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 not only is 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 the top management team of a production system with an integrated framework to shape a better strategic decision process about firm performance, which is to treat the sources of inefficiencies and ultimately take corrective actions over the long run. Put differently, 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 of the organisation. In the 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.