An interval efficiency analysis with dual-role factors
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An interval efficiency analysis with dual‑role factors Mehdi Toloo1,2 · Esmaeil Keshavarz3 · Adel Hatami‑Marbini4 Received: 1 December 2019 / Accepted: 4 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Data envelopment analysis (DEA) is a data-driven and benchmarking tool for evaluating the relative efficiency of production units with multiple outputs and inputs. Conventional DEA models are based on a production system by converting inputs to outputs using input-transformation-output processes. However, in some situations, it is inescapable to think of some assessment factors, referred to as dual-role factors, which can play simultaneously input and output roles in DEA. The observed data are often assumed to be precise although it needs to consider uncertainty as an inherent part of most real-world applications. Dealing with imprecise data is a perpetual challenge in DEA that can be treated by presenting the interval data. This paper develops an imprecise DEA approach with dual-role factors based on revised production possibility sets. The resulting models are a pair of mixed binary linear programming problems that yield the possible relative efficiencies in the form of intervals. In addition, a procedure is presented to assign the optimal designation to a dual-role factor and specify whether the dual-role factor is a nondiscretionary input or output. Given the interval efficiencies, the production units are categorized into the efficient and inefficient sets. Beyond the dichotomized classification, a practical ranking approach is also adopted to achieve incremental discrimination through evaluation analysis. Finally, an application to third-party reverse logistics providers is studied to illustrate the efficacy and applicability of the proposed approach. Keywords Data envelopment analysis · Dual-role factors · Production possibility sets · Imprecise data · Third-party reverse logistics providers
* Mehdi Toloo [email protected]; [email protected] http://homel.vsb.cz/~tol0013/ Extended author information available on the last page of the article
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1 Introduction Due to the growth of new technologies, complex business environment and environmental legislation, the firms are involved in recycling and re-manufacturing functions through third-party logistics providers (3PLPs), which may positively influence the performance of the firm. Reverse logistics (Fig. 1) is a group of processes for moving a new array of products, goods and parts from one destination to another with the aim of creating value at the end of common direct supply chains (Rogers and Tibben-Lembke 2001; Dowlatshahi 2000). For example, this new array of products at the point of consumption includes (1) failed products and goods that can be repaired or reused (2) obsolete products and parts that still have value and (3) unsold products by retailers (Du and Evans 2008). Needless to say, these products, goods and parts provide increasingly economic values at the end of th
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