Optimal Pricing Research Articles

The Impacts of Payment Schemes and Carbon Emission Policies on Replenishment and Pricing Decisions for Perishable Products in a Supply Chain

In the supplier–retailer–consumer system, the retailer’s replenishment and pricing strategies impact the entire transaction process, forming a comprehensive trading market. Suppliers offer advance-cash-credit payments to retailers, while retailers provide customers with cash-credit payment options. In the current health-conscious consumer market, purchasing decisions are influenced not only by commodity prices but also by the freshness of products, particularly perishable goods. Growing awareness of climate change and the advent of carbon emission policies have raised concerns about the environmental costs of business transactions. This study focuses on perishable products whose demand is influenced by both price and freshness. It explores the adoption of various payment methods by suppliers and retailers, as well as the impact of carbon emission cap-and-trade policies or carbon tax policies on management and pricing strategies. Suitable inventory models are established to determine the optimal replenishment and pricing strategies for maximizing the current value of total profit. We illustrate that the current value of total profit demonstrates joint concavity concerning both the selling price and the replenishment time. Finally, we verify the proposed models using numerical examples and present the findings of sensitivity analyses. The findings of this study yield several valuable insights for inventory management of perishable goods.

Research on automatic pricing and replenishment decision of vegetable commodities based on optimization model

In fresh food superstores, because vegetable commodities are characterized by perishability and high value loss, superstores usually replenish daily commodities based on the historical sales and demand of various commodities. In order to make the optimal replenishment decision, this paper firstly firstly uses Matlab fitting toolbox to get the functional relationship between the total sales volume and the cost-plus pricing, so as to analyze the relationship between the total sales volume and the cost-plus pricing of each vegetable category, and then takes the category as a unit, and then constructs the optimization model, and solves the optimal replenishment volume and pricing strategy. The replenishment decision is obtained by filtering out the most profitable single product among the factors of unit price, sales volume, and total replenishment volume through objective planning under the constraints of considering the single product category and minimum display volume.

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.

Optimal pricing and capacity management in service systems with delay-sensitive mixed-risk customers

In service systems with delay-sensitive customers, customer decisions to join the queue or balk influence demand, impacting service provider profits. Studies show that customers can be risk-seeking for short waits and risk-averse when waits exceed expectations. Prior research on this mixed-risk attitude is limited, focussing on optimal pricing policies from a social welfare perspective. This study fills this gap by investigating the impact of this behaviour on customer joining strategies and the provider's pricing and capacity policies. We analyse a profit-maximising firm managing an unobservable queue where customers display mixed-risk behaviour towards delay parameterised by a risk-switching point and a degree of risk propensity. Customers join or balk based on expected utility, while the firm determines the service price and rate to maximise expected profit. We derive optimal strategies for both customers and the firm under scenarios with concave or convex capacity costs. Computational experiments show that optimal pricing, capacity, and profit peak at intermediate risk-switching points. For smaller points, optimal price and capacity rise with the customers' degree of risk propensity, while larger points have minimal impact. Numerical exploration emphasises the significance of capacity cost and the effectiveness of leveraging price over controlling capacity for maximising firm profitability.

Optimal pricing strategy in the closed-loop supply chain using game theory under government subsidy scenario: A case study

Automotive battery production always receives government supports which directly affect the recycling of used products collected from secondary markets. Accordingly, an optimal product pricing strategy and efficient policy suggestions must be provided for this industry. This study used Stackelberg models to analyze three categories of pricing strategies related to the recycling process of car batteries when government subsidy is paid. These models are applied to make optimal decisions in two centralized and decentralized modes to investigate the links between and influences of different parameters of the problem on one another. Finally, a numerical example based on a real case study in Iran is applied to the models. The results indicate that making centralized decisions leads to a higher level of profitability than decentralized decision-making in the under-study industry. Accordingly, maintaining coordination and integration among the supply chain components in the decision-making process increases the profitability of the entire network.

Bundling products and service on influencer channels

This study investigates the optimal service pricing strategies for manufacturers within the burgeoning field of influencer live-streaming marketing. By examining a dynamic where manufacturers collaborate with social media influencers, the research evaluates the efficacy of bundling products and services versus separate pricing under varying conditions. The study uncovers that the gap between the two service pricing models will increase as the service cost increases. Moreover, the lower the service cost, the more obvious the relative advantage of the bundling model. That is, bundling is most beneficial when service costs are low, whereas separate pricing becomes advantageous as service costs escalate. In addition, the decrease in the rate of product defects can lead to an increase in the relative advantage of the bundling model. Intriguingly, the optimal promotional approach for influencers shifts in response to these pricing strategies, favoring a combined product-service promotion when services are priced separately. The study further reveals a direct correlation between product defect rates and profitability, especially under separate pricing scenarios. These insights offer valuable guidance for manufacturers and influencers in strategizing their offerings and promotions in the digital marketplace.

Demand‐driving innovation, advertising nuisance, and a media platform optimal pricing

AbstractThis paper explores the incentives of a monopolistic media platform to invest in demand‐driving innovation when the interactions between its customer groups (eyeballs and advertisers) are countervailing. We investigate whether media innovation contributes to resolving the trade‐off between catering to both groups (or sides) and minimizing advertising nuisance. We identify an innovation threshold guiding the media platform on when to charge more eyeballs than advertisers, effectively reversing the standard divide‐and‐conquer pricing strategy. Moreover, we show that the media platform invests more in research and development (R&D) on the side with the strongest reference market, and we highlight the role of excessive inertia and momentum in shaping innovation. Furthermore, we find that when the relative advertising nuisance is low, the platform is less encouraged to innovate on both sides when the ad nuisance increases marginally. However, when the relative advertising nuisance is high, we infer an R&D see‐saw rule: a marginal increase in the ad nuisance reduces the R&D efforts undertaken on one side and increases those on the other. Our findings provide insights into the complex interplay between media platform innovation and pricing strategy in the presence of advertising nuisance and a challenging chicken‐and‐egg problem.

Optimization of ticket pricing for high-speed railway considering full competitive environment

The rapid development of high-speed railways (HSR) worldwide has provided a fast, convenient, safe, and comfortable mode of transportation. It is also an important public transportation tool for green travel, contributing to the reduction of carbon emissions. HSR has a strong competitive advantage in long-distance passenger transportation, but it faces significant competition from the aviation industry. Airlines attract passengers with discounted fares and differentiated pricing strategies, apart from shorter travel times. Therefore, it is necessary for railway enterprises to enhance their competitiveness through differentiated pricing methods for HSR. In this study, we focus on optimizing a long-distance origin-destination (OD) pair and creating a competitive market environment by considering all operating trains and flights for the selected OD pair. We aim to improve the realism of the study by considering passengers’ fully rational travel choice behavior. To reduce the complexity of variables, passengers are grouped based on their expected departure time and income level. A mixed integer linear programing model is developed to address the problem, aiming to minimize overall travel costs for passengers while ensuring that the income of the railway enterprise does not fall below a specified value. By setting this specific value, the maximum revenue of HSR train tickets can be obtained.

Optimal introductory pricing as an investment decision

ABSTRACT In this article, we propose a model that can be used to calculate the optimal introductory price for any product or service offered in a market. We view the introductory pricing problem as an investment decision with uncertain future cash flows. In this setup, the initial investment is the foregone income of lower period 1 revenues to generate higher expected cash flows from subsequent periods. We empirically test the model using data from a survey in the alpine skiing industry and show that it provides meaningful results.

Socio-economic determinants of pricing water for domestic use: A comparison of blocks and linear tariffs

This article explores a model in which an agency can adopt different tariff schemes (block tariff or linear tariff) for selling water to a domestic buyer (a household), considering socio-economic factors like household size and income level. Through the formulation and examination of a static game involving a buyer and an agency, where the latter considers also the buyer’s welfare in its decisions, the socio-economic determinants significantly affect the optimal pricing within each of the two suggested tariff schemes. This analysis leads to the identification of conditions under which the agency deems a block tariff more advantageous compared to a linear tariff, as well as circumstances where adopting a linear pricing strategy emerges as the optimal approach. By introducing a (discrete-time) dynamic extension of the model, in which the agency is assumed to operate as a boundedly rational agent, we investigate the role of the altruism that the agency decides to adopt toward the buyer, observing that it ends up affecting the price dynamics (defined by a gradient-like mechanism). In addition, we apply the model to the real case of the Apulia region in Italy, comparing the unit price currently applied in the region with the results of applying the model in the Apulian territory.

Reference Dependence in Queue Design and Pricing Strategies

This research investigates the effect of reference dependence on waiting times in service systems which formerly used a first-in-first-out (FIFO) service but have introduced a priority line with a fee. Our model combines reference-dependent gain-loss utility with standard customer utility, and we posit that customers are pleased with shorter-than-expected waiting times, whereas longer-than-expected times lead to dissatisfaction and an increased likelihood of balking. The study explores two scenarios: a captive customer system (CCS) and a noncaptive customer system (NCCS), with a focus on optimal pricing and segmentation strategies for revenue and social welfare maximization. The results reveal that, in a CCS, the service provider should implement observed and unobserved customer segmentation to optimize revenue and social welfare, respectively. In an NCCS, the impact of customer segmentation on revenue maximization depends on the value of regular customers, their loss reference-dependent preferences, and the system’s offered load. Alternatively, if the service provider seeks to maximize social welfare, the provider’s use of customer segmentation relies solely on the system’s offered load and customers’ reference-dependent preferences. Our findings also indicate that reference dependence can have varying impacts under different conditions, suggesting the effectiveness of tailored service and pricing strategies. Notably, a CCS generates more revenue than does an NCCS because of its captive nature, and, surprisingly, increasing the service rate can decrease revenue while improving social welfare. These insights have significant implications for service management strategies for a CCS and an NCCS. Funding: J. Liu was supported by the National Natural Science Foundation of China (General Program) [Grant 72071112]. J. Chen was supported by the National Natural Science Foundation of China (Major Program) [Grant 71490723]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/serv.2023.0033 .

Newsvendor model for a dyadic supply chain with push-pull strategy under shareholding and risk aversion

This paper investigates the optimization and coordination problem in the framework of classic push and pull newsvendor models under shareholding and CVaR criterion. A decentralized supply chain consisting of upstream supplier and the downstream manufacturer is considered. Firstly, taking the risk aversion into account, the optimal decision-makings are investigated under shareholding in push, pull supply chain respectively. By comparison it is found that the optimal order or production quantity depends on the degree of member’s risk aversion and shareholding ratio. Furthermore, the combined contracts are designed to coordinate the supply chain and optimal coordination parameters are obtained. Besides, the impacts of risk-averse preference and the shareholding fraction on supply chain performance are also investigated. The results indicate that in push supply chain the optimal ordering increases in the risk-averse parameter of the downstream manufacturer and the percentage of shares held by the upstream supplier in the downstream manufacturer. However, the optimal wholesale price makes the opposite change. In pull supply chain, the optimal production quantity is independent of the shareholding fraction and decreases with regards to the supplier’s risk aversion. Lastly, some numerical examples are given to illustrate the theoretical results and some suggestions to supply chain management are also provided.

Demand response model: A cooperative-competitive multi-agent reinforcement learning approach

This study introduces a novel Demand Response (DR) Model based on Multi-agent Reinforcement Learning (MARL-DR), comprised of a pricing and incentives scheme aimed at improving the accuracy of existing demand response strategies. Furthermore, this new approach represents a flexibility solution to prevent sharp price variations caused by the high penetration of unconventional renewable energy, which are directly passed on to end-users. The model employs a cooperative-competitive MARL-DR technique based on Q-learning, with the goal of determining optimal prices and incentives that maximize benefits for both customers and electric Service Provider (SP). In this regard, the model has the capability to offer customers pricing options in both real-time and time-of-use, to actively adjust each user's consumption. Additionally, through demand characterization factors, such as the coincidence factor (CF), the of typical user behavior is improved, and the influence of individual user demand on system peak demand is more accurately detected. It is also demonstrated that the cooperative-competitive approach offers better performance compared to other approaches. Finally, a sensitivity analysis is presented at various stages of the model to verify its accuracy and efficiency in pricing and incentives formulation.

A Literature Review on Pricing Decisions for Complementary Supply Chains Considering Social Preference Behavior

In practice, many enterprises have achieved better market results through the implementation and continuous optimization of the complementary products strategy. Although complementary products can bring higher value and utility to customers' consumption experience, thus affecting the production operation and sales price decisions of enterprises, the strategic choices of complementary supply chain members will be affected when facing the different social preference behaviors of the members in the complementary supply chain and the complex supply chain structure. Based on this, this paper considers the vertical altruistic preference of the manufacturer over the retailer and the horizontal altruistic preference of the manufacturer over the manufacturer of the complementary product under different altruistic preference dimensions for a two-level supply chain system consisting of two manufacturers producing complementary products and a common retailer, and analyzes the optimal pricing strategies of supply chain members under different altruistic preference levels, which is of great significance for the stable operation of the supply chain.

To Skim or not to Skim: Studying the Optimal Pricing Strategy for Technology Products

Pricing of technology products often follows a skimming strategy in which a firm charges the highest price at product launch then reduces the price over time to attract additional buyers. Price-skimming has not been adequately examined in the literature related to technology products. Most pricing models proposed in the literature consider only initial product purchases while ignoring repeat purchases. However, for technology products, frequent upgrades often result in substantial repeat purchases. To fill this void, we develop an optimization model that accounts for both initial and repeat purchases. We find that the effectiveness of price skimming is highly dependent on the rate of repeat purchases. When the repeat purchase rate is low, firms may be better off delaying price reduction to accumulate more profit earlier in the product lifecycle, thus compensating for the decline in sales that occurs later in the lifecycle. For example, price skimming may not be the optimal pricing strategy for fad products with low repeat-purchase rates due to the product losing popularity in a short time period. Furthermore, contrary to common expectations, in markets highly sensitive to price changes firms may get away with charging a higher introductory price but must decrease the price over time to motivate sales.

Multi-agent-based decentralized residential energy management using Deep Reinforcement Learning

In smart grid, energy consumption has grown exponentially in residential houses, which necessitates the adoption of demand response management. To alleviate and handle the energy management in residential houses, an efficient residential energy management (REM) system can be employed to regulate the energy consumption of appliances for several energy loads such as non-shiftable, shiftable, and controllable loads. Many researchers have focused on the REM using machine learning and deep learning techniques which is not able to provide secure and optimal energy management procedure. Thus, in this paper, a multi-agent-based decentralized REM, i.e., MD-REM approach is proposed using Deep Reinforcement Learning (DRL) with the utilization of blockchain. Furthermore, The combinatorial model DQN, i.e., Q-learning and deep neural network (DNN) is employed, to gain the optimal price based on the reduced energy consumption by appliances associated with different energy loads utilizing the Markov Decision Process (MDP). Here, multiple agents are designed to handle different energy loads and consumption is controlled by the DQN agent, then reduced consumption data is securely shared among all stakeholders using blockchain-based smart contract. The performance evaluation of the proposed MD-REM approach seems to be efficient in terms of reduced energy consumption, optimal energy price, reward, and total profit analysis. Moreover, blockchain-based result is evaluated for the proposed MD-REM approach considering the performance metrics such as transaction efficiency, Interplanetary File System (IPFS) bandwidth utilization, and data storage cost comparison.

Cruise market investigation and price optimization: what do consumers want?

PurposeThis study aims to examine consumer perception during COVID-19 and identifies cruise industry marketing strategies to fill a gap in crisis management and product pricing literature.Design/methodology/approachThis study developed and validated two-factor measurement scales (vaccine perception and protective behavior), which predicted cruise intents well. This study revealed how geo-regional factors affect consumer psychology through spatial analysis.FindingsThis study recommended pricing 7-day cruises at $1,464 (the most preferred length). The results also showed that future price hikes would not affect demand and that coastal marketing would help retain customers.Originality/valueThis study contributed to the business, hospitality and tourism literature by identifying two new and unique factors (vaccine perception and protective behaviors), which were found to affect consumers’ intention to travel by cruise significantly. The result provided a better understanding of cruise tourists’ pricing preferences and the methods utilized could easily be applied to other cruise markets or tourism entities.

Research on enterprise production decision‐making considering consumer heterogeneity under carbon labeling system

AbstractThe article focuses on consumers with heterogeneous preferences for product carbon footprints under two carbon labeling systems: carbon reduction labels and carbon footprint labels. Using mathematical models, the study explores the optimal decision‐making behavior of enterprises under the carbon labeling system based on consumer utility theory at the enterprise level. It also investigates consumer surplus, environmental improvement, and social welfare under different production modes of the carbon reduction label and carbon footprint label systems at the societal level. The research findings are as follows: (1) At the level of economic benefits for enterprises, choosing to produce products with carbon reduction labels is more favorable when the investment costs for emission reduction are high, while choosing to produce products with carbon footprint labels is more favorable when the investment costs for emission reduction are low. The optimal prices of products under the two carbon labeling systems show opposite trends compared to the investment costs for emission reduction. (2) At the level of environmental benefits for enterprises, under the carbon reduction labeling system, whether through full production or a mixed production mode, enterprises are only willing to reduce the carbon footprint of products to the standard value. However, under the carbon footprint labeling system, especially in the mixed production mode, enterprises show a stronger willingness to overachieve in emission reduction target. (3) At the level of social benefits, compared to the situation under the carbon reduction labeling system, when the investment costs for emission reduction are low, the carbon footprint labeling system is more favorable in terms of consumer surplus and social welfare. However, this advantage gradually diminishes as the investment costs for emission reduction increase. (4) Excessive investment costs for emission reduction are detrimental to the implementation of both carbon reduction and carbon footprint labeling systems. The research conclusions suggest that companies should develop appropriate production strategies based on actual circumstances. Additionally, it is necessary for both the government and companies to reduce investment costs in emissions reductions by improving the system and optimizing emission reduction methods in order to better implement carbon labeling policies.

Searching for a Carbon Laffer Curve: Estimates from the European Union Emissions Trading System

AbstractCarbon prices have grown remarkably in the European Union (EU) Emissions Trading System (ETS) in recent years, raising distributional concerns. Revenues are expected to grow with higher carbon prices, thus providing resources to address distributional issues. Beyond a certain point, however, higher prices can discourage the purchase of allowances and ultimately reduce revenues, describing a Carbon Laffer Curve (CLC). We empirically investigate the CLC in the EU ETS between 2012 and 2021 using auction revenues at the country level. Results indicate that ETS revenues follow an inverted‐U relationship in both the volume and the price of auctioned allowances, with an estimated optimal price between 86 and 125 euros.

Collaborative Vehicle-to-Grid Operations in Frequency Regulation Markets

Problem definition: We study the operations of electric vehicles (EVs) providing frequency regulation services to the electric grid in vehicle-to-grid (V2G) systems. In particular, individually owned EVs collaboratively bid in the regulation market, coordinated by a platform that operates the network of charging equipment. We study how the platform determines optimal pricing incentives for drivers to plug in their EVs, accounting for heterogeneous driving schedules. Methodology/results: We model the platform’s pricing optimization problem as a bilevel program: At the upper level, the platform determines hourly rebates for EV owners to plug in their EVs and capacity bids in the regulation market; at the lower level, individual travelers optimize their travel and charging schedules in response to pricing incentives. To account for uncertainties and heterogeneity in regulation market prices and travel patterns, we adopt distributionally robust optimization techniques to formulate the problem as a mixed-integer second-order cone program. We conduct a computational study based on the California Household Travel Survey data set and actual frequency regulation prices. Our results show that the ability to offer time-varying rebates and install workplace chargers can significantly improve the V2G platform’s expected profits. Managerial implications: As EV adoption progresses past the nascent stage, V2G business models become more viable. Successful implementation of V2G provides economic incentive for switching to EVs, potentially helps sustain adoption growth, and complements the growth of renewable power by helping stabilize the grid. Our findings shed light on the design of driver incentives for V2G systems. Funding: R. Tang acknowledges support from the National Natural Science Foundation of China [Grant 72201206]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/msom.2022.0133 .