Measuring performance with common weights: network DEA

Abstract

In conventional data envelopment analysis (DEA), a production system has been seen as a black box for measuring the efficiency without any attention to what is happening inside the system. However, in practice, performance improvement often requires observing the internal structure of the producing system in order to find the sources of inefficiencies. In addition, weight flexibility as a key property of the multiplier DEA models allows a system to totally disregard an assessment factor, either input or output, from the evaluation process by assigning a value of zero or epsilon to its weight. This paper contributes to the existing literature by proposing a common-weights DEA model when the production system includes a number of interrelated processes. To this end, we propose an aggregate DEA model to calculate the most favourable common weights for determining the efficiency of all production systems and their processes at the same time. Our proposed aggregate model is not only linear for equitably evaluating the producing units on the same scale, but also enables us to deal with the mixed network structures. Furthermore, the network system is decomposed into a series system to build a relational network DEA model that emphasises separate relatedness. This greatly reduces the computational complexities for enormous volumes of data in many real applications and treat difficulties in network DEA models including the zero-value and fluctuating weights and multiple solutions. Managerially speaking, this paper aims to provide top management teams of a production system with an integrated framework to shape a better strategic decision process coupled with superior firm performance, which is to determine the sources of inefficiencies and ultimately take corrective actions over the long run. The proposed framework helps top managers make proper decisions in complex situations with a view of improving a firm's efficiency in all production divisions, which can be identified as a core competency leading to competitive advantages. In a context of performance management, our study is equipped with a simple numerical example and a case study of the non-life insurance companies to demonstrate the applicability of the proposed common-weights network model.

Fuzzy efficiency evaluation in relational network data envelopment analysis: application in gas refineries

“…In this section, the sensitive and comparison analysis are provided from different perspectives. Moreover, the obtained results are compared with those derived from Kao [43] and Hatami-Marbini and Saati [39].…”

“…In this section, first, the mathematical model of relational network data envelopment analysis with crisp data is formulated. Then the concept of efficiency for the processes and system of the corresponding model is described [39,43]. i .…”

“…By comparing the results in Table 7 with those in Table 9, we investigate whether the efficiencies of system and processes properly show the performance of all DMUs. In this regard, we do a comparison between the methods proposed by Kao [43] and Hatami-Marbini and Saati [39] (Table 9) and our proposed fuzzy relational network in the case of α 1(the last column of Table 9), as our proposed approach gives the fuzzy efficiencies. For process 1, the resulting efficiencies from Kao's [43] model, Hatami-Marbini and Saati's [39] model and our proposed model are {1, 0.8188, 0.5618, 0.5990, 0.7273},{1, 0.8000, 0.5714, 0.6000, 0.7273}, and {1, 0.7924, 0.5684, 0.5985, 0.7213}, respectively, that are quite similar.…”

“…In this regard, we do a comparison between the methods proposed by Kao [43] and Hatami-Marbini and Saati [39] (Table 9) and our proposed fuzzy relational network in the case of α 1(the last column of Table 9), as our proposed approach gives the fuzzy efficiencies. For process 1, the resulting efficiencies from Kao's [43] model, Hatami-Marbini and Saati's [39] model and our proposed model are {1, 0.8188, 0.5618, 0.5990, 0.7273},{1, 0.8000, 0.5714, 0.6000, 0.7273}, and {1, 0.7924, 0.5684, 0.5985, 0.7213}, respectively, that are quite similar. By taking into account, the ranking order derived from three models, it is observed the obtained rankings are same.…”

Using a MACBETH based multicriteria approach for virtual weight restrictions in each stage of a DEA multi-stage ranking process

“…According to our literature review, the proposed approaches either need improvements (e.g. in case of crossefficiency evaluation approach and the challenge of non-unique optimal weights; Lin et al 2016;Kao and Liu 2019) or generally are computationally expensive (Aldamak and Zolfaghari 2017) and often less attractive to decision-makers without experience with DEA theory (Hatami-Marbini and Saati 2020). Furthermore, the assessment of DMUs that are characterized by considerable heterogeneity and the resulting implications on weight restrictions is also challenging, as discussed by Wang et al (2016).…”