The composition and the weak-link approaches to Network Data Envelopment Analysis
Κορωνάκος, Γρηγόρης Γ.
KeywordsData Envelopment Analysis (DEA) ; Composition approach ; Weak-link approach ; Multi-objective programming ; Network DEA ; Περιβάλλουσα Ανάλυση Δεδομένων ; Περιβάλλουσα Ανάλυση Πολυσταδιακών Διεργασιών ; Συνθετική προσέγγιση ; Μέθοδος του αδύναμου κρίκου ; Πολυκριτήριος προγραμματισμός
The systematic performance evaluation of the organizations as well as the target setting are key aspects for its proper operation and viability. Thus, the adoption of evaluation methods is necessary, which are capable of taking into account all the environmental factors of the organization, identifying the inefficient production processes and suggesting adequate ways to improve them. Such a method is Data Envelopment Analysis (DEA), which is the most popular non-parametric technique for assessing the efficiency of homogeneous decision making units (DMUs) that use multiple inputs to produce multiple outputs. The DMUs may consist of several sub-processes (also known as stages, sub-units, divisions etc.) that interact and perform various operations. However, the classical DEA models treat the DMU as a “black box”, i.e. a single stage production process that transforms some external inputs to final outputs. In such a setting, the internal structure of the DMU is not taken into consideration. Thus, the conventional DEA models fail to mathematically represent the internal characteristics of the DMUs, as well as they fall short to provide precise results and useful information regarding the sources that cause inefficiency. In order to take into account for the internal structure of the DMUs, recent methodological advancements are developed, which extend the standard DEA and constitute a new field, namely the network DEA. The network DEA methods are capable of reflecting accurately the DMUs’ internal operations as well as to incorporate their relationships and interdependences. In network DEA, the DMU is considered as a network of interconnected sub-units, with the connections indicating the flow of intermediate products (commonly called intermediate measures or links). An indicative example of such a DMU is a supply chain, which has a network structure and is composed of several members whose performances affect the overall performance of the supply chain. Therefore, the overall efficiency of the supply chain (DMU) should be evaluated by taking into account the individual efficiencies of its members in a coordinated manner. In this thesis, we conduct a critical survey and categorization of the state-of-the art network DEA methods and we classify a great volume of network DEA studies based on the assessment method they follow. We unveil the relations and the differences of the existing network DEA methods. Also, we uncover their defects concerning the returns to scale, the inconsistency between the multiplier and the envelopment models as well as the inadequate information that provide for the calculation of efficient projections. The most important network DEA methods do not secure the uniqueness of the efficiency scores, i.e. the same level of overall efficiency is obtained from different combinations of the efficiencies of the sub-processes. Also, we prove that the additive efficiency decomposition method unduly and implicitly assigns different priority to the sub-processes, hence provides biased efficiency assessments. Finally, we discuss about the inability of the existing approaches to be universally applied on every type of network structure. We develop two new approaches in network DEA that overcome effectively the deficiencies and provide unique and unbiased efficiency scores, based on a multiple objective framework. We focus our research to serial two-stage network structures and we formulate the problem of their efficiency assessment as a multi-objective mathematical programming problem. Initially, we introduce the composition approach to two-stage network DEA, which is based on a bi-objective mathematical program for the efficiency assessments. We employ two scalarization techniques, firstly based on the L1 norm we aggregate the two objective functions additively without giving any priority between them. The application of this scalarizing function yields an extreme (vertex) Pareto-optimal solution. Then, we employ a min-max scalarization technique, i.e. the Tchebycheff norm (L∞), which minimizes the distance between the ideal point and the feasible objective functions space so as to locate a point on the Pareto front not necessarily extreme. This model provides unique and unbiased efficiency scores. In the composition approach, we estimate first the stage efficiencies and then we aggregate them either additively or multiplicatively to obtain the overall efficiency. Next, we develop two methods to derive the efficient frontier in two-stage DEA and provide efficient projections. The first naturally stems from our composition approach, while the second seeks to provide efficient projections by altering the original levels of the intermediate measures at a minimum distortion. We build upon the composition approach and we introduce the “weak-link” approach to two-stage network DEA, which inherits the nice properties of the former, i.e. provides unique and unbiased efficiency scores. Also, the “weak-link” approach can be readily applied to various types of two-stage network structures. In this approach, we introduce a novel definition about the overall efficiency of the DMU, inspired by the “weak link” notion in supply chains and the maximum-flow/minimum-cut problem in networks. We incorporate this notion into the assessment by assuming that given the stage efficiencies, the system efficiency can be viewed as the maximum flow through the network and can be estimated as the min-cut of the network, i.e. the system efficiency derives as the lowest of the stage efficiencies. We mathematically represent this concept by employing a two-phase max-min optimization method in a multi-objective programming framework, which seeks to maximize the minimum weighted achievement from zero-level efficiency, i.e. maximizing the lowest of the stage efficiencies (weak link). The proposed two-phase procedure estimates the stage efficiencies and the overall efficiency simultaneously by providing a unique Pareto optimal solution. The search direction towards the Pareto front is driven by the assumption that the stage efficiencies are proportional to their independent counterparts. External priorities can be also introduced to our methodology so as to obtain alternative Pareto optimal solutions. We conduct a systematic investigation of the sensitivity of the weak link so as to identify the source of inefficiency in the two-stage processes. Finally, we revisit the work of Aviles-Sacoto et al (2015) who studied a peculiar situation of a two-stage process where some of the intermediate measures are inputs to the second stage and at the same time external outputs from that stage. We show that their modelling approach departs from the described setting and adapts a different situation, where the specific intermediate measure is viewed either as input to or as output from the second stage of the process. We alternatively propose a different modelling approach for the performance assessment of the two-stage process under examination, which rectifies the methodological problems that we observe.