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  We suggest a method for finding the non-dominated points of the production possibility set (PPS) with variable returns to scale (VRS) technology in data envelopment analysis (DEA). We present a multiobjective linear programming (MOLP) problem whose feasible region is the same as the PPS under variable returns to scale for generating non-dominated points. We demonstrate that Pareto solutions of the MOLP produce efficient units in DEA, and vice versa. We solve the MOLP problem by using a finite number of weights which are extreme rays of the cone generated by the efficient solutions. We obtain new efficient points by changing weights, and thus the efficient solutions set is produced.

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We consider an approximation scheme using Haar wavelets for solving a class of infinite horizon optimal control problems (OCP's) of nonlinear interconnected large-scale dynamic systems. A computational method based on Haar wavelets in the time-domain is proposed for solving the optimal control problem. Haar wavelets integral operational matrix and direct collocation method are utilized to find the approximated optimal trajectory of the original problem. Numerical results are also given to demonstrate the applicability and the efficiency of the proposed method.

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In many problems, it is necessary to take into account monotonic relations. Monotonic (isotonic) Regression (MR) is often involved in solving such problems. The MR solutions are of a step-shaped form with a typical sharp change of values between adjacent steps. This, in some applications, is regarded as a disadvantage. We recently introduced a Smoothed MR (SMR) problem which is obtained from the MR by adding a regularization penalty term. The SMR is aimed at smoothing the aforementioned sharp change. Moreover, its solution has a far less pronounced step-structure, if at all available. The purpose of this paper is to further improve the SMR solution by getting rid of such a structure. This is achieved by introducing a lowed bound on the slope in the SMR. We call it Smoothed Slope-Constrained MR (SSCMR) problem. It is shown here how to reduce it to the SMR which is a convex quadratic optimization problem. The Smoothed Pool Adjacent Violators (SPAV) algorithm developed in our recent publications for solving the SMR problem is adapted here to solving the SSCMR problem. This algorithm belongs to the class of dual active-set algorithms. Although the complexity of the SPAV algorithm is $𝑂(𝑛^2)$, its running time is growing in our computational experiments almost linearly with $𝑛$. We present numerical results which illustrate the predictive performance quality of our approach. They also show that the SSCMR solution is free of the undesirable features of the MR and SMR solutions.

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This paper analyzes the performance of a robotic system with two machines in which machines are configured in a circular layout and produce non-identical parts repetitively. The non-destructive testing (NDT) is performed by a stationary robotic arm located in the center of the circle, or a cluster tool. The robotic arm integrates multiple tasks, mainly the NDT of the part and its transition between a pair of machines. The robotic arm cannot complete the transition if it identifies a fault in the part. The main feature of the NDT technology is that its required time is changed by altering the testing cost. This generates a trade-off between cost and cycle time. Initially, the problem of robotic arm scheduling and part sequencing is jointly solved to supports the decision making for reliability improvement of small-scale robotic systems with NDT technologies. We show how the case of non-identical parts can be converted into a travelling salesman problem (TSP). Then, we provide a generalization of the framework based on three characteristics: pickup criterion, layout and travel time metric. The results are extended for the interval and no-wait pickup criteria, and then some notes are provided for travel time saving of different layout and travel time metric. It is shown whether circular systems are equivalent to linear systems, or they dominate linear cases in general terms.

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Here, scalarization techniques for multi-objective optimization problems are addressed. A new scalarization approach, called unified Pascoletti-Serafini approach, is utilized and a new algorithm to construct the Pareto front of a given bi-objective optimization problem is formulated. It is shown that we can restrict the parameters of the scalarized problem. The computed efficient points provide a nearly equidistant approximation of the whole Pareto front. The performance of the proposed algorithm is illustrated by various test problems and its effectiveness with respect to some existing methods is shown.

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Due to the changes of performance measures, a vital aspect for decision makers is finding optimal scale sizes of entities. Moreover, there are undesirable measures in many investigations. In the existing data envelopment analysis (DEA) approaches, optimal scale sizes (OSSs), average-cost efficiency (ACE) and average-revenue efficiency (ARE) of decision making units (DMUs) with desirable measures under strong disposability have been estimated while undesirable factors are presented in many real world examinations. Accordingly, in this research, OSSs and ARE of DMUs with undesirable outputs are addressed under managerial disposability. ARE is defined as the composite of scale and output allocative efficiencies under managerial disposability. To illustrate in detail, a two-stage DEA-based approach is rendered to estimate ARE and OSSs in the presence of undesirable outputs. A numerical example and an illustrative case are given to explain the proposed approach in this study.

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       A transportation problem involving three constraints: source, destination, and conveyance, where all parameters of the problem are fuzzy is called Fully Fuzzy Solid Transportation Problem (FFSTP). In this paper, a new method is proposed to find an optimal solution of an unbalanced FFSTP which the fuzzy numbers are considered to be k-scale trapezoidal fuzzy numbers. The k-scale trapezoidal fuzzy numbers are a generalization of symmetric trapezoidal fuzzy numbers which are considered recently in the literature. In this method, using a new ranking method, we transform the unbalanced FFSTP into a crisp linear programming formulation and find a fuzzy optimal solution for it. The considered model is not necessary balanced and introduced method will solve that without convert it to a balanced model. The advantages of the proposed method are also discussed.
 

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Supply chains often have different technologies. Additionally, organizations with multiple stages can evaluate their operational efficiency by analyzing scale elasticity, which helps determine if they are functioning optimally or if there is room for improvement. This evaluation allows for the identification of potential inefficiencies and opportunities for enhancement. Consequently, this research introduces a two-stage DEA-based approach with undesirable outputs to examine the scale elasticity of supply chains within meta and group frontiers. The measurement of group and meta performance of general systems and stages is conducted for this purpose. Moreover, the study addresses the scale elasticity of supply chains with undesirable outputs by considering the heterogeneity of technologies. To achieve this, the study focuses on the right and left scale elasticity of efficient general systems and each stage. A real-world application from the soft drink industry is provided to illustrate the proposed model. The results show the applicability of the introduced methodology.
 

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Efficiency plays a pivotal role in impacting costs and optimizing resource utilization for
businesses. This study aims to evaluate the technical and scale efficiency of 15 suppliers within
a production unit over a three-year period (2020-2022) using data envelopment analysis
(DEA). The analysis will involve assessing efficiency under two assumptions - constant returns
to scale and variable returns to scale. Variables were selected based on indicator availability,
representation principles, and expert input, with inputs including investment, nonoperating
expense costs, and operational expenses (comprising raw material costs, wages, and
overheads), while outputs encompass net sales and return on investment. Results from the study
indicated that supplier one, scoring 0.5716 assuming constant returns to scale and 0.6790
under variable returns to scale, emerged as the least efficient supplier. Interestingly, only two
suppliers (8 and 15) demonstrated higher efficiency levels. However, the net technical efficiency
of the supply chain showed an increasing concentration, which indicates the overall reduction
of the gap between suppliers and the improvement of the net technical efficiency in the supply
chain of the production unit. This study provides valuable insights into the differences between
suppliers from a macro perspective and offers guidance for manufacturing units looking to
expand their supply chain. 

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Real-world decision makers are faced with different aspects of the world, and each of the types of hard and soft operations research methods have advantages for responding to certain aspects. Based on this, it can be claimed that by using two or more combined methods, more levels and dimensions of a problematic situation can be investigated and the results are definitely more reliable.  The main goal of this research is to solve the problems of electricity shortage caused by cryptocurrency mining in Iran by combining three methods: Strategic choice Approach(SCA), Strategic Option Development and Analysis(SODA), Critical Systems Heuristics(CSH), while examining more detailed levels and dimensions of the problem, solutions or decisions should be adopted to be more reliable and more effective.The combination method is such that SCA is placed as the basis and platform of the research method, In the fourth and eighth steps of sca, soda and csh methods have been used, respectively. The results of this research show wider levels and dimensions of the problems and problems of electricity shortages caused by cryptocurrency mining and lead to the important point that the advantages and benefits of digital currencies should not be ignored due to electricity shortages.
Real-world decision makers are faced with different aspects of the world, and each of the types of hard and soft operations research methods have advantages for responding to certain aspects. Based on this, it can be claimed that by using two or more combined methods, more levels and dimensions of a problematic situation can be investigated and the results are definitely more reliable.  The main goal of this research is to solve the problems of electricity shortage caused by cryptocurrency mining in Iran by combining three methods: Strategic choice Approach(SCA), Strategic Option Development and Analysis(SODA), Critical Systems Heuristics(CSH), while examining more detailed levels and dimensions of the problem, solutions or decisions should be adopted to be more reliable and more effective.The combination method is such that SCA is placed as the basis and platform of the research method, In the fourth and eighth steps of sca, soda and csh methods have been used, respectively. The results of this research show wider levels and dimensions of the problems and problems of electricity shortages caused by cryptocurrency mining and lead to the important point that the advantages and benefits of digital currencies should not be ignored due to electricity shortages.