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The purpose of this paper is to provide an outline of the major contributions in the literature on the determination of the least distance in data envelopment analysis (DEA). The focus herein is primarily on methodological developments. Specifically, attention is mainly paid to modeling aspects, computational features, the satisfaction of properties and duality. Finally, some promising avenues of future research on this topic are stated.

DEA is a methodology based on mathematical programming for the assessment of relative efficiency of a set of decision-making units (DMUs) that use several inputs to produce several outputs. DEA is classified in the literature as a non-parametric method because it does not assume a particular functional form for the underlying production function and presents, in this sense, some outstanding properties: the efficiency of firms may be evaluated independently on the market prices of the inputs used and outputs produced; it may be easily used with multiple inputs and outputs; a single score of efficiency for each assessed organization is obtained; this technique ranks organizations based on relative efficiency; and finally, it yields benchmarking information. DEA models provide both benchmarking information and efficiency scores for each of the evaluated units when it is applied to a dataset of observations and variables (inputs and outputs). Without a doubt, this benchmarking information gives DEA a distinct advantage over other efficiency methodologies, such as stochastic frontier analysis (SFA). Technical inefficiency is typically measured in DEA as the distance between the observed unit and a “benchmarking” target on the estimated piece-wise linear efficient frontier. The choice of this target is critical for assessing the potential performance of each DMU in the sample, as well as for providing information on how to increase its performance. However, traditional DEA models yield targets that are determined by the “furthest” efficient projection to the evaluated DMU. The projected point on the efficient frontier obtained as such may not be a representative projection for the judged unit, and consequently, some authors in the literature have suggested determining closest targets instead. The general argument behind this idea is that closer targets suggest directions of enhancement for the inputs and outputs of the inefficient units that may lead them to the efficiency with less effort. Indeed, authors like Aparicio et al. (2007) have shown, in an application on airlines, that it is possible to find substantial differences between the targets provided by applying the criterion used by the traditional DEA models, and those obtained when the criterion of closeness is utilized for determining projection points on the efficient frontier. The determination of closest targets is connected to the calculation of the least distance from the evaluated unit to the efficient frontier of the reference technology. In fact, the former is usually computed through solving mathematical programming models associated with minimizing some type of distance (e.g. Euclidean). In this particular respect, the main contribution in the literature is the paper by Briec (1998) on Hölder distance functions, where formally technical inefficiency to the “weakly” efficient frontier is defined through mathematical distances.

All the interesting features of the determination of closest targets from a benchmarking point of view have generated, in recent times, the increasing interest of researchers in the calculation of the least distance to evaluate technical inefficiency (Aparicio et al., 2014a). So, in this paper, we present a general classification of published contributions, mainly from a methodological perspective, and additionally, we indicate avenues for further research on this topic. The approaches that we cite in this paper differ in the way that the idea of similarity is made operative. Similarity is, in this sense, implemented as the closeness between the values of the inputs and/or outputs of the assessed units and those of the obtained projections on the frontier of the reference production possibility set. Similarity may be measured through multiple distances and efficiency measures. In turn, the aim is to globally minimize DEA model slacks to determine the closest efficient targets. However, as we will show later in the text, minimizing a mathematical distance in DEA is not an easy task, as it is equivalent to minimizing the distance to the complement of a polyhedral set, which is not a convex set. This complexity will justify the existence of different alternatives for solving these types of models.

As we are aware, this is the first survey in this topic.

The purpose of this paper is to propose a system dynamic simulated process model for maintenance work management incorporating the Fourth Industrial Revolution (4IR) technologies.

The extant literature in physical assets maintenance depicts that poor maintenance management is predominantly because of a lack of a clearly defined maintenance work management process model, resulting in poor management of maintenance work. This paper solves this complex phenomenon using a combination of conceptual process modeling and system dynamics simulation incorporating 4IR technologies. A process for maintenance work management and its control actions on scheduled maintenance tasks versus unscheduled maintenance tasks is modeled, replicating real-world scenarios with a digital lens (4IR technologies) for predictive maintenance strategy.

A process for maintenance work management is thus modeled and simulated as a dynamic system. Post-model validation, this study reveals that the real-world maintenance work management process can be replicated using system dynamics modeling. The impact analysis of 4IR technologies on maintenance work management systems reveals that the implementation of 4IR technologies intensifies asset performance with an overall gain of 27.46%, yielding the best maintenance index. This study further reveals that the benefits of 4IR technologies positively impact equipment defect predictability before failure, thereby yielding a predictive maintenance strategy.

The study focused on maintenance work management system without the consideration of other subsystems such as cost of maintenance, production dynamics, and supply chain management.

The maintenance real-world quantitative data is retrieved from two maintenance departments from company A, for a period of 24 months, representing years 2017 and 2018. The maintenance quantitative data retrieved represent six various types of equipment used at underground Mines. The maintenance management qualitative data (Organizational documents) in maintenance management are retrieved from company A and company B. Company A is a global mining industry, and company B is a global manufacturing industry. The reliability of the data used in the model validation have practical implications on how maintenance work management system behaves with the benefit of 4IR technologies' implementation.

This research study yields an overall benefit in asset management, thereby intensifying asset performance. The expected learnings are intended to benefit future research in the physical asset management field of study and most important to the industry practitioners in physical asset management.

This paper provides for a model in which maintenance work and its dynamics is systematically managed. Uncontrollable corrective maintenance work increases the complexity of the overall maintenance work management. The use of a system dynamic model and simulation incorporating 4IR technologies adds value on the maintenance work management effectiveness.

This paper aims to present the basic assumptions for creation of social Fröhlich condensate and attract attention of other researchers (both from physics and socio-political science) to the problem of modeling of stability and order preservation in highly energetic society coupled with social energy bath of high temperature.

The model of social Fröhlich condensation and its analysis are based on the mathematical formalism of quantum thermodynamics and field theory (applied outside of physics).

The presented quantum-like model provides the consistent operational model of such complex socio-political phenomenon as Fröhlich condensation.

The model of social Fröhlich condensation is heavily based on theory of open quantum systems. Its consistent elaboration needs additional efforts.

Evidence of such phenomenon as social Fröhlich condensation is demonstrated by stability of modern informationally open societies.

Approaching the state of Fröhlich condensation is the powerful source of social stability. Understanding its informational structure and origin may help to stabilize the modern society.

Application of the quantum-like model of Fröhlich condensation in social and political sciences is really the novel and original approach to mathematical modeling of social stability in society exposed to powerful information radiation from mass-media and Internet-based sources.

This paper aims to examine the integration of lateral transshipment and road vulnerability into the humanitarian relief chain in light of affected area priority to address equitable distribution and assess the impact of various parameters on the total average inflated distance traveled per relief item.

After identifying comprehensive critical criteria and subcriteria, a hybrid multi-criteria decision-making framework was applied to obtain the demand points’ weight and ranking in a real-life earthquake scenario. Direct shipment and lateral transshipment models were then presented and compared. The developed mathematical models are formulated as mixed-integer programming models, considering facility location, inventory prepositioning, road vulnerability and quantity of lateral transshipment.

The study found that the use of prioritization criteria and subcriteria, in conjunction with lateral transshipment and road vulnerability, resulted in a more equitable distribution of relief items by reducing the total average inflated distance traveled per relief item.

To the best of the authors’ knowledge, this study is one of the first research on equity in humanitarian response through prioritization of demand points. It also bridges the gap between two areas that are typically treated separately: multi-criteria decision-making and humanitarian logistics.

This is the first scholarly work in Shiraz focused on the equitable distribution system by prioritization of demand points and assigning relief items to them after the occurrence of a medium-scale earthquake scenario considering lateral transshipment in the upper echelon.

The paper clarifies how to prioritize demand points to promote equity in humanitarian logistics when the authors have faced multiple factors (i.e. location of relief distribution centers, inventory level, distance, lateral transshipment and road vulnerability) simultaneously.

The purpose of this paper is to achieve effective governance of online rumors through the proposed rumor propagation model and immunization strategy.

The paper leverages the agent-based modeling (ABM) method to model individuals from two aspects, behavior and attitude. Based on the analysis and research of online data, we propose a rumor propagation model, namely the Untouched view transmit removed-Susceptible hesitate agree disagree (Unite-Shad), and devise an immunization strategy, namely the Gravity Immunization Strategy (GIS). A graph-based framework, namely Pregel, is used to carry out the rumor propagation simulation experiments. Through the experiments, the rationality of the Unite-Shad and the effectiveness of the GIS are verified.

The study discovers that the inconsistency between human behaviors and attitudes in rumor propagation can be explained by the Unite-shad model. Besides, the GIS, which shows better performance in small-world networks than in scale-free networks, can effectively suppress rumor propagation in the early stage.

This paper provides an effective immunization strategy for rumor governance. Specifically, the Unite-Shad model reveals the mechanism of rumor propagation, and the GIS provides an effective governance method for selecting immune nodes.

The inconsistency of human behaviors and attitudes in real scenes is modeled in the Unite-Shad model. Combined with the model, the definition of diffusion domain is proposed and a novel immunization strategy, namely GIS, is designed, which is significant for the social governance of rumor propagation.

The paper presents a mathematical problem involving quasistatic contact between a thermo-electro-viscoelastic body and a lubricated foundation, where the contact is described using a version of Coulomb’s law of friction that includes normal damped response conditions and heat exchange with a conductive foundation. The constitutive law for the material is thermo-electro-viscoelastic. The problem is formulated as a system that includes a parabolic equation of the first kind for the temperature, an evolutionary elliptic quasivariational inequality for the displacement and a variational elliptic equality for the electric stress. The author establishes the existence of a unique weak solution to the problem by utilizing classical results for evolutionary quasivariational elliptic inequalities, parabolic differential equations and fixed point arguments.

The author establishes a variational formulation for the model and proves the existence of a unique weak solution to the problem using classical results for evolutionary quasivariational elliptic inequalities, parabolic difierential equations and fixed point arguments.

The author proves the existence of a unique weak solution to the problem using classical results for evolutionary quasivariational elliptic inequalities, parabolic difierential equations and fixed point arguments.

The author studies a mathematical problem between a thermo-electro-viscoelastic body and a lubricated foundation using a version of Coulomb’s law of friction including the normal damped response conditions and the heat exchange with a conductive foundation, which is original and requires a good understanding of modeling and mathematical tools.

Due to unceasing declination in environment, sustainable agro-food supply chains have become a topic of concern to business, government organizations and customers. The purpose of this study is to examine a problem associated with sustainable network design in context of Indian agro-food grain supply chain.

A mixed integer nonlinear programming (MINLP) model is suggested to apprehend the major complications related with two-echelon food grain supply chain along with sustainability aspects (carbon emissions). Genetic algorithm (GA) and quantum-based genetic algorithm (Q-GA), two meta-heuristic algorithms and LINGO 18 (traditional approach) are employed to establish the vehicle allocation and selection of orders set.

The model minimizes the total transportation cost and carbon emission tax in gathering food grains from farmers to the hubs and later to the selected demand points (warehouses). The simulated data are adopted to test and validate the suggested model. The computational experiments concede that the performance of LINGO is superior than meta-heuristic algorithms (GA and Q-GA) in terms of solution obtained, but there is trade-off with respect to computational time.

In literature, inadequate study has been perceived on defining environmental sustainable issues connected with agro-food supply chain from farmer to final distribution centers. A MINLP model has been formulated as practical scenario for central part of India that captures all the major complexities to make the system more efficient. This study is regulated to agro-food Indian industries.

The suggested network design problem is an innovative approach to design distribution systems from farmers to the hubs and later to the selected warehouses. This study considerably assists the organizations to design their distribution network more efficiently.

Groundwater is an important source of water supply in arid and semi-arid areas. The purpose of this study is to predict the impact of climate change on groundwater recharge in an arid environment in Ilam Province, west of Iran.

A three-dimensional transient groundwater flow model (modular finite difference groundwater FLOW model: MODFLOW) was used to simulate the impacts of three climate scenarios (i.e. an average of a long-term rainfall, predicted rainfall in 2015-2030 and three years moving average rainfall) on groundwater recharge and groundwater levels. Various climate scenarios in Long Ashton Research Station Weather Generator were applied to predict weather data.

HadCM3 climatic model and A2 emission scenario were selected as the best methods for weather data generation. Based on the results of these models, annual precipitation will decrease by 3 per cent during 2015-2030. For three emission scenarios, i.e. an average of a long-term rainfall, predicted rainfall in 2015-2030 and three years moving average rainfall, precipitation in 2030 is estimated to be 265, 257 and 247 mm, respectively. For the studied aquifer, predicted recharge will decrease compared to recharge calculated based on the average of long-term rainfall.

The decline of groundwater level in the study area was 11.45 m during the past 24 years or 0.48 m/year. Annual groundwater depletion should increase to 0.75 m in the coming 16 years via climate change. Climate change adaptation policies in the basin should include changing the crop type, as well as water productivity and irrigation efficiency enhancement at the farm and regional scales.

This study aimed to assess the potential of the Clinical Dementia Rating (CDR) Scale in the prognosis of dementia in elderly subjects.

Dementia staging severity is clinically an essential task, so the authors used machine learning (ML) on the magnetic resonance imaging (MRI) features to locate and study the impact of various MR readings onto the classification of demented and nondemented patients. The authors used cross-sectional MRI data in this study. The designed ML approach established the role of CDR in the prognosis of inflicted and normal patients. Moreover, the pattern analysis indicated CDR as a strong cohort amongst the various attributes, with CDR to have a significant value of p < 0.01. The authors employed 20 ML classifiers.

The mean prediction accuracy varied with the various ML classifier used, with the bagging classifier (random forest as a base estimator) achieving the highest (93.67%). A series of ML analyses demonstrated that the model including the CDR score had better prediction accuracy and other related performance metrics.

The results suggest that the CDR score, a simple clinical measure, can be used in real community settings. It can be used to predict dementia progression with ML modeling.

To achieve sustainable development in shipping, accurately identifying the impact of artificial intelligence on shipping carbon emissions and predicting these emissions is of utmost importance.

A multivariable discrete grey prediction model (WFTDGM) based on weakening buffering operator is established. Furthermore, the optimal nonlinear parameters are determined by Grey Wolf optimization algorithm to improve the prediction performance, enhancing the model’s predictive performance. Subsequently, global data on artificial intelligence and shipping carbon emissions are employed to validate the effectiveness of our new model and chosen algorithm.

To demonstrate the applicability and robustness of the new model in predicting marine shipping carbon emissions, the new model is used to forecast global marine shipping carbon emissions. Additionally, a comparative analysis is conducted with five other models. The empirical findings indicate that the WFTDGM (1, N) model outperforms other comparative models in overall efficacy, with MAPE for both the training and test sets being less than 4%, specifically at 0.299% and 3.489% respectively. Furthermore, the out-of-sample forecasting results suggest an upward trajectory in global shipping carbon emissions over the subsequent four years. Currently, the application of artificial intelligence in mitigating shipping-related carbon emissions has not achieved the desired inhibitory impact.

This research not only deepens understanding of the mechanisms through which artificial intelligence influences shipping carbon emissions but also provides a scientific basis for developing effective emission reduction strategies in the shipping industry, thereby contributing significantly to green shipping and global carbon reduction efforts.

The multi-variable discrete grey prediction model developed in this paper effectively mitigates abnormal fluctuations in time series, serving as a valuable reference for promoting global green and low-carbon transitions and sustainable economic development. Furthermore, based on the findings of this paper, a grey prediction model with even higher predictive performance can be constructed by integrating it with other algorithms.