次模函数最大化的流算法综述

次模函数优化在计算机科学、数学、经济学等学科得到广泛研究.大数据环境下的次模优化是相对较新的研究领域,受到更多关注.特别地,考虑基于流模型的次模最大化问题.在该问题中,数据以流的形式呈现,其目的是从数据流中抽取满足某些特性的稀疏子集,最大化次模收益函数值.介绍了基于流模型的次模最大化问题的阈值和优先权方法,同时也介绍了若干次模最大化变形的流算法进展.     

对偶理论在福利经济学中的应用

本文首先在效用函数为凹的条件下,建立了政府追求社会福利最大化和资源消耗最小化的优化模型,然后运用对偶理论证明了在政府调控下,社会福利的最大化和资源消耗的最小化能够同时实现,并给出了政府对不同收入消费者实行的个人所得税率与补贴率,最后指出社会福利最大化点是帕累托最优的,     

市值升级考

当中国上市公司经营目标从追求利润最大化转向追求价值最大化,市值管理成为摆在CFO面前的升级考卷。在考卷上,有“价值创造”这样的基础题,有“价值实现”这样的问答题,也有“价值经营”这样的加分题。考试成绩决定着上市公司的生死存亡,并且,没有补考。     

兼顾多种决策目标的一类资本结构优化模型

本建立了一个兼顾利润最大化、企业价值最大化、股东财富最大化和经理利益最大化目标的资本结构优化模型，模型最优化条件隐含：在利润最大化前提下，经理利益最大化目标和股东财富最大化目标之间存在冲突，双方冲突协调的结果有利于实现企业价值最大化。     

确定阀值下社会影响力最大化模型研究

确定阀值下社会影响力最大化问题:在社会网络中,如果用户来自邻居的影响力超过固定阀值,则该用户保持激活并影响其他的未激活邻居,当未有新的激活用户时停止扩散,如何选择最初的初始种子使得最终激活的用户数量最大化。该问题广泛存在于新产品扩散、技术推广、信息传播等营销活动。本文分别根据影响力扩散的扩散结果和扩散过程建立了两个整数规划模型。通过计算实验,我们发现基于扩散过程的模型更容易被商业优化软件(Gurobi)求解。同时,实验显示缩减扩散阶段只损失少量的激活数量,却可以节约大量的计算时间。最后,论文在求解模型的基础上,测试了贪婪算法的计算绩效。     

基于离差最大化的挤奶机方案综合评价

针对以往挤奶设备方案评价过程中权重确定存在的主观随意性,提出了一种新的基于离差最大化方法的挤奶机方案综合评价方法.首先从经济性、技术性和质量三个角度建立了多层次的挤奶机方案综合评价指标体系,然后介绍了属性权重完全未知时利用离差最大化方法确定属性权重的基本原理.在此基础上,建立了基于离差最大化方法的挤奶机方案综合评价模型.最后通过仿真实例对三型挤奶机方案进行了评价和分析,验证了方法的可行性和有效性.     

处理单调性，数列、函数不尽相同

在经济领域里，厂商都要追求利润的最大化，同时，厂商对利润的追求要受到市场条件的限制，不可能实现无限大的利润。     

次模函数最大化的流算法综述

次模函数优化在计算机科学、数学、经济学等学科得到广泛研究.大数据环境下的次模优化是相对较新的研究领域,受到更多关注.特别地,考虑基于流模型的次模最大化问题.在该问题中,数据以流的形式呈现,其目的是从数据流中抽取满足某些特性的稀疏子集,最大化次模收益函数值.介绍了基于流模型的次模最大化问题的阈值和优先权方法,同时也介绍了若干次模最大化变形的流算法进展.     

基于广告、技术、奖励的二级供应链效益最大化研究

研究了做广告、引进先进技术、奖励员工对供应链效益影响问题.针对单个制造商与单个零售商组成的二级供应链,基于弹性需求,在促销-价格敏感需求、质量-敏感需求与奖励-敏感成本条件下构建模型.以整个供应链的利润之和最大,且制造商与零售商利润之差的平方和最小为目标.首先,通过Lagrange数乘法求解,判断对应的Hesse矩阵.其次,确定了广告、技术与奖励员工的最佳投入量,实现供应链效益最大化,提高供应链的经济效益.同时,也通过收益共享,实现供应链的协调性,优化供应链产业结构.最后运用数值实验来具体说明各因素对供应链最大效益的影响.     

基于网络效用最大化的多路径网络拥塞控制研究

随着互联网的飞速发展,互联网用户和应用都在快速增长,对于网络服务质量的要求也越来越高,拥塞控制已经成为一个十分重要的问题.基于网络效用最大化的模型研究了多路径网络的拥塞控制问题,将此问题建模为基于用户发送速率的凸规划问题,基于对偶分解得到了分布式的求解方法,仿真结果验证了算法的收敛性.研究内容对多路径的TCP开发具有一定的参考意义.     

消费者公平偏好对制造商开通直销渠道的影响研究

研究了消费者公平偏好对制造商开通直销渠道的影响,并分析消费者公平偏好对制造商和零售商的最优决策、制造商开通直销渠道意愿、零售商利润、以及消费者剩余等的影响。最后通过算例分析消费者公平偏好对制造商开通直销渠道意愿的影响。研究发现:不存在消费者公平偏好时,制造商仅在直销成本较小时开通直销渠道;当直销成本较大时,制造商不应开通直销渠道。然而,消费者公平偏好会降低制造商开通直销渠道的意愿;即使无直销成本,若消费者公平偏好较大,制造商也可能不会开通直销渠道。     

Optimal payoff under the generalized dual theory of choice

We consider portfolio optimization under a preference model in a single-period, complete market. This preference model includes Yaari’s dual theory of choice and quantile maximization as special cases. We characterize when the optimal solution exists and derive the optimal solution in closed form when it exists. The optimal portfolio yields an in-the-money payoff when the market is good and zero payoff otherwise. Finally, we extend our portfolio optimization problem by imposing a dependence structure with a given benchmark payoff.     

Proper equality constraints and maximization of index vectors

In solving many practical problems, we have to deal with conflictive multiple objectives (in performance, cost, gain, or payoff, etc). Can all such objectives be achieved simultaneously? The general answer is negative. That is, most multiple-objective problems do not have supreme solutions that can satisfy all of the objectives. Many broader definitions of optimality like Pareto optimum, efficient point, noninferior point, etc, have been introduced in various contexts, so that most multiple-objective problems can have optimal solutions. But such optimal solutions do not in general yield unique vectors of optimal indexes of the conflictive multiple objectives. In most cases, we have to make appropriate tradeoffs, compromises, or choices, among those optimal solutions. To obtain the set of all such optimal solutions (in particular, the set of all optimal index vectors), say for a comprehensive study on appropriate tradeoffs, compromises, or choices, a usual practice is to optimize linear combinations of the multiple-objective functions for various weights. The success of such approach relies heavily on a certain directional convexity condition; in other words, if such convexity is absent, this method will fail to obtain essential subsets. The method of proper equality constraints (PEC), however, relies on no convexity condition at all, and through it we can obtain the entire set. In this paper, we attempt to lay the foundation for the method of PEC. We are mainly concerned with obtaining the set of all maximal index vectors, for most of the broader-sense optimal solutions are actually expressed in terms of maximal index vectors (Ref. 1). First, we introduce the notion of quasisupremal vector as a substantially equivalent substitute for, but a rather practical and useful extension of, the notion of maximal vector. Then, we propose and develop the method of PEC for computing the set of all quasisupremal (or maximal) index vectors. An illustrative example in the allocation of funds is given. One of the important conclusions is that optimizing the index of one objective with the indexes of all other objectives equated to some arbitrary constants may still result in inferior solutions. The sensitivity to variations in these constants are examined, and various tests for quasisupremality (maximality, or optimality) are derived in this paper.     

Maximising entropy on the nonparametric predictive inference model for multinomial data

The combination of mathematical models and uncertainty measures can be applied in the area of data mining for diverse objectives with as final aim to support decision making. The maximum entropy function is an excellent measure of uncertainty when the information is represented by a mathematical model based on imprecise probabilities. In this paper, we present algorithms to obtain the maximum entropy value when the information available is represented by a new model based on imprecise probabilities: the nonparametric predictive inference model for multinomial data (NPI-M), which represents a type of entropy-linear program. To reduce the complexity of the model, we prove that the NPI-M lower and upper probabilities for any general event can be expressed as a combination of the lower and upper probabilities for the singleton events, and that this model can not be associated with a closed polyhedral set of probabilities. An algorithm to obtain the maximum entropy probability distribution on the set associated with NPI-M is presented. We also consider a model which uses the closed and convex set of probability distributions generated by the NPI-M singleton probabilities, a closed polyhedral set. We call this model A-NPI-M. A-NPI-M can be seen as an approximation of NPI-M, this approximation being simpler to use because it is not necessary to consider the set of constraints associated with the exact model.     

Green product development under competition: A study of the fashion apparel industry

Motivated by the observed industrial issues, we analytically develop a fashion supply chain consisting of one manufacturer and two competing retailers and investigate how retail competition and consumer returns affect green product development in fashion apparel. In the basic model, that is, the pure “product greenness level” game, we find that the optimal greenness level of the fashion product decreases along with the level of market competition. This finding implies that a more competitive market leads to a lower optimal greenness level. We also identify that when the consumer return rate increases, the optimal product greenness level is substantially reduced. In the extended model with joint decisions on greenness and pricing, we find that the optimal product greenness level for the whole channel is always higher in the scenario when both retailers charge a higher retail price than in the case with a lower retail price. As such, the underdevelopment of green fashion products is a result of fashion industry features, such as an extremely competitive environment for green product development, relatively low retail prices for fashion products, and high consumer return rates. Therefore, fashion companies should join a co-opetition game for the green product market and simultaneously enhance their efficiency in managing consumer returns. To support our analytical findings, we conduct extensive industrial interviews with various representative companies. Based on this multi-methodological approach (MMA), this paper generates practice-relevant managerial insights that not only contribute to the literature, but also act as valuable references for industrialists.     

部分信息情形下利率非零时的最优消费投资模型研究

考虑了部分信息情形下市场利率非零时的最优消费投资模型,讨论了相应的最优消费投资策略.最后探讨了当扩散系数可逆且漂移系数服从已知分布时的贝叶斯特例,给出了最优交易策略的明确表达式.     

基于线上评论的生鲜产品供应链定价策略

随着网络购物的普及,线上评论对消费者的购买决策发挥着越来越重要的作用,零售商和制造商可以利用这些评论调整、优化生产流程。本文基于消费者效用理论,构建了由一个零售商和一个制造商组成的生鲜产品供应链定价决策模型,研究了三种决策模式下生鲜产品零售价、利润和保鲜努力水平的差异。研究发现:集中决策下生鲜产品的最优零售价最低、利润最高;随着运输时间增加,保鲜努力水平和新鲜度均呈现下降趋势;当成本分担系数较高时,在成本分担和收益共享的分散决策模式下,保鲜努力最优水平高于集中决策模式下保鲜努力最优水平。     

B2C零售商退货渠道策略研究

基于全渠道环境下,考虑B2C零售商提供全额退款保证,建立了同渠道退货策略和全渠道退货策略下的博弈模型,研究B2C零售商的退货渠道策略选择问题。结果表明,全渠道退货策略下,B2C零售商总是会实施高价策略,且当消费者线上退货损失较大时,最优定价随着消费者线上退货损失递增,反之递减;当B2C零售商实体店退货产品处理成本较小时,全渠道退货策略能有效增加消费者需求,实施全渠道退货策略是占优的;从消费者的角度看,当产品匹配率和消费者线上退货损失较高时,B2C零售商将会实施全渠道退货策略。     

A multiple criteria model for pricing alcoholic beverages

In this paper we discuss the problem of determining optimal price changes in an alcohol sales monopoly. In Finland, the pricing of alcoholic beverages is entrusted to a State Monopoly (Alko Ltd.). The price decisions are considered to be among the most important alcohol policy measures. The pricing problem is not only a profit maximization problem. Other relevant objectives include the restriction of sales with the intention of reducing harmful effects due to alcohol consumption, and the minimization of the impact of price increases on the consumer price index.A multiple criteria model for finding the most preferred solution for the problem of pricing alcoholic beverages is developed. The model includes three criteria: profit (max.), consumption of absolute alcohol (min.), and impact on the consumer price index (min.). Using logarithms of relative changes instead of absolute criterion values makes it possible to operate with a fully linear model.The model can be solved by using any existing multiple criteria decision method. Reflecting our own bias, we use a visual interactive goal programming method developed by Korhonen and Laakso [3] and further refined by Korhonen and Wallenius [4]. The method is implemented on an IBM/PC1 under the name VIG (Visual Interactive Goal Programming).     

Portfolio selection problem with multiple risky assets under the constant elasticity of variance model

This paper focuses on the constant elasticity of variance (CEV) model for studying the utility maximization portfolio selection problem with multiple risky assets and a risk-free asset. The Hamilton-Jacobi-Bellman (HJB) equation associated with the portfolio optimization problem is established. By applying a power transform and a variable change technique, we derive the explicit solution for the constant absolute risk aversion (CARA) utility function when the elasticity coefficient is −1 or 0. In order to obtain a general optimal strategy for all values of the elasticity coefficient, we propose a model with two risky assets and one risk-free asset and solve it under a given assumption. Furthermore, we analyze the properties of the optimal strategies and discuss the effects of market parameters on the optimal strategies. Finally, a numerical simulation is presented to illustrate the similarities and differences between the results of the two models proposed in this paper.