Resource allocation is a critical challenge in the banking sector. This research introduces an innovative centralized resource allocation model based on data envelopment analysis (DEA) designed for a three-stage network production system. The model incorporates shared inputs, integer-valued data, and undesirable outputs, providing a comprehensive framework to address the complexities of banking operations. We establish an axiomatic production technology set for this three-stage network, which forms the basis for our enhanced Russell method-based model. The effectiveness of the proposed model is demonstrated through a case study of 45 bank branches in West Azerbaijan Province, Iran, covering the stages of "Internet banking," "production," and "profitability." By applying this model to real-world data, we illustrate its practical utility in achieving precise resource allocation and setting benchmarks to improve operational performance. Furthermore, we use the Li test to show that the hypothesis of similarity in target setting and benchmarking between the proposed DEA approach and traditional methods—considering the effects of integrality and undesirable factor assumptions—is rejected. This study not only offers a novel approach to resource allocation but also demonstrates its applicability in practical banking scenarios.

This study proposes a novel framework for evaluating the efficiency of two-stage network decision-making units by integrating the hyperbolic distance function (HDF) with conic optimization. Building on the direct HDF model of Hassanasab et al. (2019), the problem is reformulated within a conic programming structure that explicitly captures internal flows and inter-stage dependencies. The proposed model measures overall efficiency by simultaneously contracting inputs and expanding both intermediate products and final outputs. Unlike conventional approaches, it introduces two stage-specific hyperbolic efficiency parameters, enabling input contraction and output expansion at each stage while implicitly regulating intermediate products and preserving the sequential production structure. The resulting primal and dual linear programming formulations provide additional economic insights, including stage-level shadow prices. Numerical experiments using synthetic and real-world data demonstrate improved discriminatory power and clearer managerial guidance. These results underscore the effectiveness of the proposed conic two-stage HDF framework for evaluating complex multi-stage systems.

Due to the harmful pollution caused by the consumption of fossil fuels with high pollution, there is a great desire to use fossil fuels with low pollution and renewable energies. In this sense, it is recommended to replace polluted fuels with less polluting fuels in industrial sectors. In this contribution, the production process in the electricity industry is considered as a two-stage process with production and distribution sections in the presence of undesirable outputs and expandable inputs from both stages. A novel data envelopment analysis (DEA) model along with a bootstrap DEA procedure have been developed to estimate the technical efficiency, bias and bias-corrected efficiency scores of production entities along with the optimal values of reducible and expandable inputs and outputs. The network DEA model presented in this paper enables the calculation of individual network component performance within a unified framework, as well as the performance of the entire network. To perform sensitivity analysis of the efficiency with respect to the inputs and outputs, a robustness analysis is proposed. To demonstrate the applicability of the proposed model, we apply it to real-life data on 21 fossil-fueled power plants.

Traditional data envelopment analysis (DEA) models are concerned with measuring the relative efficiency of units with respect to multiple inputs and multiple outputs. These models assume real-valued inputs and outputs. In these models, the role of the measures in relation to the input and/or output is known, and these models also neglect the intervening or linking activities. However, in the real world, there are situations where some inputs and/or outputs can only take integer values, and a measure can also play the role of either an input or an output. In this paper, we propose network DEA models that can handle intermediate products when some inputs and/or outputs have integer values and flexible factors are available.

Although data envelopment analysis (DEA) assumes deterministic data, a great volume of data might be stochastic. The global Malmquist productivity index (GMPI) is a highly effective instrument for productivity analysis in DEA. This paper extends GMPI in the presence of stochastic data. Our new stochastic DEA model is a chance-constrained programming model, which is converted to a deterministic programming problem with a linear objective function and quadratic constraints. For efficiency evaluation purposes, in this paper, the weak disposability principle is used to model Russell’s measure in the presence of undesirable outputs. The main contribution of this paper is to develop a global Russell model with stochastic data. A case study is presented to illustrate the applicability of the proposed models.

The problem of resource allocation and reallocation in management science and production theory has drawn much attention among researchers and decision-makers. In this contribution, we focus on this problem in production processes in which two parallel stages are serially connected to a third stage. We assume that in addition to stage-specific inputs, we have shared inputs between the two parallel stages. In this sense, a linear programming-based model is proposed to calculate the technical efficiency of the whole process along with an optimal split of shared resources. To demonstrate the real-world applicability of the proposed approach, a case study on 22 Indian insurance companies is conducted. The analysis reveals that only three companies are efficient across all scenarios. Furthermore, narrow bounds on shared resources and intermediate products lead to more accurate and reliable results compared to medium and wide bounds, highlighting the importance of precise resource allocation constraints.

Data Envelopment Analysis (DEA) plays a pivotal role in assessing production unit efficiency. This study extends group efficiency assessment within the banking sector by utilizing the Modified Semi-Oriented Radial Measure (MSORM) model, specifically designed to handle negative data. It introduces two distinct efficiency definitions and develops models for their evaluation within these groups. Focusing on banks as decision-making units, the MSORM model delves into the intricacies of group efficiency. By effectively addressing negative data complexities, it enables a comprehensive evaluation of bank efficiency across various group frameworks. The study further examines the efficacy of efficiency definitions based on average and weakest performances within the MSORM framework. Empirical findings reveal significant variations in group efficiency assessment under different paradigms, highlighting the impact of the evaluation approach. This research contributes valuable insights into performance variations within the banking industry and aids in enhancing efficiency evaluations in banking systems.

PurposeThe purpose of this paper is to evaluate the efficiency of a series network system with undesirable and unreturnable simultaneously.Design/methodology/approachThe research was conducted by applying data envelopment analysis (DEA) approach to measure the efficiency score of a system and substages with an undesirable output of the second and third stages separately. For each case, new production technology was introduced, and based on them, novel DEA models were proposed.FindingsOne of the most important issues in the development of a country is the banking industry. In this study, 51 branches of commercial banks as a three-stage system with undesirable and unreturnable outputs in the second stage are considered. Then, the efficiency of each branch and substages is measured by using proposed models.Originality/valueThe efficiency of a three-stage network in the presence of undesirable and unreturnable outputs was assessed. In this model, Kousmanen's technology was used.

Due to the scarcity of fossil fuels in the future, the optimal use of these products can not only increase the efficiency of power plants, but it can also be effective in reducing the production of pollutants. To deal with these situations, optimal resource allocation and reallocation was studied using the data envelopment analysis (DEA) models. The current study adopted a resource allocation model in DEA framework when undesired outputs are produced in production process. This alternative resource allocation model is, however, sensitive to uncertainty of the data. In this contribution, we, therefore, introduce a stochastic resource allocation model when there are random data and undesirable products. An applied illustrative study to the power industry consisting 21 electricity production & distribution companies for eight years (2011-2019) is performed to compare the resource reallocations and their efficiencies. The important findings are: First, if we decide to deactivate two companies, the fuel consumption, employees and net electricity generation must be reduced. These reductions will lead to a reduction in pollutants. Second, the low price of electricity in Iran leads to excessive consumption of this product, which in turn leads to the inefficiency of many companies. In order to improve the performances of the companies, the amount of sold-out electricity must significantly be increased.

This paper advances the concept of scale elasticity by examining the impact of directional input changes on both desirable and undesirable outputs. We integrate two disposability concepts into a unified measure within the Range Adjusted Measure (RAM) model, enabling the computation of both directional scale elasticity and directional scale damage. This approach allows for a comprehensive analysis of scale effects in the presence of undesirable outputs. Grounded in Data Envelopment Analysis (DEA), our research enhances the understanding of managing undesirable outputs while accounting for directional scale changes, offering significant implications for both performance improvement and environmental sustainability. The paper includes theoretical foundations, numerical examples to illustrate the methodologies, and an empirical application in the Iranian horticulture industry, demonstrating the effectiveness and adaptability of our approach.

The advent of advanced digital technologies, including the Internet of Things (IoT), image processing, artificial intelligence (AI), blockchain, robotics and cognitive computing that have been embedded in Industry 5.0, is considerably improving the sustainability, resilience, and human-centric performance of industrial organizations. Despite the increasing use of Industry 5.0 technologies in smart product platforming in industrial organizations, a critical issue remains how to assess the providers/suppliers of such technologies in highly competitive markets to fulfil personalized products and services. Following Lancaster's characteristics approach to consumer theory, in this study we contribute to assess digital technologies service providers in the Industry 5.0 era by focusing on both theoretical and empirical evidence inquiring about the convexity of conventional nonparametric frontier estimation methods. To do so, a nonparametric double frontier estimation of the hedonic price characteristics relation is developed from both the buyer's and seller's perspectives. Moreover, a separable directional distance function-based optimization model is developed for the efficiency estimation. Furthermore, a comparable estimation of the convex and nonconvex hedonic price function is proposed. We also explicitly test the impact of convexity in evaluating the efficiency of IoT service providers in the Industry 5.0 context. In this study, we also show that the hypothesis of convexity in assessing the efficiency of IoT service providers is rejected using the Li-test comparing entire densities in the case of the seller's perspective without ratio data. Differences are less pronounced for the buyer's perspective and in the case with ratio data.

This paper empirically evaluates group efficiency in the banking sector by applying an extended Common Set of Weights (CSWs) approach within a two-stage Data Envelopment Analysis (DEA) framework. Our study assesses efficiency across multiple production stages and adapts CSWs to capture the intermediate processes inherent in banking operations. We provide a comprehensive ranking of bank branches within seven prominent banking groups in Guilan province, Iran. By applying our modified methodology to real-world data, we demonstrate its practical utility in delivering precise efficiency assessments and actionable insights for enhancing operational performance. Our findings highlight the superiority of the extended CSWs methodology over traditional DEA models, offering a more accurate and fair evaluation of group efficiency in the complex and interdependent context of banking processes.

Abstract Wireless mesh networks facilitate the provision of Intranet and Internet connectivity across diverse environments, catering to a wide range of applications. It is anticipated that there will be a significant volume of traffic on these networks. The selection and placement of gateway nodes is a significant research concern due to their responsibility for transmitting traffic load. This issue holds importance as it has the potential to optimize network capacity utilization and mitigate congestion effects. Furthermore, the implementation of a multi-radio multi-channel architecture is regarded as a highly promising approach to enhance performance and mitigate interference. Channel assignment is the process of determining the optimal associations between channels and radios for the purpose of transmitting and receiving data concurrently across multiple channels. In order to maximize throughput in multi-radio multi-channel wireless mesh networks, this research investigates the problem of gateway selection and location. Our solution is distinct from the many others described in the literature because it explicitly models the delay overhead associated with channel switching. In addition, we factor in the latency problem while developing our processes. In our research, a Garter Snake Optimization Algorithm (GSO) is used to strategically place gateways. Based on our research, we know that the suggested scheme performs within a constant factor of the best solution as measured by the achieved throughput. The simulation results show that compared to random deployment, fixed deployment, and grid-based techniques, our suggested mechanism makes better use of available resources and delivers much higher network performance.

Recent pandemic outbreaks, including the COVID-19 and SARS, have revealed that supply chains (SCs) are unable to respond to such disasters. To mitigate the destructive impacts and improve the performance of SCs, Operations Research (OR) techniques have been applied to address the issues over the last two decades. The objective of this paper is to develop a network data envelopment analysis (NDEA) model to measure the resilience and sustainability of healthcare SCs in response to the COVID-19 pandemic outbreak. In the proposed NDEA model, for the first time, outputs’ weak disposability, chance-constrained programming (CCP), the convexity assumption, and the semi-oriented radial approach are aggregated. Moreover, a modified directional distance function (DDF) measure is developed to measure the overall and divisional efficiency scores. Furthermore, the proposed model can deal with different types of data such as integer-valued data, negative data, stochastic data, ratio data, and undesirable outputs. Also, several useful and interesting properties of the novel efficiency measure are presented. Finally, we measure the performance of 28 healthcare SCs to demonstrate the applicability and capability of our proposed approach.

Abstract The utilization of meta-heuristics has been widespread in resolving optimization problems, with constant development of new and effective algorithms. Thisresearch presents the Garter Snake Optimization Algorithm (GSO), which ismotivated by the mating behavior of garter snakes and leverages various techniques such as screening, grafting, and annual growth to conduct a productive andthorough search of the exploration space. The algorithm incorporates both socialand personal behaviors to accomplish a balance between exploration and exploitation of the best solutions. To assess the performance of the proposed algorithm,it is tested on four restricted benchmark problems and a frequently utilized realengineering problem, and the optimization results are compared with other algorithms. In many respects, the GSO outperforms other algorithms, demonstratingits superiority and potential in addressing constrained optimization problems.

Data Envelopment Analysis (DEA) is a powerful technique for estimating the efficiency of decision-making units (DMUs) by assigning appropriate weights.To enhance the discriminative capabilities of DEA in evaluating DMUs, the cross-efficiency evaluation method has been introduced, based on peer evaluations.However, a significant challenge in cross-efficiency analysis lies in the nonuniqueness of optimal weights.In this paper, we propose a novel approach to crossefficiency evaluation, emphasising the selection of weighted profiles within nondecreasing returns to scale (NDRS) production technologies.This approach introduces conditions to ensure non-zero weights and reduce weight disparities.Additionally, we present two optimisation models from benevolent and aggressive viewpoints as secondary goals.To illustrate the effectiveness of the new approach, we provide numerical examples and an empirical application involving the performance evaluation of 14 airline companies.

Conventional Network Data Envelopment Analysis (NDEA) models often make an assumption of data precision, which frequently does not align with the realities of many real-world scenarios. When dealing with ambiguous data, whether it involves input, output, or intermediate products represented as bounded or ordinal data, the accurate assessment of efficiency scores poses a significant challenge. This study addresses the crucial issue of handling interval data within NDEA structures by introducing an innovative methodology that integrates both optimistic and pessimistic strategies. Our proposed methodology goes beyond the mere determination of upper and lower bounds for efficiency scores; it also incorporates target-setting and improvement approaches. Through the calculation of interval efficiency for each decision-making unit (DMU), our approach offers a comprehensive framework for efficiency classification. To underscore the effectiveness of this methodology, the study presents empirical evidence through a case study in the agriculture industry. The results not only showcase the advantages of our proposed methodology but also emphasize its potential for practical application in diverse and complex real-world contexts.

Several studies have been conducted on non-parametric data envelopment analysis (DEA). According to these studies, the performance analysis of network structure is usually about the desirable intermediate measures considered as the outputs in the first stage. These measures are utilized as inputs for the second stage. Notably, both the desirable and undesirable products constitute said intermediate measures in many actual cases. Scholars and academics working in the field of DEA have recently begun paying special attention to this issue. In this regard, the main contributions of this study are summarized as follows: (i) Examining the existing methods for dealing with undesirable products and choosing the appropriate method, (ii) Designing a new DEA model for reallocating resources in the presence of undesirable products, and (iii) Developing a model for two-stage production networks involving undesirable intermediate outputs. Moreover, a simple numerical example is discussed to address the applicability of the proposed model. Finally, a real case study is conducted on 30 provincial-level regions in mainland China to verify the applicability of the proposed approaches.

Conventional data envelopment analysis (DEA) models are often extended for constant or variable returns to scale assumptions based on the under-investigated technology. It is assumed that all inputs and outputs are real-valued data. However, in many practical applications, proportionality or convexity axioms require to be modified. This study attempts to further expand upon the hybrid returns to scale DEA models in the presence of integer-valued input and output data. We refine the previous axioms to introduce a new minimal extrapolation technology set. Moreover, we formulate a couple of mixed-integer linear programming models for efficiency evaluation and target setting. An empirical application on 30 high schools in Iran is provided to validate the proposed approach. The data analysis, including efficiency evaluations along with providing benchmark units, is also performed.

Blood supply chains (BSCs) play a strategic and crucial role in healthcare systems especially in unexpected situations such as earthquakes and pandemic outbreaks. Nevertheless, measuring the sustainability and resilience of BSCs is a major challenge for many decision-makers in healthcare systems. To this end, this paper presents an advanced network data envelopment analysis (NDEA) method to evaluate the sustainability and resilience of BSCs. We deal with BSCs, including blood collection centers (BCCs), blood production centers (BPCs), and blood distribution centers (BDCs). A new directional distance function (DDF) is also developed for evaluating both the overall and stage efficiency scores. Our proposed model can deal with different types of data, including integers, undesirable outputs, negative, zero, and positive. The undesirable outputs are the outputs that adversely impact the performance of DMUs. Moreover, the developed method addresses the sustainability and resilience of BSCs. A case study is provided to demonstrate the usefulness of the proposed model.