Abstract: The problem of resources allocation widely exists in public services and production activities, such as allocating hospitals, schools, production equipment and workloads in quantity, time or space. Efficiency and fairness are two important objectives. However, in real economic activities, the government usually pays attention to the fairness goal while enterprises care more about the input-output efficiency. Since the enterprise plays an important role in the social resources allocation, its utilitarian behaviors fail to achieve maximum social welfare. Therefore, the following questions are mainly studied:What are the motivations of enterprises and governments to consider efficiency and fairness? Do they have different preferences and goals? How to describe it in the recourse allocation models? What are the optimal solutions under different fairness preference scenarios? Are there differences in decision-making results among the enterprise and government?
In this paper, the customers' fairness preference is regarded as the main motivation for enterprises, while the maintenance of social fairness and stability as the government's motivation. The concepts of customers' envy and variable weight are applied to depict them in decision-making models. By calculating the unfair loss based on customers' envy, a multi-objective enterprise model is constructed with the profit goal. The variable weight method is introduced to construct the government model is built where maximizing the service coverage is the efficiency goal and maximizing the minimum individual utility is the fairness goal. Besides, efficiency and fairness trade-off methods are designed by measuring the preferences to choose the appropriate fairness degree. Models are transformed into variational inequalities and solved by modified projection algorithm. Finally, behavior differences between those two subjects, the selection and influence of fairness parameters are further analyzed.
The results indicate that the optimal efficiency decisions of the enterprise and government are basically the same, while the optimal fairness decisions are quite different. With the increase of customers' fairness preference, the allocation polarization of enterprise resources become more significant. As to the government, higher fairness preference of decision makers results in more equal allocation among all individuals. Our research provides a theoretical supplement for understanding the resource allocation strategies and mechanisms of different subjects, which also expands the existing methods to reflect the preferences of enterprises and governments.

Key words: resource allocation, efficiency, fairness, envy value, variable weight