Congestion is one of the important concepts in data envelopment analysis that occurs when excessive inputs reduce the maximally possible outputs. identification and elimination of congestion have a significant impact on reducing inputs along with increasing outputs. Hence, various studies have been conducted to detect and evaluate congestion. However, in today's world, no organization can achieve its final output with just one process of input. In other words, today's organizations have a network structure that consists of several subsections. Ignoring the existing influences among the subsections processes may lead to inadequate or even incorrect results for evaluating the congestion. While all of the existing methods only evaluate the congestion of each subsection or the whole system independently. Therefore, in this paper, the concept of congestion is developed for a specific and so practical case of network structure called “two-stage network structure”. This case of network structure consists of two series stage such that stage 1 consume some primary inputs to produce some intermediate outputs. In the following, the intermediate outputs are used as the inputs of stage 2 to produce the final output. Here, the concept of congestion is defined for systems with a two-stage structure. Then, to examine the congestion of each stage as well as the congestion of the whole system, a single linear programming model is proposed. The validity of the proposed model is investigated using several theorems and it is shown that the new definition is a generalization of the previous definitions of the congestion for the black-box systems. Finally, the proposed model is applied to a case study including 24 non-life insurance companies in Taiwan.

flexibility differences and whale optimization algorithm (WOA) was applied to localize and quantify damages in large-scale double-layer truss structures. In first stage, damage locating vector (DLV) method using EDS (exponential decreased stress) was employed to find the real damaged elements of structure; then, WOA algorithm was used to determine the severity of suspected damaged elements obtained from the first stage. To evaluate the reliability of the proposed approach, two large-scale double-layer truss structures were studied. Furthermore, to assess the effect of noise on the accuracy of damage detection, the article compares the results of EDS with NCE. Calculation results demonstrate that the combination of DLV method using EDS and WOA algorithm provides an effective tool to carefully determine the location and the severity of structural damages in noisy condition directly. Moreover, the approach determines damages even though there are the low number of used mode shapes and a high number of structural elements.

Since system identification of a tumor model is a primary need for controlling tumor model system, accessing suitable and applicable identification methods is a necessary object. In this paper, firstly, for estimating controlled auto-regressive moving average (CARMA) systems, two  identification methods, namely generalized projection algorithm (GPA) and two-stage GPA (2S-GPA), are introduced and presented in order to estimate unknown parameters of a specific and vital tumor model. Furthermore, effectiveness of such methods, like convergence rate and estimation error, are discussed and considered. The introduced algorithms are simulated to prove these methods effectiveness, and data derived from the simulations are depicted through tables and figures.

In this paper, we discuss the two-stage and the modified two-stage procedures for the estimation of the threshold autoregressive parameter in a first-order threshold autoregressive model (${\rm TAR(1)}$). This is motivated by the problem of finding a final sample size when the sample size is unknown in advance. For this purpose, a two-stage stopping variable and a class of modified two-stage stopping variables are proposed. Afterward, we {prove} the significant properties of the procedures, including asymptotic efficiency and asymptotic risk efficiency for the point estimation based on least-squares estimators. To illustrate this theory, comprehensive Monte Carlo simulation studies is conducted to observe the significant properties of the procedures. Furthermore, the performance of procedures based on Yule-Walker estimators is investigated and the results are compared in practice that confirm our theoretical results. Finally, real-time-series data is studied to demonstrate the application of the procedures.

An efficient methodology is proposed to detect the multiple damages in structural systems. The methodology consists of two main stages. In the first stage, an exhaustive search is performed using the adaptive neuro-fuzzy inference system (ANFIS) to quickly identify the most potentially damaged elements (MPDE). In the second stage, a particle swarm optimization (PSO) is presented to accurately determine the actual damage extents using the first stage results. In order to assess the performance of the proposed methodology for structural damage detection, two illustrative test examples are considered. The numerical results demonstrate the computational efficiency of the proposed methodology when comparing with those of the methods found in the literature.

Organizations and institutions have internal departments that the overall performance of the organization is the result of the performance of each of these departments or stages. Each stage has its own input and output factors as well as connecting factors between stages. The factors between stages are called intermediate indicators. In a two-stage structure, the intermediate indicators are the outputs of the first stage, which are used as the input of the second stage. Evaluation performance of an organization should be determined by considering the performance of each of its stages. Data envelopment analysis is one of the appropriate methods to evaluate performance based on several indicators. In practice, it is not possible to determine these indicators with exact values. In this paper, we proposed a model for determining the performance of two-stager systems in a fuzzy environment, also as well as the allocation of resources to it. We apply inverse data envelopment analysis and propose a multi-objective programming model that, by increasing the output of the unit under evaluation, determines the rate of increase of the first stage inputs and intermediate indicators in a way that maintains its efficiency. Then we illustrate the proposed model to allocate resources to bank branches.