Input Output Weights Research Articles

Positive weights in data envelopment analysis

AbstractData Envelopment Analysis (DEA) models give each decision making unit freedom to assign values to the input-output weights maximising its efficiency score. However, there is no guarantee that the optimal weights obtained from a DEA model are always positive which poses a problem, in both theory and practice. This paper offers new linear programming models to deal with the zero weights problem without restricting the weights or placing prior value judgments on them while maintaining the original DEA frontier. These models generate a profile of weights with the maximum number of positive weights applicable to both envelopment and multiplier DEA settings. These linear programs still allow weight flexibility and are independent of the solver. We show how these models can be modified to provide unit-specific positive weights. We illustrate the relevance of our approach using artificial and real world data.

A neutral cross-efficiency measurement for general parallel production system

There are some problems in the efficiency evaluation for parallel systems. From the applicability of existing models, the parallel models based on self-evaluation may produce the low distinguishing power and unreasonable input–output weights. From the accuracy of efficiency, the weights of partial production-units may be assigned zero values, and thereby the fail of the production-units will lead to the incomprehensibility of system efficiency. The neutral cross-efficiency model maximizes the evaluated decision-making unit (DMU) and simultaneously makes each output of the DMU being as efficient as possible, which effectively avoids the difficulty in choosing between aggressive and benevolent models, and reduces the number of zero output weights. Based on this, this paper proposes the neutral cross-efficiency evaluation method fo r general parallel systems. First, the self-evaluation models for parallel system and its production-units are developed, and the model can enable each production-unit to participate in the evaluation effectively. Then, the neutral cross-efficiency model is proposed to overcome the defects of self-evaluation model. Particularly, the proposed model is also suitable to special general parallel systems with shared resources. More importantly, the proposed models assign different input–output weights for the production-units to avoid the production-units being forced to run under identical production mechanism. Finally, two real-world examples prove the availability and effectiveness of the proposed method.

Deep Regression Ensembles

We introduce a methodology for designing and training deep neural networks (DNN) that we call "Deep Regression Ensembles" (DRE). It bridges the gap between DNN and two-layer neural networks trained with random feature regression. Each layer of DRE has two components, randomly drawn input weights and output weights trained myopically (as if the final output layer) using linear ridge regression. Within a layer, each neuron uses a different subset of inputs and a different ridge penalty, constituting an ensemble of random feature ridge regressions. Our experiments show that a single DRE architecture is at par with or exceeds state-of-the-art DNN in many data sets. Yet, because DRE neural weights are either known in closed-form or randomly drawn, its computational cost is orders of magnitude smaller than DNN.

Environmental Regulations on the Spatial Spillover of the Sustainable Development Capability of Chinese Clustered Ports

For years, China has adopted environmental regulations in developing ports to improve their sustainability. Based on the data of Chinese ports from 2009 to 2018, this paper presents a data envelopment analysis model with subdividing input-output indicator weights and develops it further in two stages with the weight preference and the slacks-based measure, respectively. After assessing the sustainable development capability (SDC) of Chinese ports and their spatial correlation, it revealed that Chinese ports are clustered in several regions and their SDC has spilled over into their neighbors. Further study revealed the SDC is affected by environmental regulations in different ways: as a key measure among regulations to improve the SDC, voluntary regulation has a spatial spillover effect, but neither the mandatory regulation nor public media regulation can significantly improve the SDC. This suggests that the port authority should enact environmental regulations based on the port spatial difference and the port should expand its operation scale and market size and recruit more top talent, which is good for improving its productivity and reducing its carbon emissions.

An Optimal Weight Semi-Supervised Learning Machine for Neural Networks with Time Delay

In this paper, an optimal weight semi-supervised learning machine for a single-hidden layer feedforward network (SLFN) with time delay is developed. Both input weights and output weights of the SLFN are globally optimized with manifold regularization. By feature mapping, input vectors can be placed at the prescribed positions in the feature space in the sense that the separability of all nonlinearly separable patterns can be maximized, unlabeled data can be leveraged to improve the classification accuracy when labeled data are scarce, and a high degree of recognition accuracy can be achieved with a small number of hidden nodes in the SLFN. Some simulation examples are presented to show the excellent performance of the proposed algorithm.

An integrated data envelopment approach for evaluating the meat companies efficiency

The purpose of this study is to apply the assurance region (AR) concept to restrict the range of input-output weights with expert opinions in the data envelopment approach (DEA). Opinions from 34 experts were collected by a questionnaire in order to rank the importance of cost and revenue sources and measure the influence of business factors with the fuzzy analytic hierarchy process (FAHP). This article suggests that a DEA with AR specification in variable weights can present realistic results to measure and rank the performance of twenty meat auction companies (MAC) in Taiwan. We categorise MACs into four groups by decomposing their two revenue sources with auction and slaughter priority and recommend the managerial strategies for each group to improve operational efficiency. This consideration is more critical for small samples or industries that are close to the spatial competitive market structure.<br />

System efficiency evaluation of homogeneous parallel production systems: An aggregation approach

Existing models, for efficiency evaluation of DMUs with homogeneous parallel production-units, have limitations in the sense that production process of a DMU is compared with the production possibility set of all production-units. Moreover, same set of input-output weights is used to evaluate the efficiency, project inputs-outputs of a DMU and all its production-units. This means, all the production-units of a DMU operate in a similar way in the long run as if they are not separate production-units but one single entity. We propose an aggregation approach to evaluate the efficiency of DMUs with homogeneous parallel production-units. We also introduce Weighted Average Efficiency and System Efficiency. As opposed to the existing methodology, different set of weights are used to evaluate efficiency of different production-units of a DMU. Finally, the proposed methodology has been used to evaluate the efficiency of higher education sector of Bihar, one of the largest states in India.

Hybrid Regularized Echo State Network for Multivariate Chaotic Time Series Prediction.

Multivariate chaotic time series prediction is a hot research topic, the goal of which is to predict the future of the time series based on past observations. Echo state networks (ESNs) have recently been widely used in time series prediction, but there may be an ill-posed problem for a large number of unknown output weights. To solve this problem, we propose a hybrid regularized ESN, which employs a sparse regression with the L1/2 regularization and the L2 regularization to compute the output weights. The L1/2 penalty shows many attractive properties, such as unbiasedness and sparsity. The L2 penalty presents appealing ability on shrinking the amplitude of the output weights. After the output weights are calculated, the input weights, internal weights, and output weights are fine-tuning by a Hessian-free optimization method-conjugate gradient backpropagation algorithm. The fine-tuning helps to bubble up the input information toward the output layer. Besides, the largest Lyapunov exponent is used to calculate the predictable horizon of a chaotic time series. Experimental results on benchmark and real-world datasets show that our proposed method is superior to other ESN-based models, as sparser, smaller-absolute-value, and more informative output weights are obtained. All of the predictions within the predictable horizon of the proposed model are accurate.

The role of multiplier bounds in fuzzy data envelopment analysis

The non-Archimedean epsilon $$\varepsilon $$ is commonly considered as a lower bound for the dual input weights and output weights in multiplier data envelopment analysis (DEA) models. The amount of $$\varepsilon $$ can be effectively used to differentiate between strongly and weakly efficient decision making units (DMUs). The problem of weak dominance particularly occurs when the reference set is fully or partially defined in terms of fuzzy numbers. In this paper, we propose a new four-step fuzzy DEA method to re-shape weakly efficient frontiers along with revisiting the efficiency score of DMUs in terms of perturbing the weakly efficient frontier. This approach eliminates the non-zero slacks in fuzzy DEA while keeping the strongly efficient frontiers unaltered. In comparing our proposed algorithm to an existing method in the recent literature we show three important flaws in their approach that our method addresses. Finally, we present a numerical example in banking with a combination of crisp and fuzzy data to illustrate the efficacy and advantages of the proposed approach.

A note for weight restriction in the ARIII model based on correlation coefficients

Data envelopment analysis (DEA) is a very popular mathematical programming technique that is used to evaluate relative efficiency of decision-making units (DMUs). Beside its popularity, DEA has some drawbacks such as unrealistic input–output weights. Therefore, even if they are important, inputs or outputs of some DMUs can be assigned zero (0) or very small weights. Furthermore, because of this drawback, weights can take extreme high values, which cause unrealistic results. Mecit and Alp [1] described the restricted model to handle these problems using additional constraints that include correlation coefficients for weight restriction. However, in the case that negative correlations occur between variables, the constraints related with these negative correlations become useless and have no contribution in the restriction of assurance region (AR), which may result in no contribution of additional constraints in the ARIII model. This study proposes a modification by taking into account absolute values of correlation coefficients to handle the negative correlation problem of ARIII for some special cases.

Bayesian GVAR with k-endogenous dominants & input–output weights: Financial and trade channels in crisis transmission for BRICs

In this work, we study the transmission of shocks (e.g. financial, monetary) between countries by developing a novel approach which relies on Bayesian techniques in order to estimate the GVAR model as a system of simultaneous equations, which we call Bayesian System GVAR (BSGVAR), while providing two procedures to select the dominant economies. Also, we use endogenously determined time varying weights with random coefficients. In this context, we utilize the proposed model to a selected panel of world economies that account for more than 90% of global production. Our work identifies and estimates the link between countries based on the global variables of trade and finance, which act as the transmission channels that have been documented in the literature as being important. To this end, we investigate how the dominant economies of USA and EU17 will be affected by a potential slowdown in the BRICs. Consistent with international evidence, the empirical findings show that both monetary and financial variables, such as interest rates and total credit, have a significant impact on the transmission of shocks. According to our findings, the EU17 economy seems to be more vulnerable than the US economy to shocks from the BRICs.

Online Sequential Projection Vector Machine with Adaptive Data Mean Update.

We propose a simple online learning algorithm especial for high-dimensional data. The algorithm is referred to as online sequential projection vector machine (OSPVM) which derives from projection vector machine and can learn from data in one-by-one or chunk-by-chunk mode. In OSPVM, data centering, dimension reduction, and neural network training are integrated seamlessly. In particular, the model parameters including (1) the projection vectors for dimension reduction, (2) the input weights, biases, and output weights, and (3) the number of hidden nodes can be updated simultaneously. Moreover, only one parameter, the number of hidden nodes, needs to be determined manually, and this makes it easy for use in real applications. Performance comparison was made on various high-dimensional classification problems for OSPVM against other fast online algorithms including budgeted stochastic gradient descent (BSGD) approach, adaptive multihyperplane machine (AMM), primal estimated subgradient solver (Pegasos), online sequential extreme learning machine (OSELM), and SVD + OSELM (feature selection based on SVD is performed before OSELM). The results obtained demonstrated the superior generalization performance and efficiency of the OSPVM.

Extended symmetric and asymmetric weight assignment methods in data envelopment analysis

Dual weight restrictions are commonly suggested as a remedy to the problem of low discriminatory power and absurd marginal prices in conventional Data Envelopment Analysis (DEA) models. However, weight restriction models also suffer from potential problems of infeasibility, lack of exogenous determination and ambiguous interpretations. The Symmetric Weight Assignment Technique (SWAT) addresses these concerns through a symmetric endogenous weight selection process. In this paper, we extend the SWAT method by proposing four new DEA models. Symmetric and asymmetric weights are rewarded and penalized, respectively, in the proposed models. The first model takes into account the symmetrical weights assigned to the outputs in the input-oriented model. The second model takes into account the symmetrical weights assigned to the inputs in the output-oriented model. The third and fourth models simultaneously take into account symmetric input–output weights in both the input and output orientations. We demonstrate the applicability of the proposed models and the efficacy of the procedures and algorithms with an application to Danish district heating plants.

Discrete direct adaptive ELM controller for active vibration control of nonlinear base isolation buildings

Hybridization of base isolation and active control is a promising alternative to suppress the seismic vibrations in civil structures. The base-isolation system introduces hysteretic/frictional nonlinearity into the structure and hence there is a need to develop a nonlinear adaptive control approach to subdue the vibrations. In this paper, the authors propose discrete direct adaptive ELM controller for active control of nonlinear base isolated building, subjected to a set of near-fault earthquakes. A single hidden layer neural controller with random selection of input weights compensates the nonlinearity and provides desired vibration suppression. The neural controller is based on the extreme learning machine algorithm with random input weight selection and output weights are updated using Lyapunov like adaptation rule. The proposed discrete adaptive control law provides necessary stability and vibration suppression in nonlinear base isolated building. Simulation studies have been carried out using the full-scale three dimensional benchmark eight-storey building comprising hysteretic lead-rubber base-isolation. One earthquake record and perturbed model is used to train the controller offline. The offline trained controller is adapted online using the actual full-scale model for a wide range of near-fault earthquakes. The results clearly show that the proposed controller suppresses the vibration significantly without increasing superstructure responses. The comprehensive performance measures are compared with existing results reported in the literature.

An integrated methodology for supplier selection and order allocation in the presence of imprecise data

There has been numerous number of studies related to the supplier selection and problems which adopted a variety of approaches to solve them, however, based on our knowledge none of them has been considered the major decisions related to supplier selection and order allocation in the presence of imprecise data. In an attempt to fulfil this gap, we present an integrated framework which involves two stages including supplier evaluation and order allocation. An augmented imprecise data envelopment analysis (AIDEA) is proposed for supplier evaluation as the basic IDEA model has two main drawbacks, i.e., unrealistic input-output weights and poor discriminating power among all suppliers. Then, an integer programming with fuzzy objectives and constraints is formulated to assign optimal quantity of order to allocated suppliers. The efficiency of suppliers derived from evaluation stage is an important link which integrates these two stages. Finally, the integrated methodology is implemented in a case study organisation.

Orthogonal Least Squares Algorithm for Training Cascade Neural Networks

This paper proposes a novel constructive training algorithm for cascade neural networks. By reformulating the cascade neural network as a linear-in-the-parameters model, we use the orthogonal least squares (OLS) method to derive a novel objective function for training new hidden units. With this objective function, the sum of squared errors (SSE) of the network can be maximally reduced after each new hidden unit is added, thus leading to a network with less hidden units and better generalization performance. Furthermore, the proposed algorithm considers both the input weights training and output weights training in an integrated framework, which greatly simplifies the training of output weights. The effectiveness of the proposed algorithm is demonstrated by simulation results.

Alternative mixed integer linear programming models for identifying the most efficient decision making unit in data envelopment analysis

A mixed integer linear model for selecting the best decision making unit (DMU) in data envelopment analysis (DEA) has recently been proposed by Foroughi [Foroughi, A. A. (2011a). A new mixed integer linear model for selecting the best decision making units in data envelopment analysis. Computers and Industrial Engineering, 60(4), 550–554], which involves many unnecessary constraints and requires specifying an assurance region (AR) for input weights and output weights, respectively. Its selection of the best DMU is easy to be affected by outliers and may sometimes be incorrect. To avoid these drawbacks, this paper proposes three alternative mixed integer linear programming (MILP) models for identifying the most efficient DMU under different returns to scales, which contain only essential constraints and decision variables and are much simpler and more succinct than Foroughi’s. The proposed alternative MILP models can make full use of input and output information without the need of specifying any assurance regions for input and output weights to avoid zero weights, can make correct selections without being affected by outliers, and are of significant importance to the decision makers whose concerns are not DMU ranking, but the correct selection of the most efficient DMU. The potential applications of the proposed alternative MILP models and their effectiveness are illustrated with four numerical examples.

Gradient Descent Learning for Rotor Associative Memory

Complex-valued Associative Memory (CAM) is an extended model of Hopfield Associative Memory (HAM). The fundamental elements, such as input-output signals and connection weights of the CAM are extended to complex numbers. The CAM can deal with multi-states information. Rotor Associative Memory (RAM) is an extended model of the CAM. Rotor neurons are essentially equivalent to complex-valued neurons. Connection weights of the RAM are expressed by two by two matrices. Only hebb rule has been proposed for the learning of the RAM. Its storage capacity is small, so advanced learning methods are necessary. In this paper, we propose gradient descent learning rule for the RAM (GDR RAM). It is based on that for the CAM (GDR CAM) proposed by Lee. We solved the learning rule and performed computer simulations to compare the GDR CAM and the GDR RAM. At last, it turned out that the storage capacity of the GDR RAM is approximately twice as much as that of the GDR CAM and the noise robustness of the GDR RAM is much better than that of the GDR CAM.

Improving the discrimination power and weights dispersion in the data envelopment analysis

Data envelopment analysis (DEA) has been a very popular method for measuring and benchmarking relative efficiency of peer decision making units (DMUs) with multiple input and outputs. Beside of its popularity, DEA has some drawbacks such as unrealistic input–output weights and lack of discrimination among efficient DMUs. In this study, two new models based on a multi-criteria data envelopment analysis (MCDEA) are developed to moderate the homogeneity of weights distribution by using goal programming (GP). These goal programming data envelopment analysis models, GPDEA-CCR and GPDEA-BCC, also improve the discrimination power of DEA.

A note on a new method based on the dispersion of weights in data envelopment analysis

In a very recent paper by Bal et al. (Bal, H., Örkcü, H. H., & Çelebioğlu, S. (2008). A new method based on the dispersion of weights in data envelopment analysis. Computers & Industrial Engineering, 54(3), 502–512), a data envelopment analysis (DEA) model which incorporates the coefficients of variations (CVs) of input–output weights was proposed to improve the discrimination power of DEA and balance input–output weights. This note points out that the input and output weights in DEA are of different dimensions and units. The weights with different dimensions and units cannot be simply added together and averaged. In other words, the DEA model with the inclusion of CVs of input–output weights, which was referred to as CVDEA model for short, makes no sense if input and output data are not normalized to eliminate their dimensions and units. This note also illustrates the facts that the CVDEA model can cause significant efficiency changes when a scale transformation is performed for an input or output and may produce multiple local optimal solutions due to its nonlinearity, leading to totally different assessment conclusions. These facts reveal that the CVDEA model suffers from serious drawbacks and its applications for efficiency assessment should be very cautious.