Table of Content

15 October 2025, Volume 42 Issue 5 Previous Issue   

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Study on Single-machine Problem with Variable Processing Time and Rejection and a Deteriorating Maintenance Activity ZHANG Sixian, MA Ran 2025, 42 (5):  793-805.  doi: 10.3969/j.issn.1005-3085.2025.05.001 Abstract ( 45 )   Save A single-machine production scheduling problem is addressed for jobs with outsourcing and machine with deteriorating maintenance activity. We consider the learning effect and the deteriorating effect. The actual processing time of a job is a function on its position. In order to improve the productivity of the machine, each machine has at most one deteriorating maintenance activity throughout the scheduling horizon, where the impact of performing deteriorating maintenance activities is reflected in the reduction of job processing time. The duration of the maintenance activity increases linearly with its starting time. The objective is to find the position of the maintenance activity and the most available processing order of the task such that the sum of the maximum, the total completion time, the total weighted completion time and the cost to be paid for outsourcing is minimized. When the scheduling measures are the makespan, total completion time, we provide polynomial time algorithms to solve these problems, respectively. When the scheduling measures is the total weighted completion time, we introduce pseudo-polynomial time algorithms to solve this NP-hard problem. Related Articles | Metrics

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Performance Analysis and Optimal Control of the Inventory Strategy of Two-stage Production-service Inventory System YUE Dequan, CHI Yanwei, WEI Yining 2025, 42 (5):  806-822.  doi: 10.3969/j.issn.1005-3085.2025.05.002 Abstract ( 82 )   Save This paper studies a two-stage production-service inventory system which is composed of a  production center and a distribution center. A new production strategy, $(rQ+m,KQ)$ production strategy, is proposed for the production center. The distribution center adopts $(s,Q)$ inventory replenishment strategy. Customers arrive according to a Poisson process, and the lead time, the service time and the production time are assumed to be exponentially distributed. Firstly, the continuous-time Markov model is established, and the steady-state condition of the system is obtained by using the theory of quasi-birth-and-death process. Secondly, by solving the steady-state probability distribution of the modified system model, some steady-state probability distribution of the system is obtained. Then formula of computing of the steady-state performance indexes of the system are given. Finally, by using genetic algorithm, the optimal inventory strategies and average cost of the system that aim to minimize the average cost of the system are calculated. The four production inventory strategies of the system are compared by numerical examples. The results show that under certain conditions, the average cost of the system is the lowest when the production center adopts the $(m,KQ)$ strategy. Related Articles | Metrics

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Optimization of Picking Routing Strategies Based on the Chevron Warehouse Layout Design LIU Huwei, WANG Fan, ZHAO Junhui, YANG Jianglong, ZHOU Li 2025, 42 (5):  823-844.  doi: 10.3969/j.issn.1005-3085.2025.05.003 Abstract ( 38 )   Save To enhance the picking efficiency in modern warehousing systems, this paper is based on the improved layout design of the Chevron warehousing layout. According to its characteristics, a calculation model for the walking distance of picking paths is constructed. Genetic algorithm (GA), cuckoo search (CS) algorithm, and ant colony algorithm (ACO) are utilized as optimization approaches to improve the path optimization problem in order picking processes. These algorithms are simulated and compared with two heuristic path strategies, namely {S-shape} and {Return}. The experimental results demonstrate that when the number of locations to be accessed in order picking is 10, all three algorithms can optimize both {S-shape} and {Return} strategies. As the number of locations increases to 20 and 40, the optimization of {S-shape} strategy gradually becomes ineffective for all three algorithms. For the {Return} strategy, when the number of locations reaches 30, the GA weakens, while the CS algorithm and ACO achieve good results. However, the former has an advantage in terms of runtime. Related Articles | Metrics

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Grey Rolling Prediction of New Energy Private Passenger Vehicle Sales SONG Nannan, LI Shuliang, GONG Ke 2025, 42 (5):  845-874.  doi: 10.3969/j.issn.1005-3085.2025.05.004 Abstract ( 28 )   Save New energy private passenger vehicles play an important role in achieving the carbon peak target, and scientific and accurate prediction of sales volume is the basic prerequisite for achieving the target. The traditional grey prediction model for new energy vehicles only considers the regularity of historical data and rarely considers the significant impact of new energy vehicle sales data on future trends, resulting in differences between the model's prediction results and qualitative conclusions. To improve the accuracy of the model and reduce errors, this article uses the real number field fractional order grey generation operator to optimize the three-parameter discrete grey prediction model. Based on the principle of new information priority and combined with rolling mechanism, a three-parameter discrete grey rolling model is constructed to predict the sales of new energy private passenger vehicles in China. The results show that the sales of new energy private passenger vehicles in 2030 are 6.849~5 million units, which can achieve 88.15 of the carbon peak target for the current year. Based on the predicted values, countermeasures and suggestions are proposed to promote sales. Related Articles | Metrics

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Bipartite Consensus of Fractional Delayed Multi-agent Systems YANG Ran, LIU Song, LI Xiaoyan 2025, 42 (5):  860-874.  doi: 10.3969/j.issn.1005-3085.2025.05.005 Abstract ( 32 )   Save The bipartite consensus of fractional multi-agent systems with delay under fixed and switching topologies is addressed in the article. First, for a fixed topology, a delayed control protocol is developed and several feasible conditions of bipartite consensus are proposed with the help of fractional-order Razumikhin theory and signed graph theory. Secondly, regarding the switching topologies, the bipartite consensus is further investigated by the aid of common Lyapunov function method. The proposed way can commendably surmount the trouble arising from time delay, fractional-order derivative and switchings. Ultimately, the feasibility of theoretical conclusions is verified though two simple examples. Related Articles | Metrics

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Balanced Truncation Model Reduction of Large-scale Second-order Systems via Laguerre Functions XIE Lixin, XIAO Zhihua, DAI Liu 2025, 42 (5):  875-888.  doi: 10.3969/j.issn.1005-3085.2025.05.006 Abstract ( 24 )   Save This study considers a balanced truncation model order reduction method of large-scale second-order systems via Laguerre functions. The proposed method uses the matrix exponential functions in the space spanned by Laguerre functions to compute the low-rank decomposition. The corresponding balanced system is constructed by the singular values structure of the second-order system.  Then, the reduced second-order model is obtained by truncating the states corresponding to the small singular values. Finally, the validity of the proposed method is shown by a given numerical example. Related Articles | Metrics

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New Criteria for Generalized Nekrasov Matrices LI Qi, WANG Shiyun, LV Zhenhua, SUN Xu 2025, 42 (5):  889-904.  doi: 10.3969/j.issn.1005-3085.2025.05.007 Abstract ( 26 )   Save Generalized Nekrasov matrices, also known as nonsingular H-matrices, have a wide range of applications. Judging whether a matrix is a generalized Nekrasov matrix is an important research topic, which has attracted the attention of a large number of scholars. In this paper, two new criteria for generalized Nekrasov matrices are proposed. By constructing a positive diagonal matrix with diagonal elements less than or equal to 1, the lower triangle part of Nekrasov sum was reduced and then the new criteria improved several existing results. In order to further illustrate the results proposed in this paper, four numerical examples are designed in the last section. The numerical examples show that each of two new criteria can be better than the other one and both are weaker than some existing conditions. The method of reducing the lower triangle part of Nekrasov sum provides a new idea for the discrimination of generalized Nekrasov matrices. Related Articles | Metrics

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Solutions and Numerical Simulation of a Fractional Differential Coupling System with Atangana-Baleanu-Caputo Derivative LIN Xuefan, HU Weimin, SU Youhui, YUN Yongzhen 2025, 42 (5):  905-917.  doi: 10.3969/j.issn.1005-3085.2025.05.008 Abstract ( 36 )   Save In this paper, we are concerned with the existence and uniqueness of solutions for a class of three-point boundary value problems involving coupled differential systems with Atangana-Baleanu-Caputo fractional derivatives. The research employs upper-lower solution techniques combined with monotone iteration methods to establish sufficient conditions for the existence and uniqueness of maximal and minimal solutions. Furthermore, by constructing Green's functions and analyzing their properties, we rigorously prove the existence and uniqueness of extremal solutions while providing precise error estimates. To demonstrate the practical significance of our theoretical findings, we present a concrete application case that validates the system's effectiveness in real-world scenarios. Numerical simulations are also conducted to provide additional verification of the theoretical analysis, confirming the reliability of our proposed approach. Related Articles | Metrics

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Estimating the Security Parameters for the Implementation of Discrete Gaussian Sampling Algorithms over the Integers SHEN Jing, YANG Xin, DU Yusong 2025, 42 (5):  918-934.  doi: 10.3969/j.issn.1005-3085.2025.05.009 Abstract ( 81 )   Save Discrete Gaussian sampling over the integers is one of the fundamental building blocks of lattice-based cryptography. The sampling algorithm can usually be designed by using Knuth-Yao sampling or inversion sampling method. Since this kind of algorithms are to realize sampling from approximate discrete Gaussian distributions, a key problem is to estimate the R\'enyi divergence between the approximate distribution and the ideal distribution, and determine the tailcut bound and probability precision, so as to balance the sampling efficiency and the security of lattice-based cryptosystems. However, due to the R\'enyi divergence depending on the variations of the tailcut bound and probability precision, it needs to preset the parameters and repeatedly check whether the value of divergence achieves the upper bound of security. Based on some more detailed theoretical analysis of the R\'enyi divergence of discrete Gaussian distributions over the integers, a method of directly calculating the tailcut bound and probability precision by using estimation formulas is suggested, and two estimation formulas are given respectively. There is no need for us to preset parameters when using the estimation formulas, nor is there a need to use high-precision floating-point arithmetic. A proper tailcut bound and a probability precision can be determined only by inputting key parameters and calculating once. This greatly simplifies the process of determining them, which is helpful to the implementation of the sampling algorithm. The comparison between the estimated results and the actual results shows that, for the parameter $\sigma$ between $2$ and $50$, the difference between the tailcut bound estimated by the formula is less than $1.0$ than the minimum tailcut bound meeting the security requirement, and the difference between the probability precision estimated by the formula and the minimum precision meeting the security requirement is only with in $5$ bits. The estimation effect is good. Related Articles | Metrics

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Dynamics Modeling and Study of Echinococcosis with Sheep Input HE Yiwei, CUI Qianqian 2025, 42 (5):  935-948.  doi: 10.3969/j.issn.1005-3085.2025.05.010 Abstract ( 41 )   Save A transmission dynamic model of echinococcosis among dogs, sheep and eggs was formulated to evaluate the effect of sheep input on the spread of echinococcosis. The global dynamic behavior of the model was analyzed by Lyapunov direct method and cooperative system theory.  Without the input of infected sheep, the dynamic behavior of the model depends on the basic reproduction number $R_0$, that is, when ${{R}_{0}}<1$, the disease-free equilibrium is global asymptotically stable, and when ${{R}_{0}}>1$, the endemic equilibrium is global asymptotically stable which means that the disease persists. With the input of infected sheep, the only endemic equilibrium theoretically is global asymptotically stable, indicating that the disease persists. The numerical simulation further discussed the influence of sheep input on transmission of echinococcosis. The results showed that when sheep are input, inputting immunized sheep but not infected sheep will be beneficial to local echinococcosis prevention and control. If infected sheep are input, the success rate of screening of infected sheep is the key factor affecting the transmission of echinococcosis. The higher the success rate of screening, the fewer infected sheep are input, and the lower the prevalence of echinococcosis. These results may provide technical supports for the prevention and control of echinococcosis in areas where sheep are input. Related Articles | Metrics

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Restricted Estimation for Semi-varying Coefficient Panel Data Models with Fixed Effects HE Bangqiang, ZHAO Rui 2025, 42 (5):  949-962.  doi: 10.3969/j.issn.1005-3085.2025.05.011 Abstract ( 27 )   Save This paper investigates statistical inference for semi-varying coefficient panel data models with fixed effects subject to linear restrictions. By incorporating fixed effects to control for time-invariant heterogeneity across individuals and employing varying coefficient functions to capture nonlinear covariate-response associations, the model mitigates two key limitations: inflexibility in traditional parametric models and the curse of dimensionality in nonparametric models. It further provides theoretical support for empirically prevalent linear restrictions such as economic structural hypotheses and policy intervention conditions. The study first establishes unrestricted estimators for parametric and nonparametric smooth coefficient functions via restricted profile least squares. Subsequently, individual dummy variables are introduced to isolate fixed effects, thereby eliminating their impact on the dependent variable. Finally, linear restrictions are imposed to derive restricted estimators for parameters, nonparametric functions, and error variances using the Lagrange multiplier method. Under regularity conditions, the restricted estimators for parameters, nonparametric functions, and error variance are rigorously proven to exhibit asymptotic normality. Monte Carlo simulations demonstrate that restricted estimation significantly enhances parameter estimation accuracy in finite samples. Moreover, when the correlation between fixed effects and covariates intensifies, the robustness advantages of restricted estimation become more pronounced. Related Articles | Metrics

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Research on Slack Due-date Assignment Scheduling with a Maintenance Activity WU Wei, WANG Jibo 2025, 42 (5):  963-973.  doi: 10.3969/j.issn.1005-3085.2025.05.012 Abstract ( 35 )   Save This paper studied a single machine scheduling with a slack due-date and a maintenance activity which is deteriorating and resource-dependent, where the actual processing time of the job depends on whether it is processed before or after the maintenance activity. The due-date of the job is the sum of its actual processing time and the slack variable (i.e., the common flow allowance). The objective of this problem is to determine the sequence of the jobs, the location of the maintenance activity, the value of the slack variable, and the resources consumed by the maintenance activity to minimize the total cost of the earliness, tardiness, slack due-date and resource consumption. For a given sequence, the value of slack variable is the starting processing time of some job in the sequence, through the cases to discuss the location of the maintenance activity, the objective function is transformed into a function which is only related to the sequence of the jobs and the resources respectively. The minimum value of the objective function is obtained by transforming it into an assignment problem or using the vector matching rule. Finally, the corresponding algorithm is given and we prove that the problem is polynomially solvable. Related Articles | Metrics

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Iterative Algorithm for Matrix Optimization Problem in Salient Object Detection Model HUANG Weiming, DUAN Xuefeng 2025, 42 (5):  974-982.  doi: 10.3969/j.issn.1005-3085.2025.05.013 Abstract ( 29 )   Save In order to improve the accuracy, resolution and computational efficiency of image salient object detection, a new salient object detection model is constructed by combining Schatten-$p$ norm and $l_{2,1}$-norm by using the relationship between image background space and image space. Compared with the traditional saliency object detection model based on the low-rank approximation of the nuclear norm, the new model considers the relationship between the image feature space and the background space, and the Schatten-$p$ norm can be better approximated by the low-rank function on numerical proportional than nuclear norm. For the matrix optimization problem of the new model, a fixed-point iterative algorithm is designed for solving the problem, and the feasibility is verified on the standard data sets of four salient object detection models, and the comparison experiments with four commonly used algorithms are also carried out. The experimental results verify that the algorithm has high computational efficiency and accuracy. Related Articles | Metrics

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The Study on Characteristics of Asymptomatic Patients of COVID-19 in China Based on Change-point Models SUN Zhiguo, JIN Hao, SU Menglin 2025, 42 (5):  983-990.  doi: 10.3969/j.issn.1005-3085.2025.05.014 Abstract ( 35 )   Save Based on the data released by the National Health Commission on the total number of COVID-19 patients and the number of asymptomatic patients from December 12, 2021 to December 12, 2022, this paper discusses the evolving trend of the proportion of asymptomatic patients in the total number of COVID-19 patients. Using the mean multiple point model and binary segmentation method, the Ratio test statistic is introduced and the Block Bootstrap method is used to empirically analyze the fluctuation law of the observed data. The results showed that the proportion of asymptomatic infections in the total number of COVID-19 infections showed a significant upward trend, with high volatility and high jump characteristics. According to the multiple change point location estimation method, the data is divided into five stages. On this basis, the mechanism between the data changes and the types of infected strains, temperature, regional policies and other factors at different stages was explored. Related Articles | Metrics