摘要
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。
We make the attraction of the lottery project to be its evaluation standard. The attraction can be divided into two aspects. One is from the amount of prize, and the other is from the winning probability. We uae the utility function in economics to synthesize the two aspects by weight. Furthermore, each aspect of the attraction can also be synthesized by every single grade of prize or winning probability. The attraction of a single grade is the prize or the winning probability s increasing and upwards bulgy function. We use the transfer function of a High-Pass-Filter. We calculate the weight by analytic hierarchy process and entropy method, and then finish the evaluation (project 5 and 6 are better). In problem 2, we establish a dynamic optimization model and work out the optimized lottery project.
出处
《工程数学学报》
CSCD
北大核心
2003年第5期74-80,共7页
Chinese Journal of Engineering Mathematics
