2020年美国大学生数学竞赛优秀论文集：挖掘评价精华与销售关联

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"《2020年美赛优秀论文集-C-2004647.pdf》是一份关于美国大学生数学竞赛的精选论文集，特别关注于数学模型在实际问题中的应用。论文中，作者探讨了数学模型在电子商务领域的关键作用，特别是通过评级与评论（Rating and Review）系统来分析消费者行为和产品评价。他们提出了一种名为Rating and Review Based Score (RRBS)模型，这个模型基于用户对产品的评级和评论内容，量化并描述了消费者对产品反应的细致程度，从而提供了对产品质量的深入评估。该模型进一步发展为声誉模型，它根据时间对产品声誉进行动态量化，揭示了产品销售与其声誉之间的强相关性。这种量化方法对于商家来说至关重要，因为它帮助他们高效地从海量用户反馈中提取有价值的信息，以便优化产品和服务，提升品牌形象，进而促进销售。论文不仅提供了理论分析，还可能包含了具体的案例研究和实证数据，展示了如何通过数学建模技术来解决实际商业问题，是大学生数学竞赛、数学模型爱好者以及电子商务研究者的宝贵参考资料。这份论文集合展示了数学在现代商业决策中的实际应用，具有很高的学术价值和实践指导意义。"

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MATHmodels

Team # 2004647 Page 5 of 24

3.1 Model Overview

As part of our metric, we deﬁne score as a measure for a company’s particular product, based

on the ratings and reviews it receives. It quantitatively indicates whether a product does well

or badly in terms of receiving positive responses from customers. We deﬁne our metric as:

score

(t)

i,k

= α

◦λ

β (1)

where:

• i ∈ {1, 2, 3} denotes products of the i

type;

• k denotes the k

model (uniquely identiﬁed by the "product_parent" value) of the i

type products;

• t denotes the t

month;

• α is an n-dimensional row vector whose value is determined by star ratings;

• β is an n-dimensional column vector whose value is determining by reviews and other

inﬂuencing factors;

• λ is an impact factor that decides the weight of ratings in terms of impacting the score

value. We initially set its value as 1.

3.2 Deﬁnition of α—the Rating Vector

The value of α is directly connected to a product’s star ratings, which vary from 1 to 5. And

the value of 1 indicates "very unsatisﬁed" while the value of 5 indicating "very satisﬁed". We

consider two star ratings, one with a value of 1 and the other one with a value of 5, have

the same degree of intensity (i.e., one indicates "very" unsatisﬁed and the other one indicated

"very" satisﬁed). Similarly, a 4-star rating is considerd having the same degree of intensity as

a 2-star rating’s. And a 3-star rating represents a neutral stance, which we consider relatively

less intense. Therefore, we conduct a mapping process, as shown in Table 2, so as to quantify

the degree of both positivity and negativity of a star rating with a uniform measure.

Table 2: Mapping from star rating values to their corresponding mapped rating values (viz.,

degree of intensity).

Star Rating Mapped Rating

1-star & 5-star 3

2-star & 4-star 2

3-star 1

As stated above, α is an n-dimensional row vector that is exclusively associated with star

ratings. The n non-zero elements in α represent n mapped rating values of a product within a

month. We can obtain:

α =

(

(t)

i,k,1

(t)

i,k,2

. . . α

(t)

i,k,j

. . . α

(t)

i,k,n

)

(2)

where α

(t)

i,k,j

∈ {1, 2, 3}.

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