quality and reference prices have great impacts on consumers’ purchasing decisions. In practice, the physical quantitative and qualitative deterioration of perishable foods usually occur simultaneously. However, the extant literature of perishable items largely focuses on quantitative deterioration. In this paper, we propose a dynamic pricing model for perishable foods with quality and quantity deteriorating simultaneously under reference price effects. An optimal control model is formulated to maximise the total profit, where the demand depends on the sales price, the quality and the reference price. The optimal dynamic pricing strategy is obtained by solving the optimal control model based on Pontryagin's maximum principle. Additionally, numerical examples and sensitivity analysis are implemented. Finally, some managerial insights are presented.

Dynamic pricing for perishable items with costly price adjustments

Dynamic pricing is widely adopted in inventory management for perishable items, and the corresponding price adjustment cost should be taken into account. This work assumes that the price adjustment cost comprises of a fixed component and a variable one, and attempts to search for the optimal dynamic pricing strategy to maximize the firm’s profit. However, considering the fixed price adjustment cost turns this dynamic pricing problem to a non-smooth optimal control problem which cannot be solved directly by Pontryagin’s maximum principle. Hence, we first degenerate the original problem into a standard optimal control problem and calculate the corresponding solution. On the basis of this solution, we further propose a suboptimal pricing strategy which simultaneously combines static pricing and dynamic pricing strategies. The upper bound of profit gap between the suboptimal solution and the optimal one is obtained. Numerical simulation indicates that the suboptimal pricing strategy enjoys an efficient performance.