环的投射自由性的研究

引进了两类新环,进而研究了其投射自由性,得到了群环上的模结构,推广了Quillen-Suslin定理.     

自由群的直积的检验元素的注记

本文研究了自由群的直积的检验元素,通过对直积的自同态的分解,得到了直积中的元素为检验元素的充分必要条件,改进了O'neill和Turner的结果.此外,构造了两类具体的检验元素.     

幂格与商格的关系的注记

研究了分配格上的幂格,给出了格的相对凸子格的概念,得到了分配格上的幂格的一个充要条件,建立了幂格与商格的联系.     

基于GRA-DEA模型的有关农民收入的九城市的评价

有关农民收入,文章以山西省九个城市为例进行了评价.首先用灰色关联分析法分析了2016年这些城市的有关数据,筛选出影响农民收入的主要因素;其次构建了指标体系,利用数据包络分析法对有关农民收入九个城市进行了DEA有效性评价;再次对非DEA有效的城市,借助投影公式探索了改进方法;最后得出了九城市分为两类的结论,提出了针对性的建议.     

标准体系的使用期的模型与分析

本文提出了关于标准体系使用期的两个模型。首先定义了标准使用期,然后讨论了模型的合理性。通过模型讨论了标准使用期的性质,给出了数值示例。提出了需进一步研究的问题。     

基于FAHP的择偶偏好的探讨

择偶是社会成员以婚恋为目的选择异性对象的一种行为,是婚姻过程中一个十分重要的环节,如何选择一个适合自己的配偶就成为了当今社会的一个重要问题.从解决多属性决策问题的角度来思考择偶问题,并采用了层次分析法与模糊理论相结合的方法对择偶的评价与选择进行了分析,初次提出了择偶吻合度的概念,并在此基础上建立了择偶指标评价体系模型.通过案例具体分析了择偶的评价与选择的过程,分析结果表明方法处理择偶问题是有效的.     

随机环境下的一类衍生的ARCH模型的极限行为

提出了随机环境下的幂变换门限自回归条件异方差模型,得出了其以几何速率收敛的充分条件.该模型反映了动力系统受随机环境干扰的现象,能更好的拟合现实世界中的诸多实际问题.另一方面,本文推广了自回归条件异方差模型,改善了模型的适应性程度,能够更好地适用于各种不同的金融市场价格行为波动的现象.     

含有共轭三键的高聚物的掺杂机制的探讨

本文从实验事实出发,对含有共轭三键的共轭高聚物——聚丁二炔的掺杂及电导的特点进行了详细的分析;对聚丁二炔晶体掺杂的机制进行了初步的探讨;从结构相变的角度出发,提出了一个掺杂模型,并从能量的角度估算了由于掺杂引起链段结构改变所需的能量,较好地解释了聚丁二炔晶体掺杂未取得成功的原因.     

由自然数的因子构成的半群

本文首先介绍了半群、群的定义,研究了自然数n取何值时,通过定义相应的代数运算,使得它的因子集构成半群、群,从而为半群的代数理论提供了一个有趣的实例.     

区间数的绝对值与区间值函数的极限

研究了区间数的绝对值和区间值函数的极限问题.首先,讨论了区间数的H-差的性质,得到了H-差的两个运算法则;然后,给出了区间数的绝对值概念,并讨论了区间数绝对值的性质;最后,借助区间数的H-差和绝对值的概念,建立了区间值函数极限概念的一种新的表达方式,给出了极限存在的充分必要条件,证明了极限值的唯一性及对加法运算和数乘运算的封闭性.     

三种新变形的全一问题

该文研究三种新变形的全一问题及最小全一问题. 原始的全一问题可被形象的称为顶点点亮顶点问题, 而这三类新问题则分别被称为顶点点亮边问题,边点亮顶点问题,边点亮边问题. 顶点点亮顶点问题已经得到了广泛的研究. 比如,解的存在性问题和求解的有效算法已经被解决,一般图上的最小顶点点亮顶点问题已经被证明是NP- 完备的,树、单圈图和双圈图上的最小顶点点亮顶点问题的线性时间最优算法也已被给出等. 该文对于顶点点亮边问题,证明一个图有解当且仅当它是二部图,因此只可能有两组解和最优解. 对于边点亮顶点问题,证明一个图有解当且仅当它包含偶数个顶点,并通过将其最优问题多项式变换成最小权的完美匹配问题,得出一般图上的最小边点亮顶点问题可在多项式时间内求解. 边点亮边问题可归约成线图上的顶点点亮顶点问题.     

一种新的向量互补问题

本文在实局部凸空间中引入了一种新的向量互补问题,这一向量互补问题不仅包含了由Ｙｕ和Ｙａｏ提出的广义向量互补问题由Ｃｈｅｎ和Ｙａｎｇ定义的弱向量互补问题,而且还包含了Ｉｓａｃ意义下的隐互补问题。本文还讨论了新的向量互补问题,向量变分不等式,向量单向极小化问题和最小元问题之间的关系,给出了这一向量互补问题解的存在定理。     

Production planning with discounting and stochastic demands

A general continuous review production planning problem with stochastic demand is considered. Conditions under which the stochastic problem may be correctly solved using an equivalent deterministic problem are developed. This deterministic problem is known to have the same solution as the stochastic problem. Moreover, conditions are established under which the deterministic equivalent problem differs from a commonly used deterministic approximation to the problem only in the interest rate used in discounting. Thus, solving the stochastic problem is no more difficult than solving a commonly used approximation of the problem.     

The Vehicle Routing-Allocation Problem: A unifying framework

Summary In this paper the Vehicle Routing-Allocation Problem (VRAP) is presented. In VRAP not all customers need be visited by the vehicles. However customers not visited either have to be allocated to some customer on one of the vehicle tours or left isolated. We concentrate our discussion on the Single Vehicle Routing-Allocation Problem (SVRAP). An integer linear programming formulation of SVRAP is presented and we show how SVRAP provides a unifying framework for understanding a number of the papers and problems presented in the literature. Specifically the covering tour problem, the covering salesman problem, the median tour problem, the maximal covering tour problem, the travelling salesman problem, the generalised travelling salesman problem, the selective travelling salesman problem, the prize collecting travelling salesman problem, the maximum covering/shortest path problem, the maximum population/shortest path problem, the shortest covering path problem, the median shortest path problem, the minimum covering/shortest path problem and the hierarchical network design problem are special cases/variants of SVRAP.     

Pendants-median支撑树及其一个相关问题:复杂性和算法

The complexity status of Pendants-median spanning tree problem is an open problem. Using the complexity of the X3C problem, the paper proves that Pendants-median spanning tree problem is NP-complete. Global-median spanning tree problem is a related problem. Using the complexity of 3SAT, the paper proves that this problem is also NP-complete, and a polynomial -time algorithm to this problem is given, whose time complexity is O(n^3).     

Complexities and algorithms for synchronized scheduling of parallel machine assembly and air transportation in consumer electronics supply chain

In this paper, we study the problem of synchronized scheduling of assembly and air transportation to achieve accurate delivery with minimized cost in consumer electronics supply chain. This problem was motivated by a major PC manufacturer in consumer electronics industry. The overall problem is decomposed into two sub-problems, which consist of an air transportation allocation problem and an assembly scheduling problem. The air transportation allocation problem is formulated as an integer linear programming problem with the objective of minimizing transportation cost and delivery earliness tardiness penalties. The assembly scheduling problem seeks to determine a schedule ensuring that the orders are completed on time and catch the flights such that the waiting penalties between assembly and transportation is minimized. The problem is formulated as a parallel machine scheduling problem with earliness penalties. The computational complexities of the two sub-problems are investigated. The air transportation allocation problem with split delivery is shown to be solvable. The parallel machine assembly scheduling problem is shown to be NP-complete. Simulated annealing based heuristic algorithms are presented to solve the parallel machine problem.     

图论中若干著名问题的历史注记

考察了哥尼斯堡七桥问题,最小生成树问题,旅行推销员问题,分派问题,最大流问题,中国邮递员问题和四色问题等著名图论问题的历史背景.     

Single machine stochastic JIT scheduling problem subject to machine breakdowns

In this paper we research the single machine stochastic JIT scheduling problem subject to the machine breakdowns for preemptive-resume and preemptive-repeat.The objective function of the problem is the sum of squared deviations of the job-expected completion times from the due date.For preemptive-resume,we show that the optimal sequence of the SSDE problem is V-shaped with respect to expected processing times.And a dynamic programming algorithm with the pseudopolynomial time complexity is given.We discuss the difference between the SSDE problem and the ESSD problem and show that the optimal solution of the SSDE problem is a good approximate optimal solution of the ESSD problem,and the optimal solution of the SSDE problem is an optimal solution of the ESSD problem under some conditions.For preemptive-repeat,the stochastic JIT scheduling problem has not been solved since the variances of the completion times cannot be computed.We replace the ESSD problem by the SSDE problem.We show that the optimal sequence of the SSDE problem is V-shaped with respect to the expected occupying times.And a dynamic programming algorithm with the pseudopolynomial time complexity is given.A new thought is advanced for the research of the preemptive-repeat stochastic JIT scheduling problem.     

限制情况下装卸工问题的最优解

装卸工问题是从现代物流技术中提出的一个实际问题,这个问题的雏形早在上个世纪60年代中国科学院数学研究所就提出和研究过.现代物流技术迅速发展,促成和推动装卸工问题的提出和研究.装卸工问题是一个新的NP困难的组合优化问题,首先介绍装卸工问题及限制情况下装卸工问题的数学模型,然后分析限制情况下的装卸工问题的性质,最后给出该问题的所有最优解.     

关于二层规划的逼近问题

下层问题以上层决策变量作为参数,而上层是以下层问题的最优值作为响应 的一类最优化问题——二层规划问题。我们给出了由一系列此类二层规划去逼近原二层规划的逼近法,得到了这种逼近的一些有趣的结果.