Optimal Pricing Model Research Articles

Research on fair residential critical peak price: Based on a price penalty mechanism for high-electricity consumers

We construct a fair residential critical-peak price (CPP) optimization model based on a penalty mechanism to address the peaking pressure on the grid and the cost of new energy abandonment caused by the yearly increase in residential electricity load and the significant increase in new energy capacity. According to the electricity consumption habits of different residential consumers, we use the K-means clustering method to identify and classify high-electricity consumers (HECs), low-electricity consumers (LECs), and normal-electricity consumers (NECs) during the critical peak and valley load hours respectively, and design a penalty mechanism of electricity price for HECs (PMEP-H) that penalizes HECs during the critical peak load hours, and compensates the total penalty amount to LECs during the critical peak load hours and HECs during the valley load hours, then calculate the residential electricity load after implementation of PMEP-H based on consumer psychology. The CPP optimization model is constructed by considering the constraints of consumer satisfaction with electricity, tariff penalty, compensation balance, penalty and compensation price, power balance and new energy-generating units output power, and the objective function of high comprehensive system efficiency represented by the difference between peak cost of thermal generation, the benefit of new energy consumption and benefit of the grid side. The model is then solved using an improved particle swarm optimization algorithm for a real residential area in a populated area in northern China. The results show that the developed model can connect the generation, grid and user sides through the electricity consumption tariff, which generates considerable benefits in both peak cutting and new energy consumption targets and can enhance the comprehensive benefits of the generation, grid and user sides system to achieve the supply-grid-load linkage, providing a reference for the improvement of the CPP mechanism in China.

Multi-objective based demand response strategy optimization considering differential demand on reliability of power system

The reliability of power system will vary with different demand response strategies, and it is significant to make a decision on demand response for satisfying differential reliability demand of power system. First, a peak-valley period partition model with an objective of maximizing silhouette coefficient was established based on the fuzzy clustering and step-wise iteration technology. Second, this paper proposed a multi-objective time of use electricity price optimization model considering the interests of both supply and demand sides, as well as reliability demand, and a multi-objective simulated annealing particle swarm optimization algorithm was developed to obtain solution. Third, the Pareto front curve of the dual-objective function was fitted by using a third-order Hermite interpolation algorithm, and the time of use prices corresponding to the reliability demand was obtained by using the back propagation neural network algorithm. Finally, the proposed model and algorithm were verified by the RBTS system, and the results indicate good rationality and effectiveness of the proposed method.

How to realize the power demand side actively matching the supply side? ——A virtual real-time electricity prices optimization model based on credit mechanism

Intermittence and fluctuation of renewable energy increase the cost of real-time balance of power supply and demand, which will affect the stability of the power grid. How to design the incentive mechanism to increase the flexibility of the distributed energy system and reduce the cost of real-time supply–demand balance is an urgent problem to be solved. In this study, from the perspective of the demand side actively matching the supply side, a virtual real-time electricity price optimization model based on the credit mechanism is proposed. We use the linear decreasing inertia weight particle swarm optimization algorithm to optimize the user's electricity price and realize the minimization of the total electricity cost. The influence of the virtual real-time electricity price incentive mechanism on the matching degree between the power load curve and the distributed energy output curve is also studied. Moreover, a novel index is put forward to quantitatively measure the matching degree between users’ power load curve and distributed energy output curve. Taking a multi-microgrid system in a China’s industrial park as the case, we have found the results that the virtual real-time electricity price optimization model can not only reduce users’ total power cost by 7.8108%, but also improve the matching degree between the demand side and the supply side by 2.4643%. The new demand response incentive mechanism we have presented in this paper may promote the effective utilization of distributed energy and reduce the impact of renewable energy on power grid.

Strategic Pricing of Electric Vehicle Charging Service Providers in Coupled Power-Transportation Networks

Electric vehicles (EVs) are developing at a rapid pace. The EV charging station (EVCS) plays an indispensable role in supplying EV charging demand and promoting the transportation electrification. This work proposes a pricing method to maximize the profit of EVCS owners, charging service providers. First, the tri-level pricing framework is established where EVCSs set charging prices at the upper level, EVs make route and charging options at the middle level, and the electricity price is cleared in power distribution network at the lower level. Second, the singlelevel optimal pricing model is established with traffic flow assigned, power generation scheduled and electricity price explicitly contained via KKT conditions. The proposed model considers the impact of EVCS configuration on traffic assignment and pricing strategy. The operation risk brought by uncertainties is managed via Conditional value at risk. Third, a decomposition solution algorithm is proposed, which tackles the computational burdens and overcomes the infeasibility of existing algorithms. Finally, the real-world urban network-based case studies verify the effectiveness and merits of the proposed method.

Pricing in non-convex electricity markets with flexible trade-off of pricing properties

For the pricing in the non-convex electricity markets, the various pricing properties including supporting a competitive equilibrium, non-discrimination, cost recovery of participants, and revenue adequacy of the market operator can hardly be simultaneously fulfilled. Current pricing methods cannot balance these properties because there lacks a computationally tractable pricing model that explicitly formulates these properties as objective functions or constraints. In this paper, we propose a pricing optimization model taking prices as decision variables and taking important pricing properties as objective functions or constraints. Based on duality theory, the Karush-Kuhn-Tucker conditions of the self-dispatch problem processed by convex relaxation are extended to construct the constraints related to supporting a competitive equilibrium. Taking advantage of the modeling flexibility, the constraints for non-discrimination, cost recovery, and revenue adequacy are established. The delicately designed pricing optimization model is a linear programming problem with an acceptable computational burden. It applies to the market clearing problem with non-convexity, time-coupling and network transmission characteristics. To be specific, the application of the proposed pricing method for the unit commitment problem is provided. The reasonability, scalability, and tractability of the proposed approach are illustrated in systems with over 2000 buses. Numerical experiments show that the proposed method shows better performance compared with other representative pricing methods.

Research on Pricing Decision Considering Advertising Benefit and Consumer Psychological Benefit

For perishable goods, the optimal pricing models studied by current scholars seldom consider price effect, psychological benefit and consumption time. Based on the current basic newsboy model, this paper focuses on the price characteristics and consumer psychology of perishable products under the background of single dealer, in order to build a complete optimal price decision model of perishable products. According to the two-stage ladder pricing of perishable products in the pricing stage, this paper constructs the optimal price decision model of dealers in different sales stages by representing consumer demand and dealer profit equation, so as to provide enterprises with the maximum optimal strategy. Moreover, sensitivity analysis of parameters in the model is carried out to ensure the stability of the model.

A deterministic bounding algorithm vs. a hybrid meta-heuristic to deal with a bilevel mixed-integer nonlinear optimization model for electricity dynamic pricing

In the electricity retail market, the retailer company aims to determine the optimal time-of-use (ToU) prices to maximize profits resulting from buying energy in organized (long-term, day-ahead, balancing) markets and selling it to consumers. Therefore, the retailer should take into account the consumer’s demand response actions to minimize the electricity bill in face of time varying prices. In this paper, this problem is formulated as a bilevel mixed-integer nonlinear programming model in which the retailer is the leader and the consumer is the follower. The consumer’s problem encompasses the integrated optimization of all home energy resources, considering re-scheduling appliance operation, charging/discharging of electric vehicle and stationary batteries, local microgeneration and (buying and selling) exchanges with the grid. The accurate physical modelling of appliance operation to generate effective load scheduling solutions imposes a high computational burden. Two algorithms are proposed to address this problem: a deterministic bounding algorithm (DBA) using an optimal-value-function approach for bilevel optimization, and a hybrid meta-heuristic using a particle swarm optimization algorithm to tackle the upper-level problem that calls an exact mixed-integer linear programming solver to deal with the lower-level problem. In the framework of the DBA, three different techniques were implemented to deal with the nonlinearities arising from the products of integer and continuous variables (bilinear terms): 1) solving the (non-convex) subproblems of DBA using a mixed-integer nonlinear solver, 2) using the McCormick envelopes to approximate the bilinear terms by linear ones, and 3) expressing the integer variables by binary ones and linearizing the bilinear terms using an exact form. Computational experiments are presented and discussed for real data settings of the problem under study considering a computational budget to compare the different algorithms and techniques employed. The results showed that the DBA with the approximate linearization technique (2) leads to the best solutions.

An optimal pricing and quality assessment model for consumer returns in a multi-period closed-loop supply chain

An optimal pricing and quality assessment model for consumer returns in a multi-period closed-loop supply chain

More Than a Penny’s Worth: Left-Digit Bias and Firm Pricing

Abstract Firms arguably price at ninety-nine-ending prices because of left-digit bias—the tendency of consumers to perceive a $4.99 as much lower than a $5.00. Analysis of retail scanner data on 3500 products sold by twenty-five U.S. chains provides robust support for this explanation. I structurally estimate the magnitude of left-digit bias and find that consumers respond to a one-cent increase from a ninety-nine-ending price as if it were more than a twenty-cent increase. Next, I solve a portable model of optimal pricing given left-digit biased demand. I use this model and other pricing procedures to estimate the level of left-digit bias retailers perceive when making their pricing decisions. While all retailers respond to left-digit bias by using ninety-nine-ending prices, their behaviour is consistently at odds with the demand they face. Firms price as if the bias were much smaller than it is, and their pricing is more consistent with heuristics and rule-of-thumb than with optimization given the structure of demand. I calculate that retailers forgo 1–4% of potential gross profits due to this coarse response to left-digit bias.

Impact of Own Brand Product Introduction on Optimal Pricing Models for Platform and Incumbent Sellers

Sales on the e-commerce platform in the United States have experienced explosive growth and are projected to surpass $740 billion in 2023. The expansion of the platform’s traditional role as a reseller into an online marketplace and the introduction of its own brand products have stoked a huge fear among the incumbent sellers. The platform’s unfair anti-competitive practice further aggravates the situation. Consequently, politicians and regulators have proposed prohibiting platforms from introducing own brand products to protect the incumbent sellers. This study addresses two questions of critical interest to the policymakers and the incumbent sellers. First, how does the platform’s introducing its own brand product affect the incumbent sellers? Second, how effective is the proposed policy in terms of protecting the incumbent sellers? We examine the impact of the platform’s own brand introduction on the incumbent sellers under two prevailing sell-on and sell-to pricing contracts. We find that the proposed legislation “that prohibits platforms from both offering a marketplace for commerce and participating in that marketplace” does not have the desired outcome of helping the incumbent sellers. Instead, it forces the platform to adopt only the sell-to contract with its own brand introduction which hurts the sellers under most market conditions.

Trilevel Optimization Model for Competitive Pricing of Electric Vehicle Charging Station Considering Distribution Locational Marginal Price

We study the competitive pricing problem of electric vehicle charging station (EVCS). The EVCS determines its optimal pricing strategy considering the competition from the other EVCS and the impact of charging loads on the distribution locational marginal price (DLMP) of the power network. A trilevel optimization model is proposed, where the upper and middle level capture the profit maximization problems of this EVCS and its competitor respectively, while the lower level represents the optimal power flow problem of distribution network. Due to its computational challenge, this model is reformulated into a single level one, and their equivalence is rigorously proved. Furthermore, we develop an exact algorithm to achieve the global optimal solution, and also prove its finite convergence. Finally, numerical results validate our trilevel model and exact algorithm, and demonstrate their merits in increasing profits for the EVCS.

Optimal Pricing Model of Environmental Quality Index Futures from the Perspective of Green Finance

In order to establish the optimal price of low-carbon products and set the optimal target carbon emissions in the production cycle so as to maximize profits, this paper proposes the optimal pricing model of environmental quality index futures from the perspective of green finance. This paper mainly studies the optimal pricing and carbon emission strategy of low-carbon products of a single enterprise under the carbon trading system based on the quota system. When enterprises join the carbon trading system, how to optimally determine their target carbon emissions in the production cycle and the optimal price of their low-carbon products in order to maximize their own profits, based on the carbon emission quotas freely allocated by the government in the face of exogenous carbon trading prices and different consumer preferences for low-carbon products in the market, is discussed in detail. The experimental results show that the low marginal cost of emission reduction will urge enterprises to implement low-emission strategies as much as possible, and the marginal cost of a specific size will enable enterprises to implement low-carbon policies with low emissions, and the optimal emissions will decline with the increase of carbon prices. However, from the perspective of 50–300 carbon trading prices, the profits generated are less than those of the minimum emission strategy, and the difference between the two is generally one order of magnitude. Therefore, if the internal conditions permit and the external carbon trading price is reasonable, enterprises should reduce carbon emissions as much as possible. The properties obtained from the model analysis and the numerical conclusions given in the example part reflect the relationship between the enterprise product pricing, the marginal cost of emission reduction, and the target emission decision-making and draw some valuable information for the enterprise and the government decision-making.

How Load Aggregators Avoid Risks in Spot Electricity Market: In the Framework of Power Consumption Right Option Contracts

There is uncertainty in the electricity price of spot electricity market, which makes load aggregators undertake price risks for their agent users. In order to allow load aggregators to reduce the spot market price risk, scholars have proposed many solutions, such as improving the declaration decision-making model, signing power mutual insurance contracts, and adding energy storage and mobilizing demand-side resources to respond. In terms of demand side, calling flexible demand-side resources can be considered as a key solution. The user's power consumption rights (PCRs) are core contents of the demand-side resources. However, there have been few studies on the pricing of PCR contracts and transaction decisions to solve the problem of price forecast deviation and to manage the uncertainty of spot market prices. In addition, in traditional PCR contracts, PCRs are mostly priced using a single price mechanism, that is, the power user is compensated for part of the electricity that was interrupted or reduced in power supply. However, some power users might engage in speculative behaviours under this mechanism. Further, for load aggregators, their price risk avoidance ability has not substantially improved. As a financial derivative, options can solve the above problems. In this article, firstly, the option method is used to build an option pricing optimization model for power consumption right contracts that can calculate the optimal option premium and strike price of option contracts of power consumption rights. Secondly, from the perspective of power users and load aggregators, a simulation model of power consumption right transaction decision-making is constructed. The results of calculation examples show that (1) Under the model in this article, the pricing of option contracts for power consumption rights with better risk aversion capabilities than traditional compensation contracts can be obtained. (2) The decision to sell or purchase the power consumption rights will converge at respective high-value periods, and option contracts will expedite the process. (3) Option contracts can significantly reduce the loss caused by the uncertainty of spot electricity prices for load aggregators without reducing users’ willingness to sell power consumption rights.

Joint bidding and pricing for electricity retailers based on multi-task deep reinforcement learning

The single-task deep reinforcement learning (STDRL)-based methods solve the joint bidding and pricing problem for the electricity retailer in a hierarchical electricity market by defining a bidding policy and a pricing policy separately, which may suffer from low learning efficiency, time-consuming training and local optimization. To deal with these issues, this paper proposes a novel Multi-task Deep reinforcement learning approach for Joint Bidding and Pricing (MDJBP) optimization model. MDJBP can deal with the bidding and pricing tasks concurrently through a shared long short-term memory (LSTM) representation network to distill meaningful temporal characteristics from high-dimensional environment states. Furthermore, we develop a deep neural network (DNN) structure consisting a regression branch for bidding task and a soft actor-critic (SAC) branch for pricing task with automating entropy adjustment and adaptive loss weighting to implement MDJBP. The proposed multi-task deep reinforcement learning (MTDRL)-based method is tested with the IEEE 30-bus system. Numerical results show that the proposed methodology succeeds in giving an optimal joint bidding and pricing policy by fully exploiting commonalities and differences between bidding task and pricing task, and thereby boosts the profit, improves learning efficiency, reduces training time, and enhances stability.

A Comparative Empirical Study of Discrete Choice Models in Retail Operations

Choice-based demand estimation is a fundamental task in retail operations and revenue management, providing necessary input data for inventory control, assortment, and price-optimization models. The task is particularly difficult in operational contexts where product availability varies over time and customers may substitute into the available options. In addition to the classical multinomial logit (MNL) model and extensions (e.g., nested logit, mixed logit, and latent-class MNL), new demand models have been proposed (e.g., the Markov chain model), and others have been recently revisited (e.g., the rank list-based and exponomial models). At the same time, new computational approaches were developed to ease the estimation function (e.g., column-generation and expectation-maximization (EM) algorithms). In this paper, we conduct a systematic, empirical study of different choice-based demand models and estimation algorithms, including both maximum-likelihood and least-squares criteria. Through an exhaustive set of numerical experiments on synthetic, semisynthetic, and real data, we provide comparative statistics of the predictive power and derived revenue performance of an ample collection of choice models and characterize operational environments suitable for different model/estimation implementations. We also provide a survey of all the discrete choice models evaluated and share all our estimation codes and data sets as part of the online appendix.This paper was accepted by Vishal Gaur, operations management.

A bi-level optimization model for electric vehicle charging strategy based on regional grid load following

Because a greater proportion of large-scale electric vehicles (EVs) are connected to the grid, their stochastic charging load has a significant impact on the power quality and economic operation of the distribution network. However, a random charging load can be transformed into flexible demand response resources through intelligent control of the EV charging process. Therefore, a bi-level optimization model for EV charging is proposed in this study based on the real-time charging price according to the regional grid load, providing more flexible charging strategies for EVs. First, the framework for a bi-level optimization control strategy for EV charging based on the load is developed. Based on the regional grid load, the charging price of each period is optimized in accordance with the load elasticity coefficient of the real-time charging price. Second, an upper-level EV charging price optimization model and a lower-level EV charging load optimization model are established. Third, an optimal control strategy for the scheduling of EV charging is developed, which considers the charging cost of EV users as the objective function and the standard deviation and peak-valley difference of the regional grid load as validation functions. Finally, using a regional power grid in China as the simulation object, the daily operation data of the grid are used to analyze and verify the proposed model. The simulation results demonstrate that the optimized real-time charging price can better respond to the regional grid load, smooth the regional grid load curve, reduce the peak-valley difference, promote clean energy consumption, and further lower the charging cost for EV users.

Joint Pricing Strategies for Tobacco Manufacturing Equipment and Optional Value-added Service

Objectives: This paper constructs an analytic model for optimal pricing in which the interrelationship between the tobacco equipment and the optional value-added service supplied by tobacco equipment manufacturers are effectively depicted, and derives the closed-form solutions of the optimal prices, which has previously been considered analytically intractable in the bundling problem of pricing two goods. The research reveals that when the marginal cost of the optional value-added service is 0 and the valuation of the service for tobacco manufacturing enterprises is relatively low, it is advisable to adopt pure bundling pricing strategy; when the marginal cost of the service is 0 but the valuation of the service is relatively high, it is advisable to adopt separate pricing strategy; when the marginal cost of the service is greater than 0, separate pricing strategy is always optimal. And it is interesting that, under separate pricing strategy, the higher valuation of the tobacco equipment leads to lower price for the service; the higher marginal cost of the service leads to higher price for the service, but lower price for the tobacco equipment. This paper also proves that there are only two basic pricing strategies for tobacco equipment manufacturers: pure bundling pricing and separate pricing of the tobacco equipment and service.

A cosh-based smoothing Newton algorithm for the real-time pricing problem in smart grid

In a smart grid system, different types of electricity users such as residential, commercial and industrial users have different utility functions. This paper proposes a nonlinear constrained optimization model for real-time pricing that maximizes the total utilities of all the different user groups. A Karush–Kuhn–Tucker equation system is employed to solve the model. However, it is a challenging task to solve the system due to the nonlinear complementary condition. To tackle the challenge, a cosh-based smoothing approximation function is proposed to substitute the nonlinear complementary condition. Subsequently, the smoothing Newton algorithm is developed to solve the new equation system. The global convergence and local quadratic convergence of the algorithm are proved. Numerical experiments are performed to test the smoothing method and compare the solutions of real-time pricing, fixed pricing and time-of-use pricing strategies applied in the smart grid system. The results show that the real-time pricing mechanism is the most suitable in saving energy and reducing peaks and troughs in energy consumption. This also indicates that it is effective to use the smoothing Newton algorithm to solve the problem of real-time electricity pricing for smart grid. We obtain that the smoothing approximation function is effective for the supply–demand balance constraints in smart grid.

Critical peak rebate strategy and application to demand response

Time-of-use (TOU) pricing strategy is an important component of demand-side management (DSM), but the cost of supplying power during critical peak periods remains high under TOU prices. This affects power system reliability. In addition, TOU prices are usually applicable to medium- and long-term load control but cannot effectively regulate short-term loads. Therefore, this paper proposes an optimization method for TOU pricing and changes the electricity consumption patterns during the critical peak periods through a critical peak rebate (CPR). This reduces generation costs and improves power system reliability. An optimization model for peak-flat-valley (PFV) period partition is established based on fuzzy clustering and an enumeration iterative technique. A TOU pricing optimization model including grid-side and customer-side benefits is then proposed, and a simulated annealing particle swarm optimization (SAPSO) algorithm is used to solve the problem. Finally, a CPR decision model is developed to further reduce critical peak loads. The effectiveness of the proposed model and algorithm is illustrated through different case studies of the Roy Billinton Test System (RBTS).

Comprehensive Evaluation Model and Empirical Research on Railway Freight Rates in a Competitive Environment

This study aims to establish criteria to evaluate performance in railway freight pricing policy and to strengthen the marketing ability of the railway freight enterprise. The evaluation method used in our study is known as the improved grey relation analysis evaluation. Fifteen factors that influence freight pricing strategy are selected in this paper to establish a freight rate evaluation index system and comprehensive evaluation index values for monthly freight rates are calculated. The improved grey relation analysis not only considers the relation between each index and freight rate but also examines the relationship between each index. We find that the comprehensive evaluation state using the improved grey relation analysis evaluation method can better fit the 2015–2017 changes in monthly railroad freight revenue than the traditional grey relation analysis evaluation. Furthermore, an optimal pricing model for freight shipping by train is built and calculated using the bi-level programming model. Finally, the S Railway Bureau’s actual coal transportation in 2017 is taken as an experiment to support the validity of the improved grey relation analysis method. We find that when the monthly results of improved grey evaluation grades are compared with the grade evaluation of the gap between the historical shipping coal rates and the optimal freight shipping rates, the comparison of results matches well. The research work is helpful to policymakers who need to judge the performance of the market price.