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Traditional laboratory measurements of soil water diffusivity (D) and soil water retention curve (SWRC) are always time-consuming and labor-intensive. Therefore, this paper aims to present a simple and robust test method for determining D and SWRC without reducing accuracy.

In this study, a D model of unsaturated soil was established based on Gardner–Russo model and then a combination of Gardner–Russo model with one-dimensional horizontal absorption method to obtain n and a parameters of Gardner–Russo model. One-dimensional horizontal absorption experiments on loam, silt loam and sandy clay loam were conducted to obtain the relationships between measured infiltration rate and cumulative infiltration with wetting front distance. Based on the obtained relationships, the measured infiltration data from the one-dimensional horizontal absorption tests were used to calculate n and a parameters and further constructing D and SWRC.

Both the calculated D and SWRC inversed from the infiltration data were in good agreement with the measured ones that obtained from the traditional horizontal absorption method and the centrifuge method, respectively. Error analysis indicated that only the infiltration data are enough to reliably synchronously determine D and SWRC.

A simple and robust method is proposed for synchronous determination of soil water diffusivity and water retention curve.

The purpose of this paper is to discuss how wind farms attract wind turbine manufacturers to get involved in wind turbines’ maintenance service with revenue sharing contract of bundled service under which the background of operation and maintenance (O&M) aftermarket of wind turbine exists. The authors also try to extend the results to the application of product plus service business mode on large-scale equipment O&M service. At present, Chinese wind power industry is suffering from production capacity redundancy. The profit levels for both wind farm and wind turbine manufacturers are relatively low. It is significant for Chinese wind power industry development to coordinate the supply chain of wind power in order to reduce O&M costs and increase revenues.

The present paper discusses product plus aftermarket service contract design on the background of closed-loop product service chain and uncertain equipment demand using revenue sharing contract model.

If centralized decision making is assumed, the authors find that the wind turbine order increases as the aftermarket service effort level and aftermarket service profit increase; aftermarket service effort level is positively correlative to the service efficiency. On the other hand, if decentralized decision making is assumed, the wind turbine order increases as share of the aftermarket service chain by manufacturer to wind farm increases and share of product supply chain by wind farm to manufacturer decreases. The optimal effort level of wind farm increases as the share of aftermarket service chain increases while the optimal effort level of the manufacturer is a concave function of share of aftermarket service chain if service quality linear correlates with effort level. Meanwhile, the authors find that the revenues of the product supply chain and aftermarket service chain have a concave relationship. This relationship is not affected by the format of relationship between service quality and effort level (linear or exponential).

The results could potentially be used to provide the wind turbine manufacturer with a greater profit space and satisfy wind farm’s equipment maintenance demand at the same time. It can also guide the practice of revenue sharing in the aftermarket service and manufacturing servitization.

In this model, the authors assumed that both the forward revenue sharing of power generation by wind farm to manufacturer and the backward revenue sharing of maintenance service by the manufacturer to wind farm exist in closed-loop product service chain. Then the authors discussed channel coordination of such cross-revenue sharing contract.

To promote the development of renewable energy, the Chinese Government adopts the policy of Feed-in Tariff and subsidy. However, the high purchase price and the intermittence limit the development of renewable energy source electricity (RES-E). The purpose of this paper is to discuss the pricing strategy for system operators to stimulate the development of the RES-E industry under the scenario of uncertain supply and demand.

The authors establish a two-echelon supply chain investment model led by a power grid operator considering the uncertainties in both demand and supply, and study the impact of the power purchase price designed by a system operator using Stackelberg’s model.

There is an optimal capacity for RES-E generators, that is, independent of the market demand. Besides, the optimal order of grid operators is independent of the uncertain RES-E supply and the purchase price of fossil fuel. By properly setting the purchase prices, the system operator can stimulate the capacity investment in renewable energy. Finally, increasing the punishment in power shortage can stimulate the capacity investment in RES-E under certain conditions.

The result of this paper can mitigate the phenomenon of power abandonment in the RES-E industry and promote the grid integration of RES-E.

Both uncertain demand and supply are considered in this paper. A heuristic algorithm is provided to compute the optimal purchase price combination.

The car-sharing market has entered the mature stage, and consumers' demand shows a diversified increasing trend. This paper considers two modes of operation and two pricing strategies, which are business-to-consumer and consumer-to-consumer modes, market pricing and platform pricing. Under these conditions, the platform's revenue-sharing ratio will be different. The purpose of this paper is to explore this research question, and seeks an optimal pricing mechanism that can achieve a win–win situation between platform and automobile manufacturer in the two market modes.

The authors design different profit functions for platform under the two contexts. Of course, the platform's function is constrained to the manufacturer's function. By introducing a revenue-sharing contract a Stackelberg game model dominated by the platform is established and the equilibrium solutions under the two pricing models are derived.

The study found that even if only market pricing is executed, the scale of the car-sharing market will continue to expand. As the car-sharing market becomes more saturated, platform pricing is better for the automobile manufacturer; in most cases, the platform prefers platform pricing, but when the number of private cars is relatively small, if the cost of car operation and maintenance for the automobile manufacturer is lower or the revenue-sharing ratio of private cars is high, then market pricing will be more favorable to the platform.

With the cross-border integration of car service platforms and the automobile manufacturing industry, the key to achieving win–win cooperation and sustainable development in the car-sharing market will converge on the question of how to design a suitable pricing mechanism and revenue-sharing method.

Authors have determined how a car-sharing platform achieves a win–win order pricing strategy with the manufacturer and private car owners, respectively. And authors combined the supply chain revenue-sharing contract with the car-sharing market to explore the application of the revenue-sharing contract in the sharing economy.

When the power generator faces uncertain and independent electricity spot price and renewable energy source supply, two different conditions need to be considered: the distributions of renewable energy source electricity and electricity spot price are independent or dependent. The purpose of this paper is to explore the capacity investment strategy under volatile electricity spot price when renewable energy penetration rate is low, taking into account these two conditions.

The authors design a capacity investment model under dual uncertainties and consider how to optimize the investment capacity in order to maximize profit under two different conditions.

The authors find that when renewable energy supply fluctuation is unrelated to spot electricity price fluctuation, the renewable energy power profitability is determined by the average cost of spot electricity price and equivalent cost. When renewable energy supply fluctuation is related to spot electricity price fluctuation, the renewable energy power profitability is determined by the market value and the construction and maintenance cost.

Faced with the conflict of the renewable energy supply, the authors need to understand how to plan the generation capacity with intermittent renewable sources. The result helps renewable energy become competitive in the electricity market under loose regulations.

The authors compare two capacity investment strategies that the renewable energy supply fluctuation is related and unrelated to spot electricity price.

This paper aims to propose a social enterprise legitimation mechanism by combining the established logic and transformational logic to test the validity of the conceptual model.

The authors construct the theoretical framework based on integrating organizational identity theory, attention-based view and collected 128 social enterprises data during the post-pandemic period in China. The authors applied multiple hierarchical regression analysis and mediation analysis to test the research hypothesis.

The results show that strong organizational identity contributes significantly to the cognitive legitimacy of social enterprise. Besides, we found that social welfare logic and digital transformation can positively mediate the correlation between organizational identity and cognitive legitimacy.

Social enterprises enhance legitimacy significantly by social welfare logic comparing with commercial logic, which indicates that social enterprises should allocate more internal resources and attention to present the organization's social value through various distributions. More importantly, social enterprises should embrace digital transformation to enhance transparency and efficiency, decrease transaction costs, enlarge organizational social impact to strengthen cognitive legitimacy.

The paper first proposed and empirically tested that digital transformation is an important mechanism to enhance the social enterprise's cognitive legitimacy.

The development of low-carbon production is impeded by the investment costs of green technology research and development (R&D) and carbon emission reduction while facing the uncertain risk of emission reduction investment. With the government's carbon emission constraints, green manufacturers implement the advance selling strategy to increase both profit and reduction level. However, few studies consider the consumer's green preference and emission constraints in advance selling market and spot market independently. The authors' paper investigates the optimal strategies of advance selling pricing and reduction effort for green manufacturers to maximize profits.

The authors' paper designs a stochastic model and investigates the manufacturer's optimal strategies of advance selling price and emission reduction efforts by categorizing different purchasing periods of low-carbon consumers. With the challenges of uncertain demand and government's emission constraints, the authors' develop the non-linear optimization model to investigate the manufacturer's profit-oriented decisions.

The results show the government's carbon constraints cannot influence the manufacturer's profit, but the consumer's low-carbon preference in the advance selling period can. Interestingly, the manufacturer will make fewer reduction efforts even when the consumers have stronger environmental awareness. In addition, the increasing consumer price sensitivity will exacerbate the profit loss from mandatory emissions reduction. Overall, for achieving a win–win situation between emission reduction and profit growth, green manufacturers should not only consider the sales strategies, market demand, and government constraints in a low-carbon market, but also pay attention to the uncertainty of green technology innovation.

With the consideration of the government's carbon emission constraints, uncertain demand, and low-carbon consumer's preferences, the authors' study innovatively incorporates the joint impacts of advance selling strategy and emission reduction effort strategy and then differentiates between two cases that pertain to the diverse carbon emission regulations.

The purpose of this paper is to examine the impact of renewable energy on the power supply chain and to study whether the renewable generator or the power grid that purchases power from the power spot market is better when the actual generation of renewable energy is insufficient. The authors want to compare and analyze the different power supply chain operation modes and discuss the optimal mode selection for renewable energy generator and power grid in different situations.

This paper studies the grid-led price competition game in the power supply chain, in which the power grid as a leader decides the price of transmission and distribution, and generators determine the power grid price. The renewable energy power generator and the traditional energy power generator conduct a price competition game; on the other hand, the power grid and power generators conduct Stackelberg games. The authors analyze the power supply of single power generator and two power generators, respectively, and research on the situation that the renewable energy cannot be fully recharged when the actual power generation is insufficient.

The study finds that both renewable and traditional power grid prices decline as price sensitivity coefficient of demand and installed capacity of renewable energy generators increase. Power grid premium decreases as the price sensitivity coefficient of demand increases, but rises as the installed capacity of renewable energy generator increases. When there is a shortage of power, if the installed capacity of renewable energy is relatively small and price sensitivity coefficient of demand is relatively large, the grid purchases the power from power spot market and shares cost with renewable energy generators, leading to higher expected profits of the renewable energy generators. On the contrary, the renewable energy generators prefer to make up power shortage themselves. For the power grid, purchasing the power by the renewable energy generators when there is a power shortage can bring more utility to the power grid when the installed capacity of renewable energy is lower and the demand price sensitivity coefficient is higher. When the installed capacity of renewable energy is high and the price sensitivity coefficient of demand is moderate, or the installed capacity of renewable energy is moderate and the demand price sensitivity coefficient is high, a generator that simultaneously possesses two kinds of energy source will bring more utility to the power grid. If the installed capacity of renewable energy and the demand price sensitivity coefficient both are small or the installed capacity of renewable energy and the price sensitivity coefficient of demand both are large, the power grid prefers to purchase the power by itself when there is a power shortage.

The goal of our paper analysis is to explore the implications of the theoretical model and address the series of research questions regarding the impact of the renewable energy on the power supply chain. The results of this study have key implications for reality. This paper sheds light on the power supply chain operation mode selection, which can potentially be used for the renewable energy generators to choose their operating mode and can also help traditional energy generators and power grid enterprises maximize their utility. This paper also has some references for the government to formulate the corresponding renewable energy development policy.

This paper studies the power operation mode under the uncertainty of supply and demand, and compares the advantages and disadvantages of renewable energy generator that makes up the shortage or the power grid purchases the power from power spot market then shares cost with the renewable energy generator. This paper analyzes the power grid-led coordination problem in a power supply chain, compares and analyzes the price competition game model of single power generator and dual power generators, and compares the different risk preferences of power grid.

The purpose of this paper is to investigate the dynamic acquisition pricing strategy for collecting used products (also known as cores or returns) in a finite planning horizon. In particular, this paper studies a cost-minimization model in which a firm offers acquisition price that impacts the quantity of the returns, and remanufactures the used product to satisfy the customer demand.

This paper uses multi-period stochastic dynamic programming theory to model a remanufacturing system that faces the random demand for remanufactured products. The number of the returns at each period is uncertain and increases linearly with the acquisition price offered.

The study shows that when the uncertainty of demand for remanufactured products increases, the remanufacturer should hold a higher core stock level to minimize the expected total cost and thus a higher acquisition price is needed to attract returns. However, given demand uncertainty, the optimal price decreases in the initial core stock level in each period. It also indicates that the optimal acquisition price increases in the variance of the returns, but decreases in the mean of the returns.

The findings suggest that a remanufacturer could reduce the expected total cost by adjusting the acquisition price according to the number of returns periodically.

Introducing the impact of supply uncertainty on the acquisition price of used products, this paper uses a multi-period dynamic model, instead of single period model in previous studies, to examine the remanufacturer’s dynamic acquisition pricing policy.

Rapidly increasing the proportion of installed wind power capacity with zero carbon emission characteristics will help adjust the energy structure and support the realization of carbon neutrality targets. The intermittency of wind resources and fluctuations in electricity demand has exacerbated the contradiction between power supply and demand. The time-of-use pricing and supply-side allocation of energy storage power stations will help “peak shaving and valley filling” and reduce the gap between power supply and demand. To this end, this paper constructs a decision-making model for the capacity investment of energy storage power stations under time-of-use pricing, which is intended to provide a reference for scientific decision-making on electricity prices and energy storage power station capacity.

Based on the research framework of time-of-use pricing, this paper constructs a profit-maximizing electricity price and capacity investment decision model of energy storage power station for flat pricing and time-of-use pricing respectively. In the process, this study considers the dual uncertain scenarios of intermittency of wind resources and random fluctuations in power demand.

(1) Investment in energy storage power stations is the optimal decision. Time-of-use pricing will reduce the optimal capacity of the energy storage power station. (2) The optimal capacity of the energy storage power station and optimal electricity price are related to factors such as the intermittency of wind resources, the unit investment cost, the price sensitivities of the demand, the proportion of time-of-use pricing and the thermal power price. (3) The carbon emission level is affected by the intermittency of wind resources, price sensitivities of the demand and the proportion of time-of-use pricing. Incentive policies can always reduce carbon emission levels.

This paper creatively introduced the research framework of time-of-use pricing into the capacity decision-making of energy storage power stations, and considering the influence of wind power intermittentness and power demand fluctuations, constructed the capacity investment decision model of energy storage power stations under different pricing methods, and compared the impact of pricing methods on optimal energy storage power station capacity and carbon emissions.

1. Electricity pricing and capacity of energy storage power stations in an uncertain electricity market.

2. Investment strategy of energy storage power stations on the supply side of wind power generators.

3. Impact of pricing method on the investment decisions of energy storage power stations.

4. Impact of pricing method, energy storage investment and incentive policies on carbon emissions.

5. A two-stage wind power supply chain including energy storage power stations.

Electricity pricing and capacity of energy storage power stations in an uncertain electricity market.

Investment strategy of energy storage power stations on the supply side of wind power generators.

Impact of pricing method on the investment decisions of energy storage power stations.

Impact of pricing method, energy storage investment and incentive policies on carbon emissions.

A two-stage wind power supply chain including energy storage power stations.