运筹学中若干离散规划问题的相对差分搜索解法

运筹学中有很多离散规划问题。其中的线性规划通常用分枝定界法或割平面法，还有图上作业法求解。不论哪种方法工作量都不小，而且效率低；至于非线性规划大都是用动态规划法求解，也很麻烦、耗时。对于大规模问题，不论线性或非线性离散规划，现有解法都受到问题规模的限制；还有资源分配和背包问题至今没有见到解决方法。本文就是为了解决这些问题，提出了相对差分搜索算法。通过5个算例和其它文献中的一些算例计算验证了本法简单、快速、有效和精确，尤其不受问题规模的限制是其最大的优点。     

Aggregation of ordinal information

Our interest is with the fusion of information which has an ordinal structure. Information fusion in this environment requires the availability of ordinal aggregation operations. Basic ordinal operations are first introduced. Next we investigate conjunctive and disjunction aggregations of ordinal information. The idea of a pseudo-log in the ordinal environment is presented. We discuss the introduction of a zero like point on an ordinal scale along with the related ideas of bipolarity (positive and negative values) and uni-norm aggregation operators. We introduce mean like aggregation operators as well weighted averages on a ordinal scale. The problem of selecting between ordinal models is considered.     

Embedding up to homotopy type— The first obstruction

For a 2n?m connected map from an n-dimensional complex to a m-dimensional manifold, an obstruction to embedding up to homotopy type is defined. The vanishing of this obstruction is a necessary and sufficient condition (in the 2n?m connected case, 2n?m ? 2, m?n ?3) to obtain an embedding up to homotopy type. In case the target manifold is Euclidean space, it is shown that the obstruction vanishes if and only if certain Thom operations are trivial. A classification theorem is given in the 2n?m+1 connected case.     

Optimal Production and Marketing Planning

This paper presents an integrated production, marketing and inventory model which determines the production lot size, marketing expenditure and products selling price. Our model is highly nonlinear and non-convex and cannot be solved directly. Therefore, Geometric Programming (GP) is used to locate the optimal solution of the proposed model. In our GP implementation, we use a transformed dual problem in order to reduce the model to an optimization of an unconstrained problem in a single variable and the resulting problem is solved using a simple line search. We analyze the solution in different cases in order to study the behaviour of the model and for each case, a numerical example is used to demonstrate the implementation of our analysis.     

状态概率的E-Bayes估计与多层Bayes估计

在文献[1]中提出了参数估计的一种方法--E-Bayes估计并给出了状态概率的E-Bayes估计的定义、E-Bayes估计公式、预测模型及其在证券投资中应用,本文在此基础上将给出状态概率的多层Bayes估计、状态概率的E-Bayes估计的性质--E-Bayes估计,多层Bayes估计的关系.最后,给出模拟算例.     

1996~2017年《Operations Research》期刊发文统计分析

《Operations Research》(OR)是运筹与管理科学领域的顶级期刊,对其刊文进行统计分析,剖析国际运筹学科领域的主流研究机构及合作影响,探究当前研究热点问题及学科发展趋势,对于促进我国运筹学科领域的发展具有十分重要的指引作用.基于对WOS核心数据库中该期刊1996至2017年间全部刊文的统计分析,得出以下结论:近年来我国学者发文量稳步提升,表明我国运筹学科领域研究水平的显著提高,但其影响力仍有待进一步提升;机构合作、国际合作都有助于文章引文量的提升;引证分析显示柔性制造(流程柔性及效率)、巢式Logit模型的应用、网络收益管理等7个研究方向是当前、并继续成为运筹领域的研究热点.     

基于碳交易的闭环供应链碳减排与定价策略研究

在消费者对低碳产品存在偏好的碳交易市场中,研究两级闭环供应链中的减排与定价决策问题.对于制造商负责回收模式下的回收再制造过程,采用指数分布来刻画废旧产品质量水平的不确定性.假设新产品和再制造品存在竞争关系,建立制造商和零售商间的Stackelberg博弈模型,给出制造商确定减排投资和回收参考价格以及零售商决定两种产品的差别定价策略,通过算例分析回收产品的残值和碳交易价格对最优策略和供应链成员利润的影响.研究表明,为了获得利润最大,当碳交易的市场价格升高时,制造商应加大减排投资,且零售商应采取提高产品零售价的策略.     

Soft set theory and uni–int decision making

We firstly redefine the operations of Molodtsov’s soft sets to make them more functional for improving several new results. We also define products of soft sets and uni–int decision function. By using these new definitions we then construct an uni–int decision making method which selects a set of optimum elements from the alternatives. We finally present an example which shows that the method can be successfully applied to many problems that contain uncertainties.     

带负顾客和非空竭服务随机休假的M~([x])/G/1可修排队系统

研究了带负顾客和非空竭服务随机休假的M~([X])/G/1可修排队系统.负顾客不仅仅移除一个正在接受服务的正顾客,而且还使得服务器损坏而立即进行修理.通过构造一个具有吸收态的马尔可夫链求得了系统稳态存在的充分必要条件.利用补充变量法求得了系统的排队指标和可靠性指标.最后我们还给出了一个数值实例.