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Nowadays, the national economy is developing rapidly and the customers' electricity demand is rising year by year. How to optimize the investment scale of electric power enterprises with the available resources and enhance the economy of power grid business and the reasonableness of investment allocation is an urgent problem to be solved. The article uses mathematical programming methods to allocate the total investment capacity of the electric power enterprise company to its corresponding subsidiaries based on the historical data of the electric power enterprise, then constructs a mathematical model for the development input allocation of each subsidiary of the electric power enterprise. The validity of the proposed model is verified by taking five subsidiaries of electric power enterprises as examples, which provides an effective reference for electric power enterprises to make reasonable investment allocation to achieve the purpose of improving quality and increasing efficiency.

In customer-intensive services, advertising can increase customers’ patience and bring more utility to customers. However, customers’ different perceptions of advertising can affect their utility and indirectly affect the decision making of the service provider. Thus, this paper uses the M/M/1 queueing model to study the optimal decision making of customer-intensive service providers in different markets according to the customers’ heterogeneity. We first classify customers into two categories: high sensitivity and low sensitivity, and then we analyze the consumption behavior of these two types of customers in the service system as the potential customer arrival rate increases. Finally, the optimal decisions of the service provider with different demands are determined. We find that the service provider can benefit from making optimal decisions based on market demand as the potential customer arrival rate increases. If the potential arrival rate exceeds a certain threshold, the service provider has more dominance in the market, and relevant decision making is no longer affected by the potential customer arrival rate. Furthermore, it is not always beneficial for the service provider to serve all customers regardless of whether there are low-sensitivity customers in the service system, and advertising can tap more highly sensitive customers and help to further increase the revenue of service providers. The results also show that ignoring the heterogeneity of customers’ sensitivity to advertising very likely leads to losses in revenue.

Purpose Long-term contract is an important developing direction of China's coal industry coordination. This paper aims to discuss how to use contract for difference (CFD) to avoid risk and effectively increase the benefit of both coal and thermal power plants in the coal-electricity supply chain. Design/methodology/approach Based on prospect theory, this paper takes the risks and benefits of the coal and coal-fired power plants in the coal supply chain under CFD into balanced consideration to construct the contract coordination mechanism. In this mechanism, the coal demand in the coal supply chain equilibrium under centralized decision-making is regarded as the total annual volume of transactions needed to design the contract coordination mechanism and solve double marginalization. Then, based on prospect theory, in the construction of CFD, this paper takes the income of power and coal enterprises when they are in equilibrium under Stackelberg non-cooperative game as the reference point. In addition, considering that coal demand is a random variable, the CFD with a one-year trading session can be designed. Findings The research derives the coal price of the contract for difference, contract trading volume and its proportion of the total trading volume. A numerical example shows that the model above can be used to effectively avoid the risk of both coal and electricity sides. Originality/value To solve the conflict between coal enterprises and thermal power plants, let the coal-electricity supply chain be converted from non-cooperative game to cooperative game. Based on the prospect theory, this paper takes the income of the non-cooperative game of coal and thermal power plants as a reference point and considers how to design the coordination mechanism, the contract for difference, so as to make the two parties cooperate to solve the double marginal utility of the non-cooperative game in a chain supply. The main innovation of the work lies in the following: first, the coal demand when the coal-electrical supply chain is in balance under centralized decision-making is taken as the total annual trading volume needed to design the contract coordination mechanism and solve double marginalization. Second, based on prospect theory, in the construction of CFD, the benefits of coal-fired power plants and coal enterprises when both sides are in equilibrium under the Stackelberg non-cooperative game are taken as the reference points, and coal demand is taken as a random variable to design the CFD with a one-year transaction period. The price of coal that is not traded through CFD is calculated according to the daily market price. Third, this paper proposes the prospect M-V criterion of the risk-benefit equilibrium of both power and coal enterprises, which means that the risk-benefit equilibrium of both sides is the prospect variance effect of both sides relative to the reference point benefit divided by the prospect expectation effect.

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