Optimal Pricing Model Research Articles

Dynamic pricing and inventory model for perishable products with reference price and reference quality

Reference price (quality) is a benchmark point used by consumers to make price (quality) judgements. Combining reference price and reference quality with dynamic pricing and inventory management, this paper applies differential equations theory to construct a optimal control model for perishable products when the quality of products declines exponentially. The demand of products depends on price, quality, reference price and reference quality, among which reference price and reference quality are influenced by consumers’ past memory. The aim is to maximize the retailer’s profit during the period. The conclusions are as follows. Firstly, a optimal dynamic pricing and inventory model for perishable products with reference price and reference quality is constructed, and the model is extended to dual decision variables, stochastic demand, time-dependent effects, competitive and infinite planing horizon setups. Secondly, through the Pontryagin maximum principle, the analytical expression of the optimal dynamic price is derived. Thirdly, a linear search method to solve the optimal static price is proposed. Finally, the sensitivity of the main parameters is analyzed and the corresponding management enlightenments are given. By comparison of dynamic and static pricing, we find that dynamic pricing can achieve more profits and take a shorter selling period. In addition, for the sales problem of perishable products affected by both reference price and reference quality, retailers should adopt skimming pricing strategy (the optimal price decreases with time). Furthermore, to obtain more profit, retails should strive to increase the sensitivity coefficients of two types of reference, and the reference quality memory coefficient, while to decrease the reference price memory coefficient.

Pricing policies of dual-channel green supply chain: considering manufacturers’ dual behavioural preferences and government subsidies

As the green economy and e-commerce evolve, some manufacturers begin to engage in green production and use online direct channels to enhance competitiveness. However, the additional cost of green production makes manufacturers often show dual behavioural preferences of fairness concern and risk aversion when making decisions. Based on this, this study constructs the optimal pricing model of a dual-channel green supply chain, considering dual behavioural preferences of manufacturers’ fairness concern and risk aversion. In addition, no government subsidy, government research and development cost subsidy and green degree subsidy are also considered. This paper uses the Stackelberg game to find the optimal solution for the model. The findings illustrate that (1) Government subsidy mechanisms cannot coordinate the effects of manufacturers’ dual behavioural preferences on pricing policies of a dual-channel green supply chain. (2) Under the three different government subsidy conditions, manufacturers’ fairness concern and risk aversion will all reduce the green degree of products and online direct price of products. (3) The government research and development cost subsidy and green degree subsidy can both improve the green degree of products, offline retail price, market demand and members’ expected profits.

Pricing Decisions in Dual-Channel Supply Chains Considering the Offline Channel Preference and Service Level

With the rapid development of e-commerce, the online channels encroaching on the offline sales market are becoming more serious, which will definitely harm the offline market. Moreover, there exists a certain percentage of consumers (mostly elderly people) who are not able to purchase online because they lack digital skills. Therefore, understanding the impact of the purchase channel preference and service level on pricing decisions is vital for the dual-channel supply chain management. Focusing on the channel preference and service level, we first develop an optimal pricing model containing centralized and decentralized decision-making for an online and offline retailer by deploying the Stackelberg game. We first develop a Stackleberg game to capture such a dual-channel supply chain with the offline channel preference and service level. Secondly, under centralized decision-making, we derive the optimal retail prices and obtain the optimal total profit. Thirdly, under decentralized decision-making, we obtain the optimal retail prices and optimal total profit as well. Moreover, extensive monotonicity properties when system parameters change are obtained. Relying on the theoretical results, firstly, we show that the improvement of the offline service level would lead to higher pricing of the commodities for both online and offline channels. From our numerical results, when the service level is improved, the offline and online optimal pricing increases by 47.5% and 31.1%, respectively, which may contradict the conventional belief that the improvement of one channel would harm another one. Secondly, we demonstrate that the benefit of improving the offline service level has a diminishing marginal effect. The numerical results show that when the current service level is low, the effectives of improving the service level is roughly five times that when the service level is high. This indicates that the investment in improving the offline service level should not be unlimited. Thirdly, we show that the pricing decision under centralized decision-making should be adopted with the existence of both the offline channel preference and offline service.

An Examination of Human Fast and Frugal Heuristic Decisions for Truckload Spot Pricing

Background: One of several logistics contexts in which pricing decisions are made involves truckload carriers using reverse auctions to bid for prices they want for their transportation services while operating under uncertainty about factors such as their (i) operations costs and (ii) rivals’ bids. This study’s main purpose is to explore humans’ use of fast and frugal heuristics (FFHs) to navigate those uncertainties. In particular, the study clarifies the logic, theoretical underpinnings, and performance of human FFHs. Methods: The study uses behavior experiments as its core research method. Results: The study’s key findings are that humans use rational FFHs, yet, despite the rationality, human decisions yield average profits that are 35% below profits from price optimization models. The study also found that human FFHs yield very unstable outcomes: the FFH coefficient of variation in profit is twice as large as price optimization. Novel contributions inherent in these findings include (a) clarifying connections between spot market auction pricing and behavioral theories and (b) adding truckload spot markets to the literature’s contexts for measuring performance gaps between human FFHs and optimization models. Conclusions: The contributions have implications for practical purposes that include gauging spot pricing decisions made under constraints such as limited access to price optimization tools.

A model for Optimal Pricing and Ordering Strategies for Perishable Goods with Delayed Deterioration, Two-Stage Demand, and Partial Backorders under Delayed Payment Acceptance

Study’s Excerpt/Novelty This study introduces a novel economic order quantity (EOQ) model for managing non-instantaneous deteriorating items under two-phase demand rates and linear holding costs, incorporating constant partial backlogging and two-level pricing strategies within a trade credit framework. The model uniquely addresses the complexities of time-dependent quadratic demand before deterioration and constant demand afterward, providing optimal solutions for maximizing total profit by determining the best timing for positive inventory, cycle length, and order quantity. The research not only establishes the theoretical existence and uniqueness of these optimal solutions but also demonstrates practical implications through numerical examples and sensitivity analyses, highlighting the critical impact of deterioration rates on inventory management and profitability. Full Abstract This research developed an economic order quantity model for non-instantaneous deteriorating items with two-phase demand rates, linear holding cost, constant partial backlogging rate and two-level pricing strategies under trade credit policy. It is assumed that the holding cost is linear time-dependent, the unit selling price before deterioration sets in is greater than that after deterioration sets and the demand rate before deterioration sets in is considered as continuous time-dependent quadratic, after which it is considered as constant up to when the inventory is completely exhausted. Shortages are allowed and partially backlogged. The purpose of the model is to determine the optimal time with positive inventory, cycle length and order quantity such that the total profit of the inventory system has a maximum value. The necessary and sufficient conditions for the existence and uniqueness of the optimal solutions have been established. Some numerical examples have been given to illustrate the theoretical result of the model. Sensitivity analysis of some model parameters on the decision variables has been carried out and suggestions towards maximising the total profit were also given. , it is seen that the higher the rate of deterioration the lower the optimal time with positive inventory ( ), cycle length order quantity and the total profit and vice versa. This implies that the retailer needs to take all the necessary measures to avoid or reduce deterioration to maximise higher profit. Based on the results application of the model led to an increase in revenue.

An Effective Method of Equivalent Load-Based Time of Use Electricity Pricing to Promote Renewable Energy Consumption

The variability and intermittency inherent in renewable energy sources poses significant challenges to balancing power supply and demand, often leading to wind and solar energy curtailment. To address these challenges, this paper focuses on enhancing Time of Use (TOU) electricity pricing strategies. We propose a novel method based on equivalent load, which leverages typical power grid load and incorporates a responsibility weight for renewable energy consumption. The responsibility weight acts as an equivalent coefficient that accurately reflects renewable energy output, which facilitates the division of time periods and the development of a demand response model. Subsequently, we formulate an optimized TOU electricity pricing model to increase the utilization rate of renewable energy and reduce the peak–valley load difference of the power grid. To solve the TOU pricing optimization model, we employ the Social Network Search (SNS) algorithm, a metaheuristic algorithm simulating users’ social network interactions to gain popularity. By incorporating the users’ mood when expressing opinions, this algorithm efficiently identifies optimal pricing solutions. Our results demonstrate that the equivalent load-based method not only encourages renewable energy consumption but also reduces power generation costs, stabilizes the power grid load, and benefits power generators, suppliers, and consumers without increasing end users’ electricity charges.

Charging station service scope division and real-time pricing strategy based on the strongest occupation method

With the rapid construction of charging stations (CSs), charging station operators need to enhance their core competitiveness by precisely planning their service areas and formulating reasonable and effective pricing strategies. However, the regional competition among multiple charging station operators is generally ignored. In the traditional model, the service scope of CSs appears as regular circles, which is inconsistent with the market distribution law. In response to the irregular relationship between the dynamic service scope of CSs and the real-time charging price, a charging station service scope (CSSS) model is proposed by introducing the variable service field strength (SFS). First, the competitiveness of CSs is evaluated quantitatively, and the SFS of CSs is defined to describe the service scope of CSs by the strongest occupation method. Second, the impact of the charging price on the charging demand is analyzed based on the CSSS division model. In addition, the revenue of charging station operators and the stability of the power grid are considered to establish a real-time pricing optimization model. Finally, the numerical simulation is operated in Furong District of Changsha. It is shown that the proposed method effectively achieves more profits for charging stations and decreases the average power deviation of the whole region.

Mathematical models for improving the quality of services in hospitality industry

The article discusses the importance of developing a high-quality hotel product in the context of modern requirements for technical, technological, and environmental standards. The paper identifies key parameters that influence the assessment of the quality of a hotel offer, such as the location of the hotel, range of services, infrastructure, service technologies, pricing, and others. In addition, various mathematical models are considered, including a customer satisfaction assessment model, a demand forecasting model, a pricing optimization model, an inventory management model, and others, which can be applied to improve the quality of service in the hotel industry. This article aims to better comprehend the dynamics of changing customer needs and effectively adapt the hotel offer to market requirements. The authors draw attention to the importance of high-quality service for creating customer satisfaction and brand loyalty. The article also discusses in detail the aspects of checking the quality of hotel services, the problem of conflict of interests between customer expectations and reality, as well as mathematical methods for studying customer preferences for hotel services.

Research on pricing and replenishment based on optimal programming model

This paper studies the law and correlatoin of different categories of vegetable commodities, and makes the total amount of replenishment and pricing strategy of each vegetable category in the next week, so as to maximize the profit of supermarket. Firstly, the correlatoin between different categories of vegetable products was analyzed based on Pearson correlatoin analysis. The results showed that flower-leaf, cauliflower, pepper had strong correlatoin with edible fungi, while aquatic rhizome and solanaceae had relatively low correlatoin with other categories of vegetables. Then, the monthly and daily sales volume of each category and single vegetable were counted, and the monthly, weekly and daily distribution function of each category and single vegetable was obtained by fitting with Python software using the least square method. The vegetable category cluster analysis based on systematic clustering was used to cluster 6 categories of vegetables, and the 6 categories of vegetables were divided into 3 categories. Then the least square method was used to fit the processed data, and the fitting function expression between the sales volume and the cost plus pricing of each category of vegetables was obtained. The replenishment quantity decision model based on time series was established, and the daily replenishment quantity decision of each vegetable category in the next week was obtained. Finally, according to the correlatoin between sales volume and price, the optimal pricing model based on dynamic market demand is established, and the most reasonable pricing is obtained and the optimal replenishment decision is made to maximize the profit of supermarket.

Optimization modeling of vegetable pricing replenishment strategy based on machine learning

Fresh supermarkets are affected by commodity attributes and transaction time, and usually need to be replenished every day. It is of great significance to study the distribution law of sales volume of each category and single product, and to give replenishment and pricing strategies for the commercial supermarket to maximize its revenue. Based on the machine learning method, this paper analyzes the sales flow records of a supermarket in the past three years, obtains the sales rules of each category, and establishes a dynamic optimization model for subsequent pricing and replenishment decisions. The steps are as follows: Firstly, data preprocessing is carried out. Secondly, the kernel density estimation method is used to analyze the distribution law of the total sales volume of each category. With the help of correlation coefficient Screening feature selection method, neural network method and regression tree method, the first 33 single vegetable variables that have an important impact on the total sales volume of vegetables and meet the given constraints are comprehensively selected. Based on these 33 variables, the revenue function of single product sales, single product pricing, single product replenishment and single product wholesale price is constructed, so that the optimization problem of the revenue function is transformed into a constrained optimization problem of a quadratic function of the cost markup rate, and the specific pricing and replenishment strategy on July 1,2023 is obtained. The model established in this study can provide some new solutions to the vegetable pricing and replenishment strategy of supermarket.

A pricing optimization modelling for assisted decision making in telecommunication product-service bundling

Product service bundle (PSB) is a marketing strategy that offers attractive product-service packages with competitive pricing to ensure sustained profitability. However, designing suitable pricing for PSB is a non-trivial task that involves complex decision-making. This paper explores the significance of pricing optimization in the telecommunication industry, focusing on product-service bundling (PSB). It delves into the challenges associated with pricing PSB and highlights the transformative impact of big data analytics on decision-making for PSB strategies. The study presents a data-driven pricing optimization model tailored for designing appropriate pricing structures for product-service bundles within the telecommunication services domain. This model integrates customer preference knowledge and involves intricate decision-making processes. To demonstrate the feasibility of the proposed approach, the paper conducts a case study encompassing two design scenarios, wherein the results reveal that the model offers competitive pricing compared to existing telecommunication service providers, facilitating PSB design and decision-making. The findings from the case study indicate that the data-driven pricing optimization model can significantly aid PSB design and decision-making, leading to competitive pricing strategies that open avenues for new market exploration and ensure business sustainability. By considering both product and service features concurrently, the proposed model provides a pricing reference for optimal decision-making. The case study validates the feasibility and effectiveness of the approach within the telecommunication industry and highlights its potential for broader applications. The model's capability to generate competitive pricing strategies offers opportunities for new market exploration, ensuring business growth and adaptability.

US efficient factors in a Bayesian model scan framework

PurposeThe author examines the impact these efficient factors have on factor model comparison tests in US returns using the Bayesian model scan approach of Chib et al. (2020), and Chib et al.(2022).Design/methodology/approachEhsani and Linnainmaa (2022) show that time-series efficient investment factors in US stock returns span and earn 40% higher Sharpe ratios than the original factors.FindingsThe author shows that the optimal asset pricing model is an eight-factor model which contains efficient versions of the market factor, value factor (HML) and long-horizon behavioral factor (FIN). The findings show that efficient factors enhance the performance of US factor model performance. The top performing asset pricing model does not change in recent data.Originality/valueThe author is the only one to examine if the efficient factors developed by Ehsani and Linnainmaa (2022) have an impact on model comparison tests in US stock returns.

OPTIMAL PRICING AND PRODUCTION LOT SIZE FOR TWO RATES OF PRODUCTION WITH PRICE-SENSITIVE DEMAND, PRICE BREAK-EVEN POINT, AND PROFIT MAXIMISATION IN HIGHER ORDER EQUATION

In the present study, optimal pricing and optimal lot size production policy models with price-sensitive demand of deteriorating products are considered, taking into account two distinct production rates. It is possible to begin production at one rate and then switch to a different rate after a period of time. Such a scenario is appealing, in that a big initial stock of produced goods can be avoided by starting production at a modest pace, thus reducing the initial investment and the holding cost. Further, the fifth-order equation is obtained when the equation for optimal pricing is derived. Maximising the profit is calculated based on a fifth-order equation. Both optimal pricing and production lot size are decision variables, and optimal cycle time is also one of the decision variables for determining price break-even points. As far as information is concerned, no researcher has examined optimal pricing and production lot size policies in two-rates-of-production models for their study.The objective of the present study is to examine the optimal production, optimal pricing, and optimal cycle time to reduce the total cost and to maximise the total profit. Both price break-even point and profit maximisation are considered. An appropriate mathematical model is developed. An illustrative example is provided and numerically validated using a sensitivity analysis. Microsoft Visual Basic 6.0 was used to code the model’s outcome validation.

A mathematical model of optimal pricing for the equilibrium budget balance of a company specializing in solid household waste collection

This paper proposes a pricing model to ensure the budget balance of a company responsible for collecting and treating solid household waste in a city. The model used is of the Principal-Agent type which considers two actors at play, namely the leader (the service provider company) and the follower (the households and establishments that are the beneficiaries of the waste collection service). The model is a constrained bi-level optimization program. The model was applied in the case of Benin to the Grand Nokoué waste management and healthiness Company (SGDS-GN) whose intervention area, in the beginning, covers five communes in the southern part of the country. The solving of the optimization program was made with three (03) scenarios: the company spends two (02) times a week for waste collection (scenario 1), the company spends three (03) times a week for waste collection (scenario 2) and the company spends four (04) times a week for waste collection (scenario 3). The simulation results show that scenario 2 with three (03) passages per week appears more optimal for both the company (the operating result is higher) and the beneficiaries of waste collection services (the rate to be paid is lower).

Can We Optimize Stock Price?—A Mathematical Driven Stock Price Optimization Model in Finance Based on Desirability Function

Can We Optimize Stock Price?—A Mathematical Driven Stock Price Optimization Model in Finance Based on Desirability Function

Dual-layer peer-to-peer energy trading method with multiple SOPs pricing in distribution networks

With the decentralization and the development of power markets, different stakeholders are emerged in distribution networks. The unbalance of distributed generators (DGs) and demand-side response in each area leads to a power transfer demand with others. Peer-to-peer (P2P) energy trading has the potential to enable different stakeholders to complement each other. Soft open points (SOPs) provide a promising physical platform for power transfer and trading. However, determining the trading price with SOP participation is an urgent issue to be addressed. Aiming at improving fair and economic operation, this study proposes a P2P energy trading method with multiple SOPs pricing in distribution networks. First, a dual-layer P2P energy trading framework is established. In the upper layer, an optimal pricing model is formulated to maximize SOP profits. An optimal dispatch model is formulated in the lower layer to conduct the power transfer based on the upper layer price. Then, the dual-layer model is converted into a second-order cone programming (SOCP) model to achieve computational tractability. Finally, a practical distribution network is utilized to validate the proposed method. The results indicate that the proposed P2P energy method is effective in reducing the operating costs and increasing the operating profits of SOPs.

Pricing optimization of product line with value-added services considering consumer choice behavior

ABSTRACT The global economy is transitioning from product economy to service economy, and the optimization of product line with value-added services is one of the important issues faced by enterprises. Therefore, this paper studies the pricing optimization of product line with value-added services considering consumer choice behavior. First, we apply the multinomial logit (MNL) model to simulate consumer choice behavior, and establish a MNL-based product line pricing optimization model considering value-added services. Then, the optimal pricing strategies for products and services are solved for three different scenarios: single product with service, homogeneous products with services, and heterogeneous products with services. Finally, through numerical experiments, we analyze the changing trends of the optimal pricing, market share and profit of products line with value-added services with some impact factors, such as product quality, service level, consumer sensitivity, and number of products under three different scenarios. We also obtain some managerial implications when an enterprise develops product line with value-added service.

Network Car Hailing Pricing Model Optimization in Edge Computing-Based Intelligent Transportation System

The purpose of this study is to investigate Network Car Hailing (NCH) price or the deficiency in NCH Platform in Edge Computing (EC)-based Intelligent Transportation System. Aiming at the uncertain capacity and unbalanced load in the car-hailing platform, this work innovatively introduces the EC to unload, constructs an EC-based online car-hailing resource allocation and pricing optimization model by combining with factors such as the number of users and reputation in the network, and further analyzes the performance of the resource allocation and pricing optimization model in the constructed car-hailing platform through simulation experiments. The experimental results show that with the increase in the number of vehicles with computing tasks, the amount of resources purchased from various car-hailing vehicles also increases, the cost of paying is showing an increasing trend, and the utility function of NCH platforms and operators has declined. In the task resource analysis, the average unloading utility of the algorithm in this work is the highest, and the average unloading utility is basically stable at about 70% when the number of vehicles is 98. With the increase of the delay weight, the delay is smaller and the energy consumption is lower. Therefore, the model constructed in this work can minimize the average cost and consumes less energy while the delay is small. It can provide a reference for intelligent pricing and resource allocation of the online car-hailing platform in the later period of intelligent transportation.

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

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

Analysis of critical peak electricity price optimization model considering coal consumption rate of power generation side.

As a flexible electricity pricing mechanism, critical peak pricing (CPP) is one of the important means of demand response under the electricity market. The existing CPP research does not take into account the carbon emission problem of units and weakens the difference between the use of terminal loads on critical peak days and non-critical peak days in the establishment of electricity price model, so this paper studies the feedback mechanism of CPP on coal consumption of power generation side units and proposes a dynamic CPP mechanism that takes into account terminal consumption satisfaction and coal consumption of power generation side units. Firstly, the influence mechanism of CPP on the power generation side is studied. Secondly, the consumer psychology theory is used to construct a user demand response model under critical peak days and non-critical peak days. Then, based on the difference in load usage of end users on critical peak days and non-critical peak days, a multi-objective CPP optimization model that considers the benefits of coal consumption and end user electricity expenditure on the power generation side is constructed. Finally, three scenarios were established to analyze the sensitivity of the user demand response model parameters, terminal satisfaction constraints, prices, and rate restrictions on CPP pricing, load improvement, and unit coal consumption reduction and verify the model's effectiveness. The results show that the proposed CPP optimization model has a significant effect on load improvement and carbon emission reduction; the user response gradient, terminal satisfaction, prices, and rate restrictions have a greater influence on the model optimization results, while the threshold and saturation values have little influence on the model optimization results.