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A New Stochastic Model for Classifying Flexible Measures in Data Envelopment Analysis Mansour Sharifi, Ghasem Tohidi, Behrouz Daneshian, Farzin Modarres Khiyabani Journal of the Operations Research Society of China    2021, 9 (3): 569-592.   DOI: 10.1007/s40305-020-00318-5 Abstract （4364）      PDF       Knowledge map    Save The way to deal with flexible data from their stochastic presence point of view as output or input in the evaluation of efficiency of the decision-making units (DMUs) motivates new perspectives in modeling and solving data envelopment analysis (DEA) in the presence of flexible variables. Because the orientation of flexible data is not pre-determined, and because the number of DMUs is fixed and all the DMUs are independent, flexible data can be treated as random variable in terms of both input and output selection. As a result, the selection of flexible variable as input or output for n DMUs can be regarded as binary random variable. Assuming the randomness of choosing flexible data as input or output, we deal with DEA models in the presence of flexible data whose input or output orientation determines a binomial distribution function. This study provides a new insight to classify flexible variable and investigates the input or output status of a variable using a stochastic model. The proposed model obviates the problems caused by the use of the large M number and using its different values in previous models. In addition, it can obtain the most appropriate efficiency value for decision-making units by assigning the chance of choosing the orientation of flexible variable to the model itself. The proposed method is compared with other available methods by employing numerical and empirical examples. Reference | Related Articles | Metrics | Comments（0）

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Transient Behavior of a Single-Server Markovian Queue with Balking and Working Vacation Interruptions Arumugam Azhagappan, Thirunavukkarasu Deepa Journal of the Operations Research Society of China    2021, 9 (2): 322-341.   DOI: 10.1007/s40305-019-00288-3 Abstract （2048）      PDF       Knowledge map    Save This paper studies the time-dependent analysis of an M/M/1 queueing model with single, multiple working vacation, balking and vacation interruptions. Whenever the system becomes empty, the server commences working vacation. During the working vacation period, if the queue length reaches a positive threshold value ‘k’, the working vacation of the server is interrupted and it immediately starts the service in an exhaustive manner. During working vacations, the customers become discouraged due to the slow service and possess balking behavior. The transient system size probabilities of the proposed model are derived explicitly using the method of generating function and continued fraction. The performance indices such as average and variance of system size are also obtained. Further, numerical simulations are presented to analyze the impact of system parameters. Reference | Related Articles | Metrics | Comments（0）

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Unbounded Serial-Batching Scheduling on Hierarchical Optimization Cheng He, Hao Lin, Li Li Journal of the Operations Research Society of China    2021, 9 (4): 909-914.   DOI: 10.1007/s40305-020-00334-5 Abstract （2375）      PDF       Knowledge map    Save The paper considers a serial-batching scheduling problem on hierarchical optimization with two regular maximum costs, where hierarchical optimization means the primary objective function is minimized, and keeping the minimum value of the primary objective function, the secondary objective function is also minimized. In serial-batching machine environment, the machine processes the jobs in batch, and the jobs in the identical batch are processed by entering into the machine together and leaving the machine together. The time taken to process a batch amounts to the total processing time of the jobs in the batch. Moreover, a fixed switching time s is inserted when a machine begins to process a new batch. We only study the unbounded model, i.e., the batch capacity is unbounded. We give an algorithm that can solve the hierarchical optimization problem in $O\left(n^{4}\right)$ time, where n denotes the number of jobs. Reference | Related Articles | Metrics | Comments（0）

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Optimization and Operations Research in Mitigation of a Pandemic Cai-Hua Chen, Yu-Hang Du, Dong-Dong Ge, Lin Lei, Yin-Yu Ye Journal of the Operations Research Society of China    2022, 10 (2): 289-304.   DOI: 10.1007/s40305-022-00391-y Abstract （1561）      PDF       Knowledge map    Save The pandemic of COVID-19 initiated in 2019 and spread all over the world in 2020 has caused significant damages to the human society, making troubles to all aspects of our daily life. Facing the serious outbreak of the virus, we consider possible solutions from the perspectives of both governments and enterprises. Particularly, this paper discusses several applications of supply chain management, public resource allocation, and pandemic prevention using optimization and machine learning methods. Some useful insights in mitigating the pandemic and economy reopening are provided at the end of this paper. These insights might help governments to reduce the severity of the current pandemic and prevent the next round of outbreak. They may also improve companies' reactions to the increasing uncertainties appearing in the business operations. Although the coronavirus imposes challenges to the entire society at the moment, we are confident to develop new techniques to prevent and eradicate the disease. Reference | Related Articles | Metrics | Comments（0）

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Local Linear Convergence of an ADMM-Type Splitting Framework for Equality Constrained Optimization Jun-Feng Yang, Yin Zhang Journal of the Operations Research Society of China    2021, 9 (2): 308-319.   DOI: 10.1007/s40305-019-00271-y Abstract （2008）      PDF       Knowledge map    Save We establish local convergence results for a generic algorithmic framework for solving a wide class of equality constrained optimization problems. The framework is based on applying a splitting scheme to the augmented Lagrangian function that includes as a special case the well-known alternating direction method of multipliers (ADMM). Our local convergence analysis is free of the usual restrictions on ADMM-like methods, such as convexity, block separability or linearity of constraints. It offers a much-needed theoretical justification to the widespread practice of applying ADMM-like methods to nonconvex optimization problems. Reference | Related Articles | Metrics | Comments（0）

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A General Jury Theorem on Group Decision Making Yu-Da Hu Journal of the Operations Research Society of China    2021, 9 (4): 869-881.   DOI: 10.1007/s40305-020-00330-9 Abstract （2071）      PDF       Knowledge map    Save This paper established a general jury theorem on group decision making where the probabilities of the individuals in making correct choice between two alternatives can be different. And we proved that the higher the probability of any decision maker in the group correctly choosing between two alternatives, the higher the probability of the group correctly choosing the same two alternatives. The general jury theorem also indicates that given two groups of individuals with the same average probability of making the correct choice, the one with a more varied or diverse distribution of probabilities will have a higher probability of making the correct choice. In particular, we proved that as the number of decision makers in the group increases to infinity, this probability tends to the limit 1. The general jury theorem presented in this paper substantially generalizes the well-known Condorcet jury theorem in the group decision making theory, which has not been generalized for 200 years until now. Reference | Related Articles | Metrics | Comments（0）

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Novel Global Optimization Algorithm with a Space-Filling Curve and Integral Function Zhong-Yu Wang, Yong-Jian Yang Journal of the Operations Research Society of China    2021, 9 (3): 619-640.   DOI: 10.1007/s40305-020-00294-w Abstract （1159）      PDF       Knowledge map    Save In this study, we consider the global optimization problem in a hypercube. We use a class of series to construct a curve in a hypercube, which can fill the hypercube, and we present an integral function on the curve. Based on the integral function, we propose an algorithm for solving the global optimization problem. Then, we perform a convergence analysis and numerical experiments to demonstrate the effectiveness of the proposed algorithm. Reference | Related Articles | Metrics | Comments（0）

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Certifying the Global Optimality of Quartic Minimization over the Sphere Sheng-Long Hu Journal of the Operations Research Society of China    2022, 10 (2): 241-287.   DOI: 10.1007/s40305-021-00347-8 Abstract （1532）      PDF       Knowledge map    Save The quartic minimization over the sphere is an NP-hard problem in the general case. There exist various methods for computing an approximate solution for any given instance. In practice, it is quite often that a global optimal solution was found but without a certification. We will present in this article two classes of methods which are able to certify the global optimality, i.e., algebraic methods and semidefinite program (SDP) relaxation methods. Several advances on these topics are summarized, accompanied with some emerged new results. We want to emphasize that for mediumor large-scaled instances, the problem is still a challenging one, due to an apparent limitation on the current force for solving SDP problems and the intrinsic one on the approximation techniques for the problem. Reference | Related Articles | Metrics | Comments（0）

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Necessary Optimality Conditions for Semi-vectorial Bi-level Optimization with Convex Lower Level: Theoretical Results and Applications to the Quadratic Case Julien Collonge Journal of the Operations Research Society of China    2021, 9 (3): 691-712.   DOI: 10.1007/s40305-020-00305-w Abstract （1309）      PDF       Knowledge map    Save This paper explores related aspects to post-Pareto analysis arising from the multicriteria optimization problem. It consists of two main parts. In the first one, we give first-order necessary optimality conditions for a semi-vectorial bi-level optimization problem:the upper level is a scalar optimization problem to be solved by the leader, and the lower level is a multi-objective optimization problem to be solved by several followers acting in a cooperative way (greatest coalition multi-players game). For the lower level, we deal with weakly or properly Pareto (efficient) solutions and we consider the so-called optimistic problem, i.e. when followers choose amongst Pareto solutions one which is the most favourable for the leader. In order to handle reallife applications, in the second part of the paper, we consider the case where each follower objective is expressed in a quadratic form. In this setting, we give explicit first-order necessary optimality conditions. Finally, some computational results are given to illustrate the paper. Reference | Related Articles | Metrics | Comments（0）

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The Continuous Knapsack Problem with Capacities Huynh Duc Quoc, Nguyen Chi Tam, Tran Hoai Ngoc Nhan Journal of the Operations Research Society of China    2021, 9 (3): 713-721.   DOI: 10.1007/s40305-020-00298-6 Abstract （1324）      PDF       Knowledge map    Save We address a variant of the continuous knapsack problem, where capacities regarding costs of items are given into account. We prove that the problem is NP-complete although the classical continuous knapsack problem is solvable in linear time. For the case that there exists exactly one capacity for all items, we solve the corresponding problem in O(n log n) time, where n is the number of items. Reference | Related Articles | Metrics | Comments（0）

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Nonuniqueness of Solutions of a Class of ℓ0-minimization Problems Jia-Liang Xu Journal of the Operations Research Society of China    2021, 9 (4): 893-908.   DOI: 10.1007/s40305-020-00336-3 Abstract （2095）      PDF       Knowledge map    Save Recently, finding the sparsest solution of an underdetermined linear system has become an important request in many areas such as compressed sensing, image processing, statistical learning, and data sparse approximation. In this paper, we study some theoretical properties of the solutions to a general class of $\ell_{0}$-minimization problems, which can be used to deal with many practical applications. We establish some necessary conditions for a point being the sparsest solution to this class of problems, and we also characterize the conditions for the multiplicity of the sparsest solutions to the problem. Finally, we discuss certain conditions for the boundedness of the solution set of this class of problems. Reference | Related Articles | Metrics | Comments（0）

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Generalizations of Sobolev’s Consistency and Values for TU-Games Jun Su, Theo S. H. Driessen, Gen-Jiu Xu Journal of the Operations Research Society of China    2021, 9 (2): 344-357.   DOI: 10.1007/s40305-019-00279-4 Abstract （2043）      PDF       Knowledge map    Save In the framework of cooperative game theory, Sobolev (Advances in game theory, Izdat., “Minitis”, Vilnius, pp 151–153, 1973) axiomatized the well-known Shapley value by means of consistency property with reference to a specifically chosen reduced game. The goal of this paper is to generalize Sobolev’s consistency approach to the class of efficient, symmetric and linear values. Reference | Related Articles | Metrics | Comments（0）

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The Odd Log-Logistic Weibull-G Family of Distributions with Regression and Financial Risk Models Mahdi Rasekhi, Emrah Altun, Morad Alizadeh, Haitham M. Yousof Journal of the Operations Research Society of China    2022, 10 (1): 133-158.   DOI: 10.1007/s40305-021-00349-6 Abstract （1452）      PDF       Knowledge map    Save A new generalization of the Weibull-G family is proposed with two extra shape parameters. The mathematical properties are derived in great detail. Using the Weibull and normal distributions as baseline distributions, two models are introduced. The first model is a location-scale regression model based on a new extension of the Weibull distribution. The second model is a new two-step financial risk model to forecast the daily value at risk. The flexibility and applicability of the proposed models are investigated by means of five real data sets on the lifetime and financial returns. Empirical findings of the study show that proposed models work well and produce better results than other well-known models for financial risk modeling and censored lifetime data analysis. Reference | Related Articles | Metrics | Comments（0）

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A Levenberg–Marquardt Method for Solving the Tensor Split Feasibility Problem Yu-Xuan Jin, Jin-Ling Zhao Journal of the Operations Research Society of China    2021, 9 (4): 797-817.   DOI: 10.1007/s40305-020-00337-2 Abstract （2157）      PDF       Knowledge map    Save This paper considers the tensor split feasibility problem. Let C and Q be non-empty closed convex set and $\mathcal{A}$ be a semi-symmetric tensor. The tensor split feasibility problem is to find x ∈ C such that $\mathcal{A} x^{m-1} \in Q$. If we simply take this problem as a special case of the nonlinear split feasibility problem, then we can directly get a projection method to solve it. However, applying this kind of projection method to solve the tensor split feasibility problem is not so efficient. So we propose a Levenberg– Marquardt method to achieve higher efficiency. Theoretical analyses are conducted, and some preliminary numerical results show that the Levenberg–Marquardt method has advantage over the common projection method. Reference | Related Articles | Metrics | Comments（0）

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Ordering and Pricing Decisions of a Retailer in the Presence of Multiple-Time Ordering Lian-Ju Ning, Yong Han, Zhen-Kai Lou, Xue-Feng Xia Journal of the Operations Research Society of China    2022, 10 (1): 159-171.   DOI: 10.1007/s40305-021-00342-z Abstract （1444）      PDF       Knowledge map    Save This paper studies ordering and pricing issues of a retailer who faces a linear-sensitive demand. The definition of a reasonable retail price is put forward. After that, a deterministic model for trading off sales revenue and total cost is constructed, in which the retailer determines the optimal ordering schedule and the optimal retail price simultaneously for the sake of maximizing its total profit. It is shown that the acquired retail prices are all reasonable. During the process of derivation, both ordering time points and the optimal retail price are expressed as functions of ordering times. By solving a quadratic programming model with an undetermined parameter, we demonstrate that the optimal ordering time points of the retailer are equidistant time points on the given selling periods. Further, the sensitivity of each parameter is analyzed and some meaningful conclusions are drawn. Finally, the ordering times is obtained by analyzing the derivatives of the profit function. Reference | Related Articles | Metrics | Comments（0）

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Semicontinuity of the Minimal Solution Set Mappings for Parametric Set-Valued Vector Optimization Problems Xin Xu, Yang-Dong Xu, Yue-Ming Sun Journal of the Operations Research Society of China    2021, 9 (2): 441-454.   DOI: 10.1007/s40305-019-00275-8 Abstract （2184）      PDF       Knowledge map    Save With the help of a level mapping, this paper mainly investigates the semicontinuity of minimal solution set mappings for set-valued vector optimization problems. First, we introduce a kind of level mapping which generalizes one given in Han and Gong (Optimization 65:1337–1347, 2016). Then, we give a sufficient condition for the upper semicontinuity and the lower semicontinuity of the level mapping. Finally, in terms of the semicontinuity of the level mapping, we establish the upper semicontinuity and the lower semicontinuity of the minimal solution set mapping to parametric setvalued vector optimization problems under the C-Hausdorff continuity instead of the continuity in the sense of Berge. Reference | Related Articles | Metrics | Comments（0）

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Optimal Reinsurance and Investment Strategy with Delay in Heston’s SV Model Chun-Xiang A, Ai-Lin Gu, Yi Shao Journal of the Operations Research Society of China    2021, 9 (2): 245-271.   DOI: 10.1007/s40305-020-00331-8 Abstract （2107）      PDF       Knowledge map    Save In this paper, we consider an optimal investment and proportional reinsurance problem with delay, in which the insurer’s surplus process is described by a jump-diffusion model. The insurer can buy proportional reinsurance to transfer part of the insurance claims risk. In addition to reinsurance, she also can invests her surplus in a financial market, which is consisted of a risk-free asset and a risky asset described by Heston’s stochastic volatility (SV) model. Considering the performance-related capital flow, the insurer’s wealth process is modeled by a stochastic differential delay equation. The insurer’s target is to find the optimal investment and proportional reinsurance strategy to maximize the expected exponential utility of combined terminal wealth. We explicitly derive the optimal strategy and the value function. Finally, we provide some numerical examples to illustrate our results. Reference | Related Articles | Metrics | Comments（0）

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Optimized Filling of a Given Cuboid with Spherical Powders for Additive Manufacturing Zoya Duriagina, Igor Lemishka, Igor Litvinchev, Jose Antonio Marmolejo, Alexander Pankratov, Tatiana Romanova, Georgy Yaskov Journal of the Operations Research Society of China    2021, 9 (4): 853-868.   DOI: 10.1007/s40305-020-00314-9 Abstract （2092）      PDF       Knowledge map    Save In additive manufacturing (also known as 3D printing), a layer-by-layer buildup process is used for manufacturing parts. Modern laser 3D printers can work with various materials including metal powders. In particular, mixing various-sized spherical powders of titanium alloys is considered most promising for the aerospace industry. To achieve desired mechanical properties of the final product, it is necessary to maintain a certain proportional ratio between different powder fractions. In this paper, a modeling approach for filling up a rectangular 3D volume by unequal spheres in a layer-by-layer manner is proposed. A relative number of spheres of a given radius (relative frequency) are known and have to be fulfilled in the final packing. A fast heuristic has been developed to solve this special packing problem. Numerical results are compared with experimental findings for titanium alloy spherical powders. The relative frequencies obtained by using the imposed algorithm are very close to those obtained by the experiment. This provides an opportunity for using a cheap numerical modeling instead of expensive experimental study. Reference | Related Articles | Metrics | Comments（0）

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Intuitionistic Fuzzy Laplacian Twin Support Vector Machine for Semi-supervised Classification Jia-Bin Zhou, Yan-Qin Bai, Yan-Ru Guo, Hai-Xiang Lin Journal of the Operations Research Society of China    2022, 10 (1): 89-112.   DOI: 10.1007/s40305-021-00354-9 Abstract （1466）      PDF       Knowledge map    Save In general, data contain noises which come from faulty instruments, flawed measurements or faulty communication. Learning with data in the context of classification or regression is inevitably affected by noises in the data. In order to remove or greatly reduce the impact of noises, we introduce the ideas of fuzzy membership functions and the Laplacian twin support vector machine (Lap-TSVM). A formulation of the linear intuitionistic fuzzy Laplacian twin support vector machine (IFLap-TSVM) is presented. Moreover, we extend the linear IFLap-TSVM to the nonlinear case by kernel function. The proposed IFLap-TSVM resolves the negative impact of noises and outliers by using fuzzy membership functions and is a more accurate reasonable classifier by using the geometric distribution information of labeled data and unlabeled data based on manifold regularization. Experiments with constructed artificial datasets, several UCI benchmark datasets and MNIST dataset show that the IFLap-TSVM has better classification accuracy than other state-of-the-art twin support vector machine (TSVM), intuitionistic fuzzy twin support vector machine (IFTSVM) and Lap-TSVM. Reference | Related Articles | Metrics | Comments（0）

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Augmented Lagrangian Methods for Convex Matrix Optimization Problems Ying Cui, Chao Ding, Xu-Dong Li, Xin-Yuan Zhao Journal of the Operations Research Society of China    2022, 10 (2): 305-342.   DOI: 10.1007/s40305-021-00346-9 Abstract （1571）      PDF       Knowledge map    Save In this paper, we provide some gentle introductions to the recent advance in augmented Lagrangian methods for solving large-scale convex matrix optimization problems (cMOP). Specifically, we reviewed two types of sufficient conditions for ensuring the quadratic growth conditions of a class of constrained convex matrix optimization problems regularized by nonsmooth spectral functions. Under a mild quadratic growth condition on the dual of cMOP, we further discussed the R-superlinear convergence of the Karush-Kuhn-Tucker (KKT) residuals of the sequence generated by the augmented Lagrangian methods (ALM) for solving convex matrix optimization problems. Implementation details of the ALM for solving core convex matrix optimization problems are also provided. Reference | Related Articles | Metrics | Comments（0）