Study And Application On Resource Allocation Based On Integration Of α-fairness With DEA Model

When the social and economic developed to a certain level, compared to people’s more and more higher demand, the resources that people can make use of are always scarce. The resource allocation refers to that, under the condition of available resources are limited, any organization or department must allocate the limited resources to their subordinate department through a certain way in order to achieve the best utilization of resources, with the least resource consumption, produce the most suitable products and services, to obtain the best benefit, which is determined by the scarcity of resources. And the study on how to allocate a resource is one important area where the operational research techniques are brought on its solution. But the problem that how do the managers to allocate a resource efficiently and fairly, which attracts the attention of both researchers and practitioners.A. Charnes and W. W. Cooper et.al proposed the data envelopment analysis (DEA) in1978. Later, the data envelopment analysis was widely used to solve the resource allocation problem. And many researchers proposed various new resource allocation models based on the DEA model. As we all know, DEA is an important technique to evaluate efficiency. However, the goals involved in resource allocation are often multi-dimensional. For example, as for a business organization, it not only has an economic goal such as the profit maximization, but also has an environmental goal such as the carbon abatement. Therefore, in the performance evaluation activities in the resource allocation problem, the decision makers need to consider both the technical effectiveness and overall effectiveness of all the decision-making units that belong to the central unit and the fairness criterion of the resource allocation. This is especially true for a nonprofit organization, the goals of which often involve many aspects of social welfare such as the efficiency and fairness. Moreover, these goals often call for a tradeoff between long-term and short-term benefits. Aside from the multidimensionality, organizational goals are conflicting in nature. Therefore, it is a tough undertaking for managers to make a rational resource allocation decision. Because of this, resource allocation has attracted much attention from both practitioners and researchers.Through the review and analysis of the relevant resource allocation literature in the domestic and abroad, we find that, in the most of the research literature on resource allocation, the most researchers considered only the efficiency criterion of the resource allocation, but ignored an important resource allocation criterion, fairness. And in some rare resource allocation literatures, which considering both efficiency and fairness criterion, many researchers adopt the Gini coefficient to measure the resource allocation process’fairness degree. However, through our analysis, we find that the Gini coefficient is not appropriate in many applications.Based on the previous study, our paper establishes a new centralized resource allocation model based on DEA under the condition of considering both the efficiency and fairness criteria. The goal we set in our paper is to allocate the resource in a fair way as much as possible under the condition of achieving the organization’s overall goal. Our paper adopts a notion of fairness, namely a-fairness, to measure the fairness degree. The α-fairness is well studied in the welfare economics and is of very practical significance. In the new established model, we integrate a-fairness and DEA to prop up the resource allocation decisions. And we combine the resource allocation model based on DEA with the utility theory to design an appropriate objective for the DM. So, the DMs can balance the efficiency and fairness by adjusting the value of the inequality aversion parameter α, according to the DMs’preferences for the fairness. We use an illustrative application of allocation of the education funds faced by the Ministry of Education to validate the proposed approach.