Table of Content

15 March 2020, Volume 24 Issue 1

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A probability model for estimating the expected number of the newly infected and predicting the trend of the diagnosed

DING Zhiwei, LIU Yanyun, KONG Jing, ZHANG Hong, ZHANG Yi, DAI Yuhong, YANG Zhouwang

2020, 24(1):  1-12.  doi:10.15960/j.cnki.issn.1007-6093.2020.01.001

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After 2019 novel cornavirus disease (COVID-19) appeared in Wuhan in early December 2019, it broke out in mid-to-late January 2020 and quickly spread throughout the country. So far, it has spread in dozens of countries and regions, the scientific and efficient understanding of epidemic development is essential for prevention and control. The number of infected people is a key indicator for assessing the situation of the epidemic, helping decision-makers formulate policies in time. This paper uses the maximum likelihood estimation method to obtain estimators of the number of newly infected people across the country except Hubei province. Moreover, Bootstrap simulation enables us to obtain confidence intervals for the estimators. Based on these solutions of the model, we further calculate the number of existing infected but undiagnosed people and predict the trend of the newly diagnosed for the next few days, providing suggestions on returning to work.

A price oriented optimal production and allocation strategy of protective suppliers in the epidemic situation

TAO Jie, GAO Yan

2020, 24(1):  13-22.  doi:10.15960/j.cnki.issn.1007-6093.2020.01.002

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The outbreak of the new coronavirus causes the shortage of protective supplies, which increases the risk of infection of medical practitioners. In the epidemic situation, the market prices of the protective suppliers are distorted and cannot be applied. In this paper, we propose a mathematical programming model to guide the production, distribution and pricing mechanism of protective suppliers. Based on the model, we propose the notion of the generalized shadow price which can be used to price the protective suppliers, and further guide the manufactures to optimize their production. The advantage of the generalized shadow price over the traditional ones is that it reflects the cost for manufactures to enhance their production capacities. Furthermore, we build the relationship between the generalized shadow price and the set of Lagrange multipliers, and propose a linear programming model to compute the generalized shadow price. The numerical simulation tests show the practical value of generalized shadow prices in pricing the protective suppliers in the epidemic situation.

Development and prospect of blockchain consensus mechanism

LIU Mingxi, GAN Guohua, CHENG Yukun, XIAO Lin, LIU Shuai, FANG Yong

2020, 24(1):  23-39.  doi:10.15960/j.cnki.issn.1007-6093.2020.01.003

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As a decentralized infrastructure and distributed computing paradigm, blockchain technology has attracted a great attention from government departments, financial institutions, technology enterprises, capital markets, and so on. As the core advantage of blockchain technology, how to obtain an efficient consensus in the distributed system is an important issue which restricts the development and application of blockchain technology. At present, several research institutions and companies have proposed different consensus mechanisms applied in different application scenarios. In this paper, we conduct an in-depth analysis of several typical consensus mechanisms and their different deformation. Through comparison, the advantages and disadvantages of existing consensus mechanisms have been illustrated. Moreover, the basic requirements of new consensus mechanism have also been defined. Finally, some basic ideas in the designing of new consensus mechanism have been proposed.

Analysis of the M/G/1 repairable queueing system with D-policy and two types of failure modes

ZHONG Yao, TANG Yinghui

2020, 24(1):  40-56.  doi:10.15960/j.cnki.issn.1007-6093.2020.01.004

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This paper studies the M/G/1 repairable queueing system with D-policy and two types of failure modes. The first type of failure is the failure of the service desk during the service of a customer, the second type of failure is the failure of the service desk during the idle period, and the failure efficiency of the two types of failure modes is different. By using the total probability decomposition, L-transform, generating function and other tools, the transient distribution and equilibrium distribution of the system queue-length are discussed from any initial state. The recursive expression of the steady-state queue length distribution and the random decomposition results of the steady-state queue length are obtained. Furthermore, on the basis of establishing the cost model, the optimal control strategy D^* is discussed, which makes the system reach the minimum value in a long-term unit time by numerical examples. The optimal control strategy under the same set of parameters is compared with the optimal control strategy when the service desk does not fail.

Output-oriented super efficiency DEA model with preference cone

ZHAO Chunying, MA Zhanxin

2020, 24(1):  57-72.  doi:10.15960/j.cnki.issn.1007-6093.2020.01.005

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In this paper, the output-oriented weight restricted comprehensive super efficiency DEA model and the projection concept is proposed, in the view of traditional DEA model can not distinguish between efficiency decision making units and the super efficiency DEA model does not consider the preference of the decision maker. The relationship between the output-oriented weight restricted comprehensive super efficiency DEA model and other super efficiency DEA models is discussed. Secondly, the relationship between the optimal objective function value of the output-oriented weight restricted comprehensive super efficiency DEA model and the effectiveness of decision making unit is analyzed. The relationship between the output-oriented weight restricted comprehensive super efficiency projection and the non-dominated solution of multi-objective programming is discussed. Finally, the scientific and technological innovation efficiency of industrial enterprises in 12 regions of western China is evaluated, and the method proposed in this paper is compared with the original methods. It is concluded that the method proposed in this paper is more advantageous and reasonable.

Optimal investment and reinsurance problem with delay under the CEV model

A Chunxiang, SHAO Yi

2020, 24(1):  73-87.  doi:10.15960/j.cnki.issn.1007-6093.2020.01.006

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This paper considers the optimal investment-reinsurance problem with delay for an insurer under a constant elasticity of variance (CEV) model. Suppose that the insurer is allowed to purchase proportion reinsurance and invest her surplus in a financial market consisting of one risk-free asset and one risky asset whose price process is described by a CEV model. Under the consideration of the performance-related capital inflow/outflow, the wealth process of the insurer is modeled by a stochastic delay differential equation (SDDE). The objective of the insurer is to maximize the expected exponential utility of terminal wealth. The optimal strategies and the optimal value functions in the closed form are derived under two cases:the investment-reinsurance case and the investment-only case. Finally, some numerical examples and sensitivity analysis are provided for our results.

An stochastic algorithm for global optimization with linear constraints based on intermittent diffusion

CHEN Yong, WANG Wei, XU Yifan

2020, 24(1):  88-100.  doi:10.15960/j.cnki.issn.1007-6093.2020.01.007

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In this paper, the nonconvex global optimization problem with linear constraints is studied. Based on the effective set algorithm, a stochastic differential equation algorithm with stochastic diffusion properties is proposed. The theoretical properties and convergence of the algorithm are discussed. It is proved that the algorithm converges to the global optimal solution of the problem with probability 1. Finally, the numerical experiment results are listed.

A partial parallel splitting LQP alternating direction method of multipliers for solving monotone variational inequalities

LI Chaoqiong, LI Feng

2020, 24(1):  101-114.  doi:10.15960/j.cnki.issn.1007-6093.2020.01.008

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Logarithmic-quadratic proximal (LQP) alternating direction method of multipliers is a very effective method for solving monotone variational inequality with separable structure. It can make full use of the objective function of the separable structure, the original problem is decomposed into multiple sub-problems which is easier to be solved. Logarithmic-quadratic proximal (LQP) alternating direction method of multipliers are also suitable ones for solving large-scale problem. For monotone variational inequality problem with three separable operators, combining the augmented Lagrangian method with the LQP alternating direction method of multipliers, a partial parallel splitting LQP alternating direction method of multipliers is obtained. We construct two descent directions, the new direction is obtained by combined with the two descent directions, and an appropriate step size is derived along this new descent direction. And we prove the global convergence of the algorithm under a weaker assumption.

A review on distributionally robust chance constrained optimization problems

GENG Xiaolu, TONG Xiaojiao

2020, 24(1):  115-130.  doi:10.15960/j.cnki.issn.1007-6093.2020.01.009

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As one of the most important models in stochastic problem, the chance constrained optimization problem has been widely used in the fields of finance, engineering, management and so on. As the practical problems become more and more complex, the probability distribution of the uncertainty is difficult to predict/estimate accurately. Distributionally robust chance constrained optimization problem, as an effective model with ambiguous distributional information about uncertainty, has been proposed in the literature. In recent years, researchers have constantly developed new models for distributionally robust chance constrained optimization problems. The main purpose of this paper is to review recent advances in emerging models for distributionally robust chance constrained optimization problems and their potential applications in practice.

Approximation algorithms for single machine parallelbatch scheduling with release dates subject to the number of rejected jobs not exceeding a given threshold

LIU Xiaoxia, YU Shanshan, LUO Wenchang

2020, 24(1):  131-139.  doi:10.15960/j.cnki.issn.1007-6093.2020.01.010

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In this paper, we consider the single machine parallel-batch scheduling problem with release dates and the number of rejected jobs not exceeding a given threshold. In this problem, we are given a set of jobs and a parallel batch processing machine. Each job has its release date and processing time; for each job, it is either to be rejected or to be accepted and processed in some batch on the machine. If one job is rejected then its corresponding rejection cost should be paid. To keep a certain service level, it is required that the number of rejected jobs is not greater than a given threshold. The task is how to partition the rejected jobs and the accepted jobs with the given constraint, and determine the batches and the orders for the accepted jobs on the machine to minimize the sum of the makespan and the total rejection cost. Since the studied problem is NP-hard, we propose a pseudo-polynomial time dynamic programming exact algorithm, a 2-approximation algorithm and a fully polynomial time approximation scheme.

Neighbor sum distinguishing edge coloring of the lexicographic product of paths

TIAN Shuangliang, YANG Huan, SUOLANG Wangqing, YANG Qing

2020, 24(1):  140-146.  doi:10.15960/j.cnki.issn.1007-6093.2020.01.011

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A proper[k]-edge coloring σ of graph G is a k-proper-edge-coloring of graph G using colors in[k]={1, 2, …, k}. Let w_σ(x) denote the sum of the colors of edges incident with x, i.e., w_σ(x)=∑_e∋x σ(e), and w_σ(x) is called the weight of the vertex x with respect to σ. A neighbor sum distinguishing edge coloring σ of G is a proper[k]-edge coloring of G such that no pair adjacent vertices receive the same weights. The smallest value k for which G has such a coloring is called the neighbor sum distinguishing edge chromatic number of G and denoted by χ'_∑(G). We obtained the exact values of this parameter for the lexicographic product P_n[H] of a path P_n and a connected simple graph H, where H is a Class 1 regular graph, a path, the complement of a complete graph, respectively.

An approximation algorithm for reclaimer scheduling

WANG Yizhan, ZHANG An, CHEN Yong, CHEN Guangting

2020, 24(1):  147-154.  doi:10.15960/j.cnki.issn.1007-6093.2020.01.012

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This paper studies the reclaimer scheduling problem that arises in the management of a stockyard at a coal terminal. In this problem, we are given a single reclaimer initially located at the left end of a stock pad of length L. The reclaimer can either travel across or reclaim stockpiles on the stock pad, with a speed ratio of s ≥ 1. The scheduler has to decide the placement positions of the stockpiles on the stock pad and sequence the reclaiming of the stockpiles so as to minimize the total time serving the arrived vessels. We show that there exists an approximation algorithm with a worst case ratio no larger than 1 + 1/4s, provided that the reclaimer has to return to the endpoints of the stock pad.

Two-sided game matching with uncertain preference ordinal

LIN Yang, WANG Yingming

2020, 24(1):  155-162.  doi:10.15960/j.cnki.issn.1007-6093.2020.01.013

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Owing to the problem of two-sided matching decision with uncertain preference ordinal (UPO), the existing methods mainly consider the overall payoff only. Yet the individual payoff and strategic operations during matching are often neglected in mutual choices. Based on the criteria of maximum satisfaction, a process for handling UPO is developed to derive payoff matrix. Then, a game-based matching model is built from the viewpoint of individual rational. This model takes account of both overall and individual payoff, which is combined with the idea of matrix game. Moreover, the results are proved to be Nash equilibrium. Finally, discussions on different strategic choices, as well as their advantages and limits analysis are presented.