Junfei Chu

Two-stage network processes with shared resources and resources recovered from undesirable outputs

Data envelopment analysis (DEA) is an approach for measuring the performance of a set of homogeneous decision making units (DMUs). Recently, DEA has been extended to processes with two stages. Two-stage processes usually have undesirable intermediate outputs, which are normally considered be unrecoverable final outputs. In many real situations like industrial production however, many first-stage waste products can be immediately used or processed in the second stage to produce new resources which can be fed back immediately to the first stage. The objective of this paper is to provide an approach for analyzing the reuse of undesirable intermediate outputs in a two-stage production process with a shared resource. Shared resources are input resources that not only are used by both the first and second stages but also have the property that the proportion used by each stage cannot be conveniently split up and allocated to the operations of the two stages. Additive efficiency measures and non-cooperative efficiency measures are proposed to illustrate the overall efficiency of each DMU and respective efficiency of each sub-DMU. In the non-cooperative framework, a heuristic algorithm is suggested to transform the nonlinear model into a parametric linear one. A real case of industrial production processes of 30 provincial level regions in mainland China in 2010 was analyzed to verify the applicability of the proposed approaches.

DEA cross-efficiency evaluation based on Pareto improvement

Cross-efficiency evaluation, as an extension tool of data envelopment analysis (DEA), has been widely applied in evaluating and ranking decision making units (DMUs). Unfortunately, the cross-efficiency scores generated may not be Pareto optimal, which has reduced the effectiveness of this method. To solve this problem, we propose a cross-efficiency evaluation approach based on Pareto improvement, which contains two models (Pareto optimality estimation model and cross-efficiency Pareto improvement model) and an algorithm. The Pareto optimality estimation model is used to estimate whether the given set of cross-efficiency scores are Pareto-optimal solutions. If these cross-efficiency scores are not Pareto optimal, the Pareto improvement model is then used to make cross-efficiency Pareto improvement for all the DMUs. In contrast to other cross-efficiency approaches, our approach always obtains a set of Pareto-optimal cross efficiencies under the predetermined weight selection principles for these DMUs. In addition, if the proposed algorithm terminates at its step 3, the evaluation results generated by our approach unify self-evaluation, peer-evaluation, and common-weight-evaluation in DEA cross-efficiency evaluation. Specifically, the self-evaluated efficiency and the peer-evaluated efficiency converge to the same common-weight-evaluated efficiency when the algorithm stops. This will make the evaluation results more likely to be accepted by all the DMUs.

Evaluating the environmental efficiency of a two-stage system with undesired outputs by a DEA approach: An interest preference perspective

In this study, we propose a new DEA model to evaluate the environmental efficiency of a two-stage system with undesired outputs. The two-stage system consists of two parts: a production subsystem and a pollution treatment subsystem. Different choices for allocating resources to each subsystem represent different interest preferences of decision makers, with the production subsystem corresponding to short-term interests and the pollution treatment subsystem corresponding to long-term interests. Based on a proposed new DEA model, three theorems are established to show the relationships between the interest preference parameter and the change of efficiency scores. An empirical analysis was conducted using the data of 30 provinces and municipalities (eight regions) of China. The empirical results show the effectiveness of the proposed model and the usefulness of the theorems for the real-world data. Optimal efficiency rankings of the eight regions are provided and the efficiency rankings truly reflect the current environmental situations of these eight regions. To examine the economic impacts and facilitate sustainable development, we also analyze the shadow prices for undesired outputs. Corresponding implications of the empirical analysis are also discussed.

DEA cross-efficiency evaluation based on satisfaction degree: an application to technology selection

Data envelopment analysis (DEA) has been extended to cross-efficiency evaluation to provide better discrimination and ranking of decision-making units (DMUs). However, the non-uniqueness of optimal weights in the traditional DEA models (CCR and BCC models) has reduced the usefulness of the DEA cross-efficiency evaluation method. To solve this problem, we introduce the concept of the satisfaction degree of a DMU towards a set of optimal weights for another DMU. Then, a new DEA cross-efficiency evaluation approach, which contains a maxmin model and two algorithms, is proposed based on the satisfaction degrees of the DMUs. Our maxmin model and algorithm 1 can obtain for each DMU an optimal set of weights that maximises the least satisfaction degrees among all the other DMUs. Further, our algorithm 2 can then be used to guarantee the uniqueness of the optimal weights for each DMU. Finally, our approach is applied to a real-world case study of technology selection.

A DEA-based approach for allocation of emission reduction tasks

Rapid economic growth has led to increasing pollution emission, leading governments to require emission reductions by specific amounts. The allocation of specific emission reduction tasks has become a significant issue and has drawn the attention of academia. Data envelopment analysis (DEA) has been extended to construct the allocation of emission reduction tasks model. These previous DEA-based approaches have strong assumptions about individual enterprise production. In this paper, we propose a new method to accurately assess the production, using each enterprise’s previously observed production to construct its own production technology plan. With emission permits decreased, the enterprise can have new production strategy based on its own technology. Assuming emission permits can be freely bought and sold, we show how each enterprise can determine the optimal amount of emission allowance that should be used for production, which may leave some allowance to be sold for extra profit or may require the purchase of permits from other firms. Considering the limitation on the total allowance from emission permits, we introduce the concept of satisfaction degree and use it in maximising the minimum enterprise satisfaction degree. Last, a numerical example is presented and an empirical application is given to verify the proposed approach.

Determining common weights in data envelopment analysis based on the satisfaction degree

The traditional data envelopment analysis model allows the decision-making units (DMUs) to evaluate their maximum efficiency values using their most favourable weights. This kind of evaluation with total weight flexibility may prevent the DMUs from being fully ranked and make the evaluation results unacceptable to the DMUs. To solve these problems, first, we introduce the concept of satisfaction degree of a DMU in relation to a common set of weights. Then a common-weight evaluation approach, which contains a max–min model and two algorithms, is proposed based on the satisfaction degrees of the DMUs. The max–min model accompanied by our Algorithm 1 can generate for the DMUs a set of common weights that maximizes the least satisfaction degrees among the DMUs. Furthermore, our Algorithm 2 can ensure that the generated common set of weights is unique and that the final satisfaction degrees of the DMUs constitute a Pareto-optimal solution. All of these factors make the evaluation results more satisfied and acceptable by all the DMUs. Finally, results from the proposed approach are contrasted with those of some previous methods for two published examples: efficiency evaluation of 17 forest districts in Taiwan and R&D project selection.

Target setting and allocation of carbon emissions abatement based on DEA and closest target: an application to 20 APEC economies

Regarded as an effective method for treating the global warming problem, carbon emissions abatement (CEA) allocation has become a hot research topic and has drawn great attention recently. However, the traditional CEA allocation methods generally set efficient targets for the decision-making units (DMUs) using the farthest targets, which neglects the DMUs’ unwillingness to maximize (minimize) some of their inputs (outputs). In addition, the total CEA level is usually subjectively determined without any consideration of the current carbon emission situations of the DMUs. To surmount these deficiencies, we incorporate data envelopment analysis and its closest target technique into the CEA allocation problem. Firstly, a two-stage approach is proposed for setting the optimal total CEA level for the DMUs. Then, another two-stage approach is given for allocating the identified optimal total CEA among the DMUs. Our approach provides more flexibility when setting new input and output targets for the DMUs in CEA allocation. Finally, the proposed approaches are applied for CEA target setting and allocation for 20 Asia-Pacific Economic Cooperation economies.

Resource allocation based on context-dependent data envelopment analysis and a multi-objective linear programming approach

DEA and MOLP are integrated to deal with the resource allocation problem.The context-dependent DEA is used to characterize the production plans.MOLP is proposed to maximize outputs, effectiveness and minimize input.We restrict the best production in the new most productive scale size region. This paper discusses a mechanism for the allocation of resources among a set of decision making units (DMUs) which are managed by a centralized control unit in an organization. Data envelopment analysis (DEA) and multi-objective linear programming (MOLP) are integrated to deal with this resource allocation problem. Also, context-dependent DEA is introduced to identify the changed production possibility set after resource allocation, which determines the production plans that are feasible with input increase or decrease in general. For the centralized unit, the MOLP approach is proposed to simultaneously maximize total output and effectiveness while minimizing the total allocated variable input consumption. Among these objectives, the effectiveness is determined by the output growth rate for all DMUs, which can reflect the effects obtained by allocating the input resources that are not used up, such as new equipment. In addition, we restrict the production of limited resources to the new most productive scale size (MPSS) region where the DMUs have the best economic characteristics. Finally, an example is employed to illustrate the approach.

Resource allocation of a parallel system with interaction consideration using a DEA approach: an application to Chinese input–output table

ABSTRACT Resource allocation is a popular and important issue in the enterprise management. Recently, data envelopment analysis (DEA) as a non-parametric method for measuring the performance of decision-making units (DMUs) has brought a new flavour to this issue. However, most of resource allocation works by DEA focused on single stage system or consider the internal production process of the system as a ‘black box.’ With the competition and relation among economic entities enhance, the system becomes more and more complex and interactive. To go inside the ‘black box’, in this paper, we propose a new DEA approach to allocate the resource in a bidirectional interactive parallel system. We consider not only the resource allocation of a certain DMU, but also the resource allocation of all DMUs for a centralized decision maker through centralized models. Moreover, the leader–follower relationship between two subunits is studied by a non-cooperative model as a theoretical extension. Finally, the approach is applied to Chinese input–output table in the cooperation scenario. We compare our approach with the traditional approach and find that it can obtain more potential gains.

Measuring environmental efficiency of thermoelectric power plants: a common equilibrium efficient frontier DEA approach with fixed-sum undesirable output

China’s rapid development in economy has intensified many problems. One of the most important issues is the problem of environmental pollution. In this paper, a new DEA approach is proposed to measure the environmental efficiency of thermoelectric power plants, considering undesirable outputs. First, we assume that the total amount of undesirable outputs of any particular type is limited and fixed to current levels. In contrast to previous studies, this study requires fixed-sum undesirable outputs. In addition, the common equilibrium efficient frontier is constructed by using different input/output multipliers (or weights) for each different decision making unit (DMU), while previous approaches which considered fixed-sum outputs assumed a common input/output multiplier for all DMUs. The proposed method is applied to measure the environmental efficiencies of 30 thermoelectric power plants in mainland China. Our empirical study shows that half of the plants perform well in terms of environmental efficiency.