彩票中的数学

本模型讨论的是如何证券传统型彩票和乐透型彩票的一般评奖方案的合理性问题。本文首先根据彩票中奖规则，利用古典概率求出了这两种类型彩票的各种奖项出现的可能性。把每注彩票中奖与否看成贝努利试验，在假设每期彩票的销售量足够多的前提下，由贝努利大数定律归结为正态分布，从而求出了每注彩票的平均收益率。在此基础上，结合公平尺度，利用彩民的博彩心理因素构造了证券方案合理性的判别函数，利用MATLAB6．1软件编程计算，判别出题目所给方案的奖金设置的优劣，并且利用这个判别函数，我们建立了求解最优方案的非线性规划模型，通过求解所建立的模型，找到在给定销售注数下最优方案及奖项和奖金额的设置。     

彩票方案的合理性优化

本文主要研究了彩票中各奖项的中奖概率、奖项和奖金的设置以及对彩民的吸引力等因素对彩票方案合理性的 影响。在问题一给出的29种方案中,我们用模糊综合评判的方法量化各个方案的合理度,分别给影响合理度的 因素加权从而求出合理度,发现方案26、27的合理度分别为0.5300和0.6414,是两套较优的方案,之后我们分析 了模型的稳定性;在问题二中,我们基于问题一中的29套方案,对于每种方案的合理度采用线性规划模型,用 Lingo软件求得相应的最优合理度和最优奖项设置,最后我们补充分析了模型中未考虑的一些因素,并向管理部 门和彩民提出了一些建议。     

彩票方案的合理性优化

本文主要研究了彩票中各奖项的中奖概率、奖项和奖金的设置以及对彩民的吸引力等因素对彩票方案合理性的影响。在问题一给出的29种方案中，我们用模糊综合评判的方法量化各个方案的合理度，分别给出影响合理度的因素加权从而求出合理度，发现方案26、27的合理度分别为0．53000和0．6414，是两套较优的方案，之后我们分析了模型的稳定性，在问题二中，我们基于问题一中的29套方案，对于每种方案的合理度采用线性规划模型，用Lingo软件求得相应的最优合理度和最优奖项设置，最后我们补充分析了模型中未考虑的一些因素，并向管理部门和彩民提出了一些建议。     

彩票方案的评价

我们把彩票方案的优劣的评价标准归结为其对彩民吸引力的大小，又把这种吸引力分为两部分：奖金额产生的吸引力和中奖面（即中奖概率）产生的吸引力。通过构造经济学中常用的效用函数，把总的吸引力归结为这两部分加权作用的结果。其中，奖金额产生的吸引力和中奖面（即中奖概率）产生的吸引力又可以分别由每个等级奖项的奖金额和中奖概率所产生的吸引力来表示。单个等级奖项的奖金额和中奖概率所产生的吸引力是该等级奖项的奖金额和中奖概率的单增、上凸函数，在这里，我们借用了高通滤波系统的传输函数。我们用层次分析法和熵值取权法确定相应的权值，对各个彩票方案进行了评价（5，6两种方案较优）。在问题二的解决中，我们建立了一个动态规化模型，求出了最优彩票方案为“34选６”，一等奖、二等奖、三等奖的奖金在整个高项奖奖金额的份额为60％、25％、15％，而对低项奖，四等奖、五等奖、六等奖的分别为370、15、8元，不设七等奖。     

彩票方案的评价

我们把彩票方案的优劣的评价标准归结为其对彩民吸引力的大小,又把这种吸引力分为两部分:奖金额产生的 吸引力和中奖面(即中奖概率)产生的吸引力。通过构造经济学中常用的效用函数,把总的吸引力归结为这两部 分加权作用的结果。其中,奖金额产生的吸引力和中奖面(即中奖概率)产生的吸引力又可以分别由每个等级奖 项的奖金额和中奖概率所产生的吸引力来加权表示。单个等级奖项的奖金额和中奖概率所产生的吸引力是该 等级奖项的奖金额和中奖概率的单增、上凸函数,在这里,我们借用了高通滤波系统的传输函数。我们用层次分 析法和妨值取权法确定相应的权值,对各个彩票方案进行了评价(5,6两种方案较优)。在问题二的解决中,我们 建立了一个动态规化模型,求出了最优彩票方案为“34选6”,一等奖、二等奖、三等奖的奖金在整个高项奖奖金额 的份额为60％、25％、15％,而对低项奖,四等奖、五等奖、六等奖的奖分别为370、15、8元,不设七等奖。     

彩票方案的优选模型

影响彩票中奖的主要因素有中奖率、奖金额的设置、彩票的规则对彩民的吸引力等。本文对各种因素进行了综合分析，建立了评价彩票发行方案合理性的目标函数，即度量各种因素对彩民吸引力程度的函数－合理度G，并由层次分析法得到模型中涉及到的各因素的权重值wj和各种 因素的标准值Cj，通过Matlab软件编程计算，评价出给定29种彩票方案的合理性，同时还设计了更好的方案。     

彩票方案的优选模型

影响彩票中奖的主要因素有中奖率、奖金额的设置、彩票的规则对彩民的吸引力等。本文对各种因素进行了综 合分析,建立了评价彩票发行方案合理性的目标函数,即度量各种因素对彩民吸引力程度的函数——合理度G, 并由层次分析法得到模型中涉及到的各因素的权重值w_j和各种因素的标准值C_j,通过Matlab软件编程计算,评 价出给定29种彩票方案的合理性,同时还设计出了更好的方案。     

彩票运行方案的合理性研究

本文建立了评价彩票销售规则及奖金设置方案合理性的模型。通过对Logistic函数的改造,建立了评价彩票对 彩民吸引程度的“吸引力指数”;运用计算机模拟的方法评价方案运行的稳定性;最后根据由以上两个因素共同 决定的综合指数作出方案合理性的评价。     

彩票运行方案的合理性研究

本文建立了评价彩票销售规则及奖金设置方案合理性的模型。通过对Logistic函数的改造，建立了评价彩票对彩民吸引程度的“吸引力指数”；运用计算机模拟的方法评价方案运行的稳定性；最后根据由以两个因素共同决定的综合指数作出方案合理性的评价。     

基于资源约束的装配线平衡问题研究

在生产线建立过程中,必须考虑人员、设备等资源和作业约束,基于此,本文建立一种含有并行工作站的装配线平衡模型,并利用模拟退火算法求解该模型．经仿真验证,该算法能够求出满足模型约束条件的最优方案或可行方案,并且能够得到不同方案的多个目标属性值,这不仅表明算法的有效性,还给决策者的方案选择提供了一定的空间．     

Papers written by Nobel Prize winners in physics before they won the prize: an analysis of their language and journal of publication

In this paper, we analyzed data relating to the language of papers written by winners of Nobel Prizes in physics before they won the prize and their journals of publication, and we identified the change in scientific language corresponding with shifts of the center of the scientific world. Using the science citation index as the main data source, we also collected information on the distribution of prize-winning scientists by country, by each scientist’s number of published papers, and by language. We then analyzed their papers in terms of the different journals based in different countries. The results are presented in three parts: (1) the main languages used in the papers are English and German. The proportion of papers in English is gradually increasing, while that of papers in German is decreasing. (2) The prize winning scientists’ papers have been published mainly in journals in their own nation and in the United States. (3) Journals based in their own countries are very helpful to these scientists early in their careers.     

基于旅客购票行为仿真的高铁票价动态调整

高速铁路需要一套基于市场竞争的票价调整策略,考虑旅客购票概率、高铁席位存量与时域动态票价,给出非同质旅客购票效益表达形式,采用动态规划原理推导计算席位存量和动态票价的递推公式,最终构建市场竞争环境下高铁票价动态调整模型。通过在某预售期60 d内京广高铁旅客购票仿真数据得出,非同质旅客购票到达概率满足非齐次泊松分布,与相同直达OD下的航空竞争其票价按席位存量500、375、270、207分4次完成动态调整,客票单价调整为900元、950元、1 000元、920元。研究旨在为综合运输背景下高铁客票定价提供仿真方法。     

基于双寡头竞争的航空客运模糊销售定价决策

针对近年来航空公司机票销售领域流行的模糊分销模式,利用Hotelling模型建立了季末单一模糊销售以及直销与模糊销售共存的双寡头竞争模型,求解供大于求和供小于求下两种销售模式各利益主体的均衡价格及收益,旨在发现哪种销售模式更有利于提高航空公司的收益。研究表明,当市场竞争激烈时,模糊分销模式存在,且季末共同销售策略下航空公司的期望总收益高于单一模糊销售,同时模糊中介商有动力实施该模式,凸显了双渠道同期销售对市场需求的引导作用。该研究结果可为航空公司竞争环境下的均衡定价决策和销售模式选择提供理论参考。     

Salesforce design with experience-based learning

This paper proposes and analyzes an integrated model of salesforce learning, product portfolio pricing and salesforce design. We consider a firm selling two products, with a pool of sales representatives that is split into separate salesforces, one for each product. The salesforce assigned to each product is faced with an independent stream of sales leads. The salesforce may also handle leads that overflow from other product salesforces. In addition, salespeople “learn by doing” over their tenure on the job. In particular, the more time they spend selling a particular product, the more productive the sales effort. The objective of the firm is to maximize profits by optimizing the size of all salesforces as well as the prices of all products. Using data collected from the salesforce of a large manufacturer, we provide evidence for the link between experience and sales, and we demonstrate how parameters of the model may be estimated from real data. Numerical experiments using parameters derived from the data analysis indicate that the optimal salesforce size increases with both sales productivity and the learning rate, and decreases with salesforce costs (e.g., wage per representative), product production costs and consumer price sensitivity. We also find that worker learning can significantly dampen the effect of rising costs (or decreasing margins) on staffing levels. Finally, we examine the impact of learning on both the optimal salesforce structure (specialists versus generalists) as well as the optimal routing of sales leads to sales representatives.     

Flexible strategies under supply disruption: the interplay between contingent sourcing and responsive pricing

Due to possible supply disruptions because of a low-cost unreliable supplier, a firm may use a high-cost reliable supplier as an additional regular supplier (dual sourcing) or an emergency backup supplier with an extra emergency cost (contingent sourcing). We consider the firm's sourcing problem when the pricing decision is made before any supply uncertainty is resolved (committed pricing) or after the supply state is realised (responsive pricing). By comparing the relative value of responsive pricing in contingent sourcing to that in dual sourcing, we study the relationship between contingent sourcing and responsive pricing in mitigating supply disruption risks. We show that the emergency cost and potential lost sales caused by disruption probability jointly impact the interplay of these two strategies. More specifically, when the emergency cost is low and the potential lost sales are lower under contingent sourcing than that under dual sourcing, contingent sourcing and responsive pricing are substitutes; otherwise, they are complements. Furthermore, we examine how disrupted capacity, i.e. the quantity that the unreliable supplier can deliver when disrupted, impacts the interplay, and find that the probability of the substitution relationship becomes higher when the disrupted capacity increases. We also find that under committed pricing, contingent sourcing is not optimal for any value of disruption probability when the emergency cost is high, a phenomenon that does not exist under responsive pricing.     

Ordering and sales effort investment for temperature-sensitive products considering retailer’s disappointment aversion and elation seeking

We investigate a retailer’s optimal policy of ordering and sales effort investment for temperature-sensitive products in a stylised newsvendor setting considering the effects of the retailer’s disappointment aversion and elation seeking. We provide a function to describe the demand for temperature-sensitive products and a psychological utility function to capture the retailer’s perceived utility of disappointment aversion and elation seeking. Next, we construct four joint ordering and sales effort decision models by integrating the profit and psychological utility for high temperature-sensitive products, medium temperature-sensitive products, low temperature-sensitive products and high–low temperature-sensitive products, respectively. By solving the constructed models, we determine the optimal policy of order quantity and sales effort level. We find that the average temperature in the selling season, the temperature sensitivity parameter, disappointment aversion degree and elation seeking degree can affect the retailer’s optimal policy, and the trends and extents of the effects for each temperature-sensitive product may be different from those for the other temperature-sensitive products. Our models also suggest that the optimal policy for temperature-sensitive products is more conservative than the one for general non-temperature-sensitive products. The policy of a retailer who is primarily concerned with disappointment aversion is more conservative than the one of a disappointment-neutral retailer. The policy of a retailer who mainly focuses on elation seeking is more radical than the one of an elation-neutral retailer. Our results show that a retailer must consider the effects of temperature and psychological behaviour on policy and should make decisions regarding order quantity and sales effort level according to the temperature sensitivity type of selling products and degrees of disappointment aversion and elation seeking.