Table of Content

15 December 2021, Volume 25 Issue 4

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Evolutionary analysis on cooperative behavior of local government and the public in the public health emergencies

Zhiqi XU, Yukun CHENG, Shuangliang YAO

2021, 25(4):  1-14.  doi:10.15960/j.cnki.issn.1007-6093.2021.04.001

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With the change of human living environment, public health emergencies occur frequently in recent years. The mutual cooperation between the public and local government is an inevitable choice to deal with the public health emergencies timely and efficiently. Based on the assumption of bounded rationality, this paper discusses the evolution process of the behaviors of the public and local governments, and obtains evolutionarily stable strategies under different conditions. MATLAB is applied for simulation and to analyze how the rewards and the punishments to the public from local governments, the punishments to local governments from the superior departments, and other factors influence the public and local government's strategies. The results in this work show that an effectively promoted mutual cooperation between the public and the government and an active epidemic prevention can be achieved by improving relevant subsidy policies, popularizing epidemic-related laws and regulations, increasing the punishment for violating the epidemic-related rules and regulations, and increasing local government penalties for loosening epidemic prevention.

Optimal control strategies for two types of M/G/1 queueing systems with N-strategy and single vacation

Beilei TANG, Yinghui TANG

2021, 25(4):  15-30.  doi:10.15960/j.cnki.issn.1007-6093.2021.04.002

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This paper considers two types of M/G/1 queueing systems with N-strategy and single vacation, one of which is uninterruptible on vacation and the other is of interruptible on vacation. Using the stochastic decomposition of the steady-state queue length, the expressions of the probability generating function of the steady-state queue length are obtained. And the sensitivity of the system's idle rate and the additional average queue-length towards system parameters is discussed. Furthermore, the explicit expressions of the long-run expected cost per unit time are derived under a given cost structure. At the same time, numerical calculation examples are used to determine the control strategy N^* for minimizing the long-run expected cost per unit time as well as the combined control strategy (N^*, T^*) when the vacation time is fixed duration T.

An approximation algorithm for Robust k-product facility location problem with linear penalties

Xiaowei LI, Xiayan CHENG, Rongheng LI

2021, 25(4):  31-44.  doi:10.15960/j.cnki.issn.1007-6093.2021.04.003

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A $k$-product facility location problem can be described as follows. There is a set of customers and a set of potential sites where facility can be set up. There are $k$ different products. Each customer needs to be served with all of the $k$ different products and each facility can be set up to provide exact one product. The problem is to select a set of facility to be set up and determine an assignment for each customer to a set of $k$ facilities to provide it with $k$ distinct products. It is assumed that the capacity of any facility is unlimited and there is a non-negative cost for shipping products between each pair of locations. The aim is to minimize the sum of the setup costs and the shipping costs from facilities to customers. For simplicity, we denote the problem by $k$-PUFLP. When the cost of setting up any facility is zero, we denote by $k$-PUFLPN. When $k\geq 3$, the approximation ratio of an existing algorithm is improved to $\frac{3k}{2}-\frac{3}{2}$. When a maximum of $q$ customers are allowed to be unserved, we call it Robust $k$-product facility location problem. For this problem, we addressed an approximation algorithm with an approximate ratio of $\frac{3k}{2}-\frac{3}{2}$. For the Robust $k$-product facility location problem of linear penalties, by considering both outliers and penalty we also designed a $\frac{3k}{2}-\frac{3}{2}$ approximation algorithm.

Location problem of production and sales under carbon tax policy

Chong XIANG, Xiaoshen LI, Guanglei SUN

2021, 25(4):  45-57.  doi:10.15960/j.cnki.issn.1007-6093.2021.04.004

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This paper considers a location problem of production and sales of a production-oriented enterprise under carbon tax policy. Consumers are distributed on a straight line with linear transportation costs. In addition to pay the transportation costs of its own products, the enterprise is also responsible for the transportation costs of consumers. A profit maximization model is established, properties of the profit function are analyzed, and a solving method is given. Numerical experiments prove the effectiveness of the solving method. They show that even if the distribution of consumers is centersymmetric, the optimal location is not necessarily center-symmetric, which corrects the illusion of people. Increasing carbon tax drives the retailers approach their respective customers, increases the enterprise's cost, but may not reduce the carbon emission, which may achieve only by flexible carbon tax policy.

A common-weights interval DEA approach for efficiency evaluation and its ranking method

Yixin LAN, Bingyan WEN, Yingming WANG

2021, 25(4):  58-68.  doi:10.15960/j.cnki.issn.1007-6093.2021.04.005

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In order to solve the inconsistency of the evaluation scale in efficiency evaluation in interval data envelopment analysis, this paper proposes a common weight interval DEA model based on the target by maximizing the sum of the upper bound efficiency and the lower bound efficiency of all decision-making units (DMUs). Thus, our approach not only makes the interval efficiency of all DMUs being comparable, but also ensures that the upper bound efficiency and the lower bound efficiency are evaluated in the same scale. To rank the interval efficiencies completely a new approach which is based on the defined possibility degree formula in considering of the decision makers' interval preference is proposed. Finally, an example of measuring the industrial efficiencies in 11 coastal provinces of China is investigated to illustrate the effectiveness and the usefulness of our approaches.

Projected Levenberg-Marquardt method for stochastic R₀ tensor complementarity problems

Liyuan CUI, Shouqiang DU

2021, 25(4):  69-79.  doi:10.15960/j.cnki.issn.1007-6093.2021.04.006

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In this paper, we consider a class of stochastic R₀ tensor complementarity problems with finitely many elements. Firstly, we use Fischer-Burmeister function to transform the problem into a constrained optimization problem. Then a projected Levenberg-Marquardt method is used to solve the constrained optimization problem. Under general conditions, the global convergence of this method is proved, and the related numerical results show the efficiency of the method.

Nonlinear characterizations for approximate Benson proper efficient solutions of set-valued equilibrium problems

Yihong XU, Xincan LONG, Bin HUANG

2021, 25(4):  80-90.  doi:10.15960/j.cnki.issn.1007-6093.2021.04.007

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In the general mathematical model, because some secondary factors should be ignored, the established model is often approximate, and the solutions of mathematical model obtained by numerical algorithm are mostly approximate solutions. On the other hand, in the case of non-compact feasible set, the set of accurate solutions is often empty, while in the weaker case, the set of approximate solutions can be nonempty. In Hausdorff locally convex topological linear spaces, the approximate Benson proper efficient solutions of unconstrained and constrained set-valued equilibrium problems are studied respectively. Without any convexity assumption, necessary and sufficient optimality conditions for approximate Benson proper efficient solutions are established by using nonlinear functional.

Multitasking scheduling considering part jobs uninterrupted assignment

Chen XU, Yinfeng XU, Feifeng ZHENG

2021, 25(4):  91-100.  doi:10.15960/j.cnki.issn.1007-6093.2021.04.008

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Multitasking scheduling can be found in various application domains, such as internet services, medical field and so on. In the original multitasking model, all jobs can be interrupted. However, some emergency jobs are not allowed to be interrupted by other jobs in the production process. Motivated by the reality, we extend the original model considering that some jobs are uninterrupted job. Our objective is to minimize the maximum completion time, the total completion time, the maximum lateness, and the weighted earliness, tardiness and common due date. We provide accurate algorithms respectively for the first three problems and an approximate algorithm for the last one. Finally, we summarize the paper and put forward suggestions for future research.

The procedural proportional solution for graph games

Guang ZHANG, Wenjun XIAO, Donghua WU

2021, 25(4):  101-110.  doi:10.15960/j.cnki.issn.1007-6093.2021.04.009

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This paper studies cooperative games with graph structure, shortly graph games. By applying the proportional rule and procedural method in feasible coalitions, a so-called proportional procedure is defined and studied regarding concepts and properties. And then, according to the over-efficiency of the proposed procedure, an efficient solution concept, the procedural proportional solution, is provided by compromising with equalratio. Moreover, the stability of the solution is also investigated. Finally, the bankruptcy problems is discussed by using the proportional procedure and the procedural proportional solution, and we obtain that the proposed solution of the related graph game coincides with the proportional rule of the bankruptcy problem.

Timetabling for new middle school entrance examination

Yan LAN, Ning DING, Jiaxin LI, Wenxue YUAN, Minghui ZHANG, Xin HAN

2021, 25(4):  111-119.  doi:10.15960/j.cnki.issn.1007-6093.2021.04.010

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The course scheduling problem is a problem that all schools need to consider. Due to limitations of school resources such as teachers and classrooms, it is a challenge for all schools to organize course scheduling effectively. In recent years, high school entrance examination has been reformed to improve the level of secondary education and comprehensive quality education and students will choose subjects. The new senior high school entrance examination is divided into two major categories of electives and compulsory. Compulsory courses are Chinese, Math and English. Elective courses are six other courses, of which three are selected. The final total score will be as a college admission criteria. This scheduling problem is even more complicated and difficult. Using gurobi to optimize the course arrangement, taking the first three courses in Beijing as an example, the scheduling problem of new high school entrance examinations was investigated and studied. The final result of the course arrangement was also given. Three teachers were added as expected on the course scheduling problem.

The Smrandachely adjacent vertex-distinguishing total coloring of 2-connected outer planar graphs with maximum degree 5

Chunmei LI, Zhiwen WANG

2021, 25(4):  120-126.  doi:10.15960/j.cnki.issn.1007-6093.2021.04.011

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The adjacent vertex distinguishable total coloring is the total coloring with different sets of adjacent vertices, while the Smarandachely adjacent vertex distinguishing total coloring is the adjacent vertex distinguishing total coloring which does not contain each other in the color set of adjacent vertices. It is a further enhancement of the condition of adjacent vertex-distinguishing total coloring. We call the minimum number of colors used for a graph to satisfy Smarandachely's adjacent vertex-distinguishing total coloring as its Smarandachely adjacent vertex-distinguishing total chromatic number. In this paper, the Smarandachely adjacent vertex distinguishing total chromatic number of 2-connected outer plane graphs with maximum degree of 5 is studied by means of analytical method and mathematical induction. It is proved that if $G$ is a 2-connected outer planar graph with $\Delta(G)=5 $, then $\chi_{\rm sat}(G)\leqslant 9$.