Optimal Pricing Research Articles

Optimal investment and equilibrium pricing under ambiguity

Optimal investment and equilibrium pricing under ambiguity

Pricing and green quality decisions in two-stage green supply chain for substitutable green products: A game-theoretic approach

Growing businesses are concerned with doing well both environmentally and economically. Pointing out this view, this paper explores the game theoretical approach (Stackelberg and Bertrand) for a two-echelon green supply chain where the duopolistic manufacturers produce two substitutable green products and sell their products through a common retailer. The demands for both green products are functions of the selling prices and green levels (GLs). The effects of power structures on optimal price and green level decisions and associated equilibrium decisions are examined in three scenarios. Firstly, trilateral competition manufacturer-led Stackelberg (MS); secondly, retailer-led Stackelberg (RS); and thirdly, vertical collaboration, and compares the optimal decisions analytically. Our investigations show that, in addition to increasing the product’s greening level, vertical collaboration creates a win–win situation for collaboration members, whereas the manufacturer outside the collaboration experiences a decline in profits. Additionally, we find that the overall profit from vertical collaboration is greater than the sum of the individual profits corresponding to two participants in the trilateral competition models (MS and RS). Further, a selection criterion is developed for retailer to select the most suitable manufacturer for vertical collaboration. Finally, a numerical example and a sensitivity analysis are performed to determine the impact of parameters.

The optimal decision of service provider considering extra waiting area value-added services – pooled or dedicated?

Service providers often provide chargeable extra waiting area value-added services (EWS) to enhance customers’ waiting experiences, e.g., in VIP and business lounges at airports, train stations, luxury brand stores, etc., to improve profitability. The impact of EWS on customers’ value perception is subject to their heterogeneous sensitivities and also depends on the reference effect due to EWS’ observable status. This paper investigates the optimal level of EWS and price decisions for a service provider facing heterogeneous customers, namely the EWS-preferring (E-type) customers and ordinary (O-type) customers, considering the observable status (observable vs. unobservable) of EWS using pooled or dedicated capacities in operations through M/M/1 queue models. The optimal price and level are solved and the optimal profit is calculated under each scenario. It is found that customers’ heterogeneous sensitivities play an important role in the price and intensity decisions. Offering observable EWS to leverage the reference effect in customers’ value perception can lead to a higher profit. Furthermore, using pooled capacity in operations with EWS is more profitable when service costs are higher. These results offer significant managerial implications and provide practical guidelines for service providers regarding the intensity of EWS, service price, and whether EWS should be observable to customers through pooled or dedicated capacities.

Optimizing energy storage configuration scheme considering optimization of electricity prices, carbon emissions, and flexible load

Optimizing energy storage configuration scheme considering optimization of electricity prices, carbon emissions, and flexible load

Evaluation of black tilapia (Oreochromis niloticus) hatchery in UPT-Perikanan Budidaya Air Tawar (PBAT) Sukorejo, Malang

Abstract Black tilapia is a freshwater fish that has become a leading commodity in the UPT-PBAT (Unit Pelayanan Teknis-Pengembangan Budidaya Air Tawar) Sukorejo Freshwater Aquaculture Fisheries with an optimal selling price. The purpose of this study was to evaluate the hatcheries activity performance in UPT-PBAT Sukorejo. The method in this research used active participation and descriptive methods. The data collection method used was from primary and secondary data. Primary data taken in this study were fertilization rate, hatching rate, and survival rate while secondary data was from literature comparison and asking directly to the staffs of UPT-PBAT Sukorejo. The results of hatchery performance showed fertilization rate of 95%, hatching rate of 98.6%, and survival rate of 93%. Hatching was carried out naturally using a 1:3 ratio (50 male fish and 150 female fish per pond). The research results indicated that hatchery activity in UPT-Freshwater Aquaculture (PBAT) Sukorejo, Malang showed good performance. However, water quality (ammonia) needs more attention to prevent negative effect in the next aquaculture cycle activity since this study found the ammonia value reached minimum tolerable value. Ammonia that exceeds the limit can cause mortality to black tilapia. Changing water is important to avoid mortality due to high ammonia content.

Agency or reselling: optimal return policy in E-commerce retail systems under cap-and-trade regulation

In recent years, the government has issued regulations on environmental protection, carbon emissions, and trading. Enterprises’ environmental awareness has increased, and the operational strategies of manufacturers and platforms have also been affected by environmental regulations. This study considers the interactive effects of agency and reselling contracts between manufacturers and platforms and the cap-and-trade regulation on return policy. Our findings reveal that government-imposed caps on total carbon emissions consistently influence optimal pricing and profits under cap-and-trade regulation, regardless of the presence of a return policy. Additionally, the emission intensity of manufacturers plays a pivotal role in determining the return policy. High manufacturer emission intensity leads decision-makers to provide return services only under specific conditions. Moreover, manufacturers opt for agency contracts when faced with low commission rates, and this threshold is intricately linked to carbon emission intensity, the cap, and the return rate. The government’s ability to adjust the cap enables control over changes in manufacturers’ profits and output, thereby influencing industrial structure and carbon emissions. Manufacturers strategically choose return policies, considering factors such as carbon intensity, return rate, and commission rate. Remarkably, even under cap-and-trade regulations, manufacturers remain inclined to offer returns under optimal conditions.

Pricing policies for a competitive dual-channel supply chain with green investment and sales effort under revenue-sharing contract

In view of the mushroom development of web-based business and green production, a few organizations have moved to produce ecological friendly items and utilized the online channel to build up the competition. This paper deals with a two-echelon sustainable dual-channel supply chain containing two manufacturers and a single retailer. One manufacturer of the investigated supply chain produces a traditional non-green item, and another one releases a substitutable green item. The demand of both the item at the online and offline channel is a function of the sales price, greenness level, sales effort of the retailer. Furthermore, we have discussed the criteria for optimal pricing and greening strategy of supply chain members and the sales effort level of the retailer under a centralized and decentralized model. To enhance the supply chain performance, a revenue-sharing contract has been proposed, subject to the pareto improvement of each channel member. The numerical result demonstrates that the proposed revenue-sharing contract can enhance the manufacturer’s profit as well as system profit compared to the centralized and decentralized model and ensure higher profit for all the members than the decentralized model. Moreover, the item in the centralized model enjoys the highest green level than all other scenarios. Sensitivity analysis exhibits that a higher value of greening cost reduces the manufacturer’s green level, decreasing the sales price.

An electricity price and energy-efficient workflow scheduling in geographically distributed cloud data centers

The cloud computing platform has become a favorable destination for running cloud workflow applications. However, they are primarily complicated and require intensive computing. Task scheduling in cloud environments, when formulated as an optimization problem, is proven to be NP-hard. Thus, efficient task scheduling plays a decisive role in minimizing energy costs. Electricity prices fluctuate depending on the vending company, time, and location. Therefore, optimizing energy costs has become a serious issue that one must consider when building workflow applications scheduling across geographically distributed cloud data centers (GD-CDCs). To tackle this issue, we have suggested a dual optimization approach called electricity price and energy-efficient (EPEE) workflow scheduling algorithm that simultaneously considers energy efficiency and fluctuating electricity prices across GD-CDCs, aims to reach the minimum electricity costs of workflow applications under the deadline constraints. This novel integration of dynamic voltage and frequency scaling (DVFS) with energy and electricity price optimization is unique compared to existing methods. Moreover, our EPEE approach, which includes task prioritization, deadline partitioning, data center selection based on energy efficiency and price diversity, and dynamic task scheduling, provides a comprehensive solution that significantly reduces electricity costs and enhances resource utilization. In addition, the inclusion of both generated and original data transmission times further differentiates our approach, offering a more realistic and practical solution for cloud service providers (CSPs). The experimental results reveal that the EPEE model produces better success rates to meet task deadlines, maximize resource utilization, cost and energy efficiencies in comparison to adapted state-of-the-art algorithms for similar problems.

Learning-based dynamic pricing strategy with pay-per-chapter mode for online publisher with case study of COL

We consider how to make dynamic pricing decision for Chinese Online (COL) at T time-points, an online publisher that allow authors to sell their ongoing book projects. Instead of paying for a book, readers pay for each chapter (pay-per-chapter mode) of the ongoing book project. This mode allows readers to pay for as many chapters as they want without taking the risk that the releasing of new chapters might be delayed or stopped. Despite of the dynamics of chapter-by-chapter released of COL products, the fixed pricing strategy (FPS) does not make fully use of the reading data generated by releasing chapters of the ongoing book. We propose a learning-based dynamic pricing strategy (LDPS) that exploits the newly information to maximize cumulative revenue for the publisher. The LDPS captures the ever changing features of readers. It employs the Thompson sampling method to balance the exploration of investigating different prices sufficiently with the exploitation of settling on the optimal price. Taking COL as a case study and implementing our strategy in the context of the aforementioned real-life data set, we show that LDPS outperform several classical strategies such as Greedy, Prior-Free TS and Prior-Given TS, and average revenue of LDPS is increased by 0.5 % average per time-point compared to the publisher's historical decisions. We also provide some management implications for the COL publisher by analyzing the pricing range of different genres of books and the choice of the exploration threshold parameter.

Low‐carbon optimal scheduling strategy for multi‐agent integrated energy system of the park based on Stackelberg–Nash game

AbstractUnder the background of achieving the dual‐carbon goal, the park is a natural experimental field for practicing the dual‐carbon goal. A low‐carbon optimal scheduling strategy for a multi‐agent park‐integrated energy system (P‐IES) based on the Stackelberg–Nash game is proposed. Firstly, a low‐carbon P‐IES scheduling model is established, considering the two‐stage operation of power‐to‐gas (P2G) technology and reward–punishment stepwise carbon trading mechanism. Then, a two‐layer game optimisation model is proposed with a park‐integrated energy system operator (P‐IESO) as the leader and multiple low‐carbon P‐IESs as followers. Among them, the parks are connected with each other through the power trading channels. Then, the Nash equilibrium solution is obtained by the iterative search method, and the uniqueness of the equilibrium solution of the game is proven, so as to determine the optimal pricing strategy of the operator. Finally, a typical industrial park is taken as an example for simulation verification. The example analysis verifies that the model can effectively reduce the system's carbon emissions and improve the park's economic benefits and low‐carbon levels, thereby achieving the coordinated development of low‐carbon and economic performance in the park.

A Blockchain and PKI-Based Secure Vehicle-to-Vehicle Energy-Trading Protocol

With the increasing awareness for sustainable future and green energy, the demand for electric vehicles (EVs) is growing rapidly, thus placing immense pressure on the energy grid. To alleviate this, local trading between EVs should be encouraged. In this paper, we propose a blockchain and public key infrastructure (PKI)-based secure vehicle-to-vehicle (V2V) energy-trading protocol. A permissioned blockchain utilizing the proof of authority (PoA) consensus and smart contracts is used to securely store data. Encrypted communication is ensured through transport layer security (TLS), with PKI managing the necessary digital certificates and keys. A multi-leader, multi-follower Stackelberg game-based trade algorithm is formulated to determine the optimal energy demands, supplies, and prices. Finally, we propose a detailed communication protocol that ties all the components together, enabling smooth interaction between them. Key findings, such as system behavior and performance, scalability of the trade algorithm and the blockchain, smart contract execution costs, etc., are presented through numerical results by implementing and simulating the protocol in various scenarios. This work not only enhances local energy trading among EVs, encouraging efficient energy usage and reducing burden on the power grid, but also paves a way for future research in sustainable energy management.

Pricing electricity from blue hydrogen to mitigate the energy rebound effect: A case study in agriculture and livestock

As the world's second largest producer of natural gas, Iran relies heavily on natural gas for 70% of its energy needs. There are, however, challenges associated with energy supply in remote regions attached to the gas pipeline network, particularly during the cold season when fuel oil is required for heating and energy provisioning. To address this issue, this research proposes the use of alternative energy sources, such as hydrogen, for non-residential energy consumption, including agriculture and livestock. A key objective of this study is to develop an optimization model for the generation of electricity from hydrogen resources, as well as formulate a robust strategy to assist electricity producers in maximizing their profits. Using this model, producers are able to set prices in accordance with their risk tolerance and present them to the market, thus mitigating price fluctuations. In the targeted sectors, the results indicate that appropriate pricing models can prevent rebound effects. Specifically, the implementation of this model can reduce natural gas consumption by up to 20% and fuel oil usage by 15% during peak seasons. Additionally, the optimal pricing strategy can lead to a 10% reduction in greenhouse gas emissions. The results of this research provide stable and reliable solutions to the energy supply challenges in these regions, thus making the energy market more resilient and environmentally friendly.

Optimal Early-Bird Discounts and the Challenges of Diversion

Variable pricing and early-bird discounts can shift some demand or the time of purchase from higher-priced periods to lower-priced periods without increasing the total demand. This diversion effect influences optimal price levels, and the present paper presents a model for calculating optimal early-bird discounts when incorporating diversion. The model also reveals the differences in price elasticities and the feasible price interval for positive profit. The paper contributes to the literature on early-bird pricing strategies and offers practical insights for service providers seeking to optimize their pricing strategies. The empirical relevance is documented using survey and real-life experimental data among skiers at a major ski resort in Norway. The main insights of the paper are that the profit-maximizing discounts and the gap between the optimal price with and without diversion increase with the length of the pre-booking period.

Who should pay for the return freight in e-commerce? Platforms, retailers or consumers

In the realm of e-commerce, various return freight modes are available, such as platform-bearing return freight (PP strategy), retailer-bearing return freight (RP strategy), and consumer-bearing return freight (CP strategy). The return freight strategy adopted by platforms plays a crucial role in responding to consumer behaviors. To analyze how platforms determine the optimal return freight strategies, we examine a supply chain comprising a platform, a retailer, and heterogeneous consumers, employing a Stackelberg game model to capture their decision dynamics. Our findings suggest that the platform should opt for the PP strategy only when the product profit margin is relatively low. If the platform refuses to adopt the PP strategy, then the RP strategy is preferable when consumers face extremely high consumer return freight costs; otherwise, the CP strategy is the equilibrium result. We also prove that the selection of the return freight strategies leads to changes in the property of the equilibrium. Under the CP strategy, how the product fit probability affects the optimal price depends on the procurement cost; while under the RP and PP strategies, the optimal price decreases with the fit probability. Moreover, under the PP strategy, an increase in the product fit probability does not always benefit the platform. Further, our analysis reveals that, while the PP strategy can reduce the retailer’s risk, it might negatively impact supply chain performance, which implies that cost sharing in the supply chain does not necessarily lead to a higher channel profit. We also investigate how the platform’s return freight strategies affect consumer surplus and identify regions for Pareto improvement where all parties benefit from the PP strategy. Finally, by exploring extensions like positive salvage values, partial refunds, platform competition, and differentiated return freight costs, we confirm the robustness of our findings and unveil new insights.

Gated ensemble of spatio-temporal mixture of experts for multi-task learning in ride-hailing system

Ride-hailing system requires efficient management of dynamic demand and supply to ensure optimal service delivery, pricing strategies, and operational efficiency. Designing spatio-temporal forecasting models separately in a task-wise and city-wise manner to forecast demand and supply-demand gap in a ride-hailing system poses a burden for the expanding transportation network companies. Therefore, a multi-task learning architecture is proposed in this study by developing gated ensemble of spatio-temporal mixture of experts network (GESME-Net) with convolutional recurrent neural network (CRNN), convolutional neural network (CNN), and recurrent neural network (RNN) for simultaneously forecasting these spatio-temporal tasks in a city as well as across different cities. Furthermore, a task adaptation layer is integrated with the architecture for learning joint representation in multi-task learning and revealing the contribution of the input features utilized in prediction. The proposed architecture is tested with data from Didi Chuxing for: (i) simultaneously forecasting demand and supply-demand gap in Beijing, and (ii) simultaneously forecasting demand across Chengdu and Xian. In both scenarios, models from our proposed architecture outperformed the single-task and multi-task deep learning benchmarks and ensemble-based machine learning algorithms.

Optimal pricing in social networks under fuzzy environment

Optimal pricing in social networks under fuzzy environment

Asymptotically Tight Bounds on the Optimal Pricing Strategy with Patient Customers

In “Asymptotically Tight Bounds on the Optimal Pricing Strategy with Patient Customers,” Qian, Su, and Zhou revisit the problem of a monopolist seller’s optimal pricing strategy when dealing with both patient and impatient customers. The authors give asymptotically tight bounds on the optimal strategy’s cycle period and long-run average revenue when the patient customers’ patience level is high. This result also addresses an open question proposed by others regarding the optimal cycle period.

EXPRESS: Joint Assortment and Price Optimization with Multiple Purchases

In this paper, we incorporate the effects of multi-unit purchases into consumer choice models and investigate the associated joint assortment and pricing problems. Under the proposed two-stage choice framework, consumers first form a consideration set, and then select a product with the optimal quantity from the consideration set to maximize their utility. For the joint assortment and pricing problem with homogeneous consumers, we find that a multi-purchase-willingness-ordered assortment is optimal under certain technical conditions, and propose a polynomial-time algorithm to find the optimal assortment and prices for general cases. We further show that the optimal prices and assortment size are not monotone in multi-purchase preference and multi-purchase resistance. For the joint assortment and pricing problem with heterogeneous consumers, we first prove that this problem is NP-hard. We then consider a scenario with discrete prices and we develop a fully polynomial-time approximation scheme by considering a finite number of consumer segments and nested consideration sets. We conduct an empirical study on the JD.com dataset and show that the new choice framework can improve model fitting and prediction accuracy compared with existing choice models with multiple purchases. We reveal that our model is especially suitable for datasets exhibiting a strong diminishing marginal effect for product variety. We further extend our analysis to price competition and establish the existence and uniqueness of a Nash equilibrium. For the joint optimization with fixed costs, we develop an algorithm that can find a solution guaranteeing at least half the optimal expected profit.

Optimal strategies in electric vehicle battery closed-loop supply chain considering government subsidies and echelon utilization

This study examines an electric vehicle battery closed-loop supply chain including a battery manufacturer and a retailer, with a focus on echelon utilization and remanufacturing of waste electric vehicle battery. Optimal pricing strategies and technological effort decision of the supply chain members are derived based on a Stackelberg game model. Three government subsidy policies are considered to promote recycling and reuse of waste electric vehicle batteries, namely, no subsidies, production research and development (R&D) subsidies and recycling subsidies, respectively. Results show that both echelon utilization and recycling subsidies can notably contribute to recycling rate of waste electric vehicle batteries. While echelon utilization boosts the profit of retailer and the whole supply chain, it may have a negative impact on manufacturer's inclination to remanufacturing and its profit. Subsidies for production research and development are preferred by the supply chain and its members from the profit-oriented perspective. Further analyses are conducted under hybrid strategies: hybrid government subsidy policy and hybrid recycling mode. Results show that hybrid strategies could significantly increase the demand and recycling volume, thus positively affecting the profitability of the entire closed-loop supply chain. Our study comprehensively considers the game relationships among manufacture and retailer, enhancing the efficiency of recycling and profitability while also providing a theoretical basis for the government to formulate reasonable subsidy policies.

Differentiated health insurance policy for coordinating healthcare referral in hierarchical healthcare systems with an internet diagnosis platform

The integration of the Internet with traditional medical services is poised to transform health insurance policies. This study aims to explore the coordinating role of differentiated health insurance policies within the context of Internet healthcare. A four-stage sequential game decision-making model is developed within a queuing framework to address scenarios involving online patient referrals and misdiagnoses. The model begins by analyzing the equilibrium arrival strategy of patients, followed by the determination of optimal service capacity strategies for a nonprofit community health center (CHC) and optimal pricing strategies for a for-profit general hospital (GH). Additionally, the model describes an optimal differentiated subsidy strategy for the government aimed at minimizing total social costs. Analysis reveals that under certain conditions, an increase in the service price at GH relative to CHC can lead to a higher influx of online patients visiting GH in person. Furthermore, when the number of online patients exceeds a specific threshold, it not only prompts the government to increase the disparity in health insurance subsidies between the two hospital tiers but also encourages GH to reduce its service prices and offer free services to online patients. Numerical experiments explore the effects of government budgets, sharing ratios, and other variables on the system's equilibrium state, providing several managerial insights. Notably, when patients' misdiagnosis costs are partially covered, increasing GH's misdiagnosis cost-sharing ratio not only enhances the patient arrival rate but also enhances GH's profitability.