Additive decomposition in two-stage DEA: An alternative approach

Typically, a two-stage production process assumes that the first stage transforms external inputs to a number of intermediate measures, which then are used as inputs to the second stage that produces the final outputs. The three fundamental approaches to efficiency assessment in the context of DEA (two-stage DEA) are the simple (or independent), the multiplicative and the additive. The simple approach does not assume any relationship between the two stages and estimates the overall efficiency and the individual efficiencies for the two stages independently with typical DEA models. The other two approaches assume a series relationship between the two stages and differ in the way they conceptualize the decomposition of the overall efficiency to the efficiencies of the individual stages. This paper presents an alternative approach to additive efficiency decomposition in two-stage DEA. We show that when using the intermediate measures as pivot, it is possible to aggregate the efficiency assessment models of the two individual stages in a single linear program. We test our models with data sets taken from previous studies and we compare the results with those reported in the literature

Additive decomposition in two-stage DEA: An alternative approach

Typically, a two-stage production process assumes that the first stage transforms external inputs to a number of intermediate measures, which then are used as inputs to the second stage that produces the final outputs. The three fundamental approaches to efficiency assessment in the context of DEA (two-stage DEA) are the simple (or independent), the multiplicative and the additive. The simple approach does not assume any relationship between the two stages and estimates the overall efficiency and the individual efficiencies for the two stages independently with typical DEA models. The other two approaches assume a series relationship between the two stages and differ in the way they conceptualize the decomposition of the overall efficiency to the efficiencies of the individual stages. This paper presents an alternative approach to additive efficiency decomposition in two-stage DEA. We show that when using the intermediate measures as pivot, it is possible to aggregate the efficiency assessment models of the two individual stages in a single linear program. We test our models with data sets taken from previous studies and we compare the results with those reported in the literature

Additive decomposition in two-stage DEA: An alternative approach

Typically, a two-stage production process assumes that the first stage transforms external inputs to a number of intermediate measures, which then are used as inputs to the second stage that produces the final outputs. The three fundamental approaches to efficiency assessment in the context of DEA (two-stage DEA) are the simple (or independent), the multiplicative and the additive. The simple approach does not assume any relationship between the two stages and estimates the overall efficiency and the individual efficiencies for the two stages independently with typical DEA models. The other two approaches assume a series relationship between the two stages and differ in the way they conceptualize the decomposition of the overall efficiency to the efficiencies of the individual stages. This paper presents an alternative approach to additive efficiency decomposition in two-stage DEA. We show that when using the intermediate measures as pivot, it is possible to aggregate the efficiency assessment models of the two individual stages in a single linear program. We test our models with data sets taken from previous studies and we compare the results with those reported in the literature

Disentangling the European airlines efficiency puzzle: a network data envelopment analysis approach

© 2015 Elsevier Ltd. In recent years the European airline industry has undergone critical restructuring. It has evolved from a highly regulated market predominantly operated by national airlines to a dynamic, liberalized industry where airline firms compete freely on prices, routes, and frequencies. Although several studies have analyzed performance issues for European airlines using a variety of efficiency measurement methods, virtually none of them has considered two-stage alternatives - not only in this particular European context but in the airline industry in general. We extend the aims of previous contributions by considering a network Data Envelopment Analysis (network DEA) approach which comprises two sub-technologies that can share part of the inputs. Results show that, in general, most of the inefficiencies are generated in the first stage of the analysis. However, when considering different types of carriers several differences emerge - most of the low-cost carriers' inefficiencies are confined to the first stage. Results also show a dynamic component, since performance differed across types of airlines during the decade 2000-2010

Bootstrapping in Network Data Envelopment Analysis

Data Envelopment Analysis (DEA) is a linear-programming method used to measure the relative efficiency of firms. The objective of this thesis is (i) to study the efficiency of the railway transport process in Europe considering its inner structure and the impact of railway noise on humans and (ii) to study the performance of bootstrapping approaches in obtaining DEA efficiency estimates when the production process has a network structure and the relation between the different stages is considered. First, the railway transport process is divided into two stages, related to assets and service provision, respectively. The negative impact of railways on people is measured as the number of people that are exposed to high levels of railway noise. The number of rail wagons in each country that is retrofitted with more silent braking technology is used as a proxy to measure the effort to reduce railway noise pollution. Data is extracted from Eurostat (2016), ERA 006REC1072 Impact Assessment (2018), and EEA (2020) and the additive efficiency decomposition approach is used. Based on the results, asset-efficient countries are usually service-efficient, but the inverse does not hold. Sensitivity analysis revealed that efficiency rankings are robust to alterations in the decomposition weight restrictions. Subsampling bootstrap was chosen as the most appropriate as it does not require any restrictive assumptions. The performance of subsampling is examined through Monte Carlo simulations for various sample and subsample sizes for general two-stage series structures. Results indicate great sensitivity both to the sample and subsample size, as well as to the data generating process-higher than in one-stage structures. A practical approach is suggested to overcome some result inconsistencies that are due to the peculiarities of the additive decomposition algorithm. The method is applied to obtain confidence interval estimates for the overall and stage efficiency scores of European railways

Animals’ Health Control Efficiency in Northwest Portugal: A Two-stage DEA Approach

A two-stage approach is employed to analyze the efficiency of cooperatives responsible for ruminants’ disease control (OPP) at the farm level in Northwest Portugal. In the first stage, Data Envelopment Analysis (DEA) is used to estimate and decompose input-based overall inefficiency for each OPP. The input-based inefficiency measures are generated using the directional input distance function. In the second stage, the inefficiency estimates are regressed on environmental and organizational factors in order to explain efficiency differentials. Despite substantial environmental differences, the empirical results indicate that most cooperatives can reduce costs by improving scale efficiency and pure technical efficiency.input directional distance function, bootstrapping, economic efficiency, animal health services., Agricultural and Food Policy,

Measuring the efficiency of banking systems: A relational two-stage window DEA approach

This study examines the efficiency of banking systems in seventeen OECD countries over the period 1999-2009. For the purpose of our analysis we introduce a window-based version of two relational two-stage DEA models. Furthermore, we apply different versions of the additive and the multiplicative decomposition approaches in order to capture the trends of the efficiencies over the examined period. The robust version of the proposed models enables us to treat deposits as an intermediate variable and therefore be able to link the “value added activity” stage with the “profitability” stage over time. Our findings reveal similarities among the results of the two models. Finally, the estimated efficiencies appear to have minor fluctuations indicating a stability of the examined banking systems over time

The use of supply chain DEA models in operations management: A survey

Standard Data Envelopment Analysis (DEA) approach is used to evaluate the efficiency of DMUs and treats its internal structures as a “black box”. The aim of this paper is twofold. The first task is to survey and classify supply chain DEA models which investigate these internal structures. The second aim is to point out the significance of these models for the decision maker of a supply chain. We analyze the simple case of these models which is the two-stage models and a few more general models such as network DEA models. Furthermore, we study some variations of these models such as models with only intermediate measures between first and second stage and models with exogenous inputs in the second stage. We define four categories: typical, relational, network and game theoretic DEA models. We present each category along with its mathematical formulations, main applications and possible connections with other categories. Finally, we present some concluding remarks and opportunities for future research.Supply chain; Data envelopment analysis; Two-stage structures; Network structures

MEASURING THE PERFORMANCE OF TWO-STAGE PRODUCTION SYSTEMS WITH SHARED INPUTS BY DATA ENVELOPMENT ANALYSIS

As a non-parametric technique in Operations Research and Economics, Data Envelopment Analysis (DEA) evaluates the relative efficiency of peer production systems or decision making units (DMUs) that have multiple inputs and outputs. In recent years, a great number of DEA studies have focused on two-stage production systems in series, where all outputs from the first stage are intermediate products that make up the inputs to the second stage. There are, of course, other types of two-stage processes that the inputs of the system can be freely allocated among two stages. For this type of two-stage production system, the conventional two-stage DEA models have some limitations e.g. efficiency formulation and linearizing transformation. In this paper, we introduce a relational DEA model, considering series relationship among two stages, to measure the overall efficiency of two-stage production systems with shared inputs. The linearity of DEA models is preserved in our model. The proposed DEA model not only evaluates the efficiency of the whole process, but also it provides the efficiency for each of the two sub-processes. A numerical example of US commercial banks from literature is used to clarify the model.Data envelopment analysis, Decision making unit, Two-stage, Shared input, Efficiency