Stochastic performance measurement in two-stage network processes: A data envelopment analysis approach

summary:In classic data envelopment analysis models, two-stage network structures are studied in cases in which the input/output data set are deterministic. In many real applications, however, we face uncertainty. This paper proposes a two-stage network DEA model when the input/output data are stochastic. A stochastic two-stage network DEA model is formulated based on the chance-constrained programming. Linearization techniques and the assumption of single underlying factor of the data are used to construct the equivalent deterministic linear programming model. The relationship between the stochastic efficiency of each stage and stochastic centralized efficiency of the whole process, at different confidence levels, is discussed. To illustrate the real applicability of the proposed approach, a real case on 16 commercial banks in China is given

A Linear Programming Relaxation DEA Model for Selecting a Single Efficient Unit with Variable RTS Technology

The selection-based problem is a type of decision-making issue which involves opting for a single option among a set of available alternatives. In order to address the selection-based problem in data envelopment analysis (DEA), various integrated mixed binary linear programming (MBLP) models have been developed. Recently, an MBLP model has been proposed to select a unit in DEA with variable returns-to-scale technology. This paper suggests utilizing the linear programming relaxation model rather than the MBLP model. The MBLP model is proved here to be equivalent to its linear programming relaxation problem. To the best of the authors’ knowledge, this is the first linear programming model suggested for selecting a single efficient unit in DEA under the VRS (Variable Returns to Scale) assumption. Two theorems and a numerical example are provided to validate the proposed LP model from both theoretical and practical perspectives

A novel cross-docking EOQ-based model to optimize a multi-item multi-supplier multi-retailer inventory management system

Nowadays, the retail industry accounts for a large share of the world’s economy. Cross-docking is one of the most effective and smart inventory management systems used by retail companies to respond to demands efficiently. In this study, the aim is to develop a novel cross-docking EOQ-based model for a retail company. By considering a two-stage inventory procurement process, a new multi-item, multi-supplier, multi-retailer EOQ model is developed to minimize the total inventory costs. In the first stage, the required items are received from suppliers and are held in a central warehouse. In the second stage, these items are delivered to several retail stores. The total inventory costs include four main parts, i.e., holding costs at the central warehouse, holding costs at the retail stores, fixed ordering costs from the suppliers, and fixed ordering costs from the central warehouse. The optimal inventory policy is obtained by analyzing extrema, and a numerical example is used to confirm the efficiency of the proposed model. Based on the obtained results, it is evident that the proposed model produces the optimal policy for the cross-docking system. Furthermore, the model enables managers to analyze the effects of key factors on the costs of the system. Based on the obtained results, the annual demand of each retailer, the ordering cost by the central warehouse, the ordering cost at each retail store, and the holding cost at each retail store have a direct impact on the optimal cost. Furthermore, it is not possible to describe the effects of the holding cost at the central warehouse on the optimal cost of the system generally

Prioritization method for frontier DMUs: a distance-based approach

In nonparametric methods, if the number of observations is relatively small as compared to the sum of number of inputs and outputs, many units are evaluated as efficient. Several methods for prioritizing these efficient units are reported in literature. Andersen et al. and Mehrabian et al. proposed two methods for ranking efficient units, but both methods break down in some cases. This paper describes a new DEA ranking approach that uses L2-norm

An Improvement to The Relative Efficiency With Price Uncertainty: An Application to The Bank Branches

Abstract This article describes the method of measuring relative efficiency, when the input and output prices are unknown. In a situation, where only the bound of input prices for the cost efficiency and the bound of output prices for the revenue efficiency are known, measurement of relative efficiency consists of two cases: optimistic and pessimistic perspective. The main object of this article is to study the pessimistic relative efficiency that eventually, with the computation of assessment of optimistic, it gives an interval efficiency for each DMU. Finally we apply the method in the analysis of bank branches activity

Efficiency assessment and managerial ability analysis of the regional electricity transmission sector with the presence of contextual variables

The electricity industry plays a pivotal role in a country's economic growth and development. Therefore, it is imperative to assess its performance and identify the strengths and weaknesses of its different sectors, such as production, transmission, and distribution, to enhance economic growth in diverse areas. Given the significance of the transmission sector, this research focuses on analyzing and evaluating the performance of 16 regional electricity companies in Iran from 1390 to 1398, with the aim of comprehending the impact of contextual variables on efficiency. To achieve this, the study will utilize two techniques - Data Envelopment Analysis (DEA) and Ordinary Least Squares (OLS) - to determine the efficiency score and estimate the effect of contextual variables on efficiency, respectively. In the first stage, the DEA technique is employed to calculate the technical efficiency of each company, considering their specific inputs and outputs. In the second stage, the logarithm of the efficiency scores obtained is regressed on contextual variables to establish their effect on efficiency. The residual derived from the regression is referred to as managerial ability. Finally, the companies are ranked based on their modified efficiency after removing the impact of contextual variables. Introduction The electricity industry comprises three key sectors: production, transmission, and distribution. It stands as one of the most crucial economic infrastructures in the country, exerting significant influence on industrial, agricultural, service, and other sectors. Undoubtedly, the growth of the electricity industry drives the nation's economic development and progress, contributing to the prosperity and comfort of its citizens (Tavassoli et al., 2020). Consequently, analyzing and examining the growth trajectory of each sector across different years becomes pivotal in mitigating adverse effects and fostering progress within this domain. In recent years, numerous researchers have conducted studies in this field. Some have independently evaluated each production, transmission, and distribution sector, while others have adopted a comprehensive approach by considering the integrated three-stage network structure. The research background highlights that the transmission sector has received less attention from researchers than other sectors. This is noteworthy because, following electricity production, the transmission process and energy accessibility to consumers are paramount. The absence of proper energy transfer can result in consumer dissatisfaction, financial losses, and stagnation within the competitive economic market. Therefore, identifying the strengths and weaknesses of the transmission sector's performance and comparing regional electricity transmission companies can effectively help enhance the performance level of each. One technique that has captured researchers' attention for evaluating the electricity industry's performance is the data envelopment analysis (DEA) technique. DEA is a non-parametric method used to assess the performance of homogeneous units, considering multiple inputs and outputs. It was initially introduced in 1978 by Charnes et al. The initial model was built upon the assumption of constant returns to scale. Subsequently, Banker et al. (1984) extended it by presenting a model under the assumption of returns to a variable scale. Importantly, traditional DEA models evaluate a system's performance based on specific inputs and outputs consumed and produced by the unit. However, various factors, such as contextual variables, managerial ability, and skill, can significantly influence performance and productivity. A crucial point to consider is that managerial abilities are not always overtly visible. This lack of direct visibility can impede accurate measurement. Hence, recognizing these variables among the existing indicators and assessing their influence on the performance and efficiency of each unit holds particular significance. This procedure enhances the precision of evaluation and opens avenues for delivering enhanced solutions aimed at improving the system's overall performance. Methodology The objective of this study is to analyze and evaluate the performance of Iran's regional electricity transmission sector while considering contextual variables and establishing a ranking methodology based on managerial ability. This perspective enables the identification of strengths and weaknesses in the system's structure from various angles and offers appropriate solutions for enhancement. To accomplish this, the first step involves identifying all variables within the transmission section, encompassing inputs, outputs, and contextual factors. Subsequently, we determine the technical efficiency of each regional power transmission company, taking into account specific inputs and outputs, using meta-frontier technology. The concept of meta-frontier in DEA measures the gap or distance between decision-making units (DMUs) across different boundaries. This approach assumes a unified boundary for all subgroups, enabling efficiency estimation based on a single boundary (Battese, 2004; O'Donnell, 2008). Its primary advantage lies in resolving the challenge of evaluating efficiency at varying levels. As a result, meta-frontier technology enhances the precision of evaluating regional power companies over multiple periods. After assessing the efficiency of each regional electricity transmission company, we employ the linear regression method to estimate the impact of contextual variables on efficiency, subsequently yielding a measure of managerial ability. Ultimately, we introduce a method for ranking each company based on managerial ability. The advantage of the proposed method is that, in addition to reviewing and analyzing the technical efficiency of each of the companies in the regional electricity transmission sector during different periods, it will be possible to evaluate the managerial ability of each of the companies. Such a perspective allows for companies to be compared from different dimensions. Moreover, providing a new ranking criterion based on managerial ability also facilitates a better and more accurate comparison. Results In this study, the performance of Iran's regional power companies was analyzed and evaluated from two systems and management perspectives during the years 1390-1398. Additionally, a new rating criterion based on managerial ability was presented to compare the performance of companies during 9 time periods. In this regard, firstly, the technical efficiency of 16 regional electricity companies during 9 time periods was calculated based on the inputs of the number of employees and receiving energy from neighboring companies and the outputs of sending energy to neighboring companies and delivering energy to distribution companies, using meta-frontier technology and the DEA approach. Then, the effect of contextual variables, such as line length, transformer capacity, and loss magnitude, on the efficiency score of each company was estimated using the ordinary least squares method (OLS). Furthermore, the managerial ability of each company was determined during different periods. Ultimately, a ranking criterion was established based on the results of technical efficiency after removing the effect of contextual variables. Conclusion The results of efficiency measurements over 9 time periods indicate that the highest and lowest average efficiencies were observed in the years 1390 and 1398, respectively. Furthermore, it's evident that, in general, the performance of Iran's 16 regional electricity companies exhibited a consistent upward trend from 1390 to 1398. Among the 16 evaluated companies, the Guilan regional electricity company consistently achieved the highest level of efficiency across all 9 time periods, reflecting its strong performance. Conversely, the Fars regional electricity company consistently had the lowest efficiency, indicating its weaker performance compared to other companies. When analyzing the companies' performance by year, it's noteworthy that the Tehran regional electricity company secured the highest rank in 1390, 1391, and 1394, while the Fars regional electricity company held the top spot in the remaining years. In contrast, the Sistan regional electricity company consistently displayed the lowest performance throughout all periods. The assessment of management performance over the 9 time periods indicates that the Kerman regional electricity company demonstrated superior performance from 1390 to 1393, whereas the Guilan regional electricity company excelled from 1394 to 1398, outperforming other companies. Conversely, the Gharb regional electricity company exhibited weaker performance compared to its counterparts. Additionally, the results of the regression analysis highlight a positive relationship between the efficiency score and two variables: line length and transformer capacity. Conversely, the relationship with loss magnitude is observed to be inversely correlated

Alternative Trade-Offs in Data Envelopment Analysis: An Application to Hydropower Plants

In multidimensional input/output space, the behavior of the firms can be analyzed by using efficient frontier or supporting surfaces of production technology. To this end, mathematicians are interested to use marginal rates of substitutions. The piecewise linear frontier of data envelopment analysis (DEA) technology is not differentiable at the extreme points and marginal rates calculation is valid only for small changes in one or more variables. The existing trade-off analysis methods calculate the maximum changes in a specific throughput when another throughput is changed. We will show that binding efficient supporting surfaces of an efficient point may be used to define different marginal rates of substitutions and in this sense, we get different marginal rates to each frontier point

Measuring the performance and returns to scale of forest management plans using data envelopment analysis approach (Case study; Iranian Caspian forests)

The aim of this study was to assess the relative efficiency of the Iranian forest management plans using the nonparametric method – Data Envelopment Analysis (DEA) as a well-known and robust technique for measuring the relative efficiency of organizations. The relative efficiency of forest management plans was calculated using the most frequency DEA models such as global technical efficiency (CCR), local pure technical efficiency (BCC) and Scale Efficiency (SE) on 12 units in Guilan Province, Iran. According to the results of CCR and BCC models, the efficiency averaged 0.83 and 0.93, respectively. The results of SE discussed a worrying aspect of these units efficiency; namely, there were only 3 efficient forest management plans (Shafaroud, Nav and Fiyab). However, the Scale Efficiency Index (SEI) brings out some interesting points; there were approximately 58% (7 units out of 12) under Increasing Returns to Scale (IRS). Therefore, the managers of forest management plans should focus more on the plans under IRS, so that they will have the opportunity to become more efficient through growth, otherwise managers will not be able to promote their overall productivity

Performance evaluation of forest management plans (Case study: Iranian Caspian forests)

The aim of this research was to measure the relative efficiency of forest management plans in north of Iran. In order to fulfill the research, data of 12 forest management plans were collected from the financial balance sheets of Shafaroud Forest Company during a ten years period. First of all, basic Data Envelopment Analysis (DEA) models (BCC and CCR) were used to determine the efficiency. Then, due to the structure of the forest management plan, cost efficiency and revenue efficiency models based on DEA were used in order to measure the efficiency. Results indicated that 8 forest management plans were efficient based on BCC and CCR models. Furthermore, the results indicated that only one forest management plan was efficient based on cost efficiency and revenue efficiency models. These results could be due to the input oriented properties of the models, rational management and optimal use of resources

Efficiency Measurement in Dynamic Two-Stage Network Structures with Flexible Intermediate Materials

Data envelopment analysis (DEA) is a nonparametric method for evaluating the relative efficiency of decision making units (DMUs) described by multiple inputs and multiple outputs. Since DEA was introduced in the 1970s, it has been widely applied to measure the efficiency of a wide variety of production and operation systems, including two-stage production systems with a series or parallel structure. The outputs from the first stage to the next stage are called intermediate factors (or measures). In some real applications, an intermediate material or some part of it can become the final output or input to the second stage of production. Previously existing models cannot be employed directly to measure the efficiency of such systems. The authors introduce a dynamic DEA model that identifies the structure of flexible intermediate factors to maximise the measure of overall system efficiency. (original abstract