2018年美国大学生数学建模大赛参赛论文B题（世界语言变迁）

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Team Control Number

For office use only

#72416

For office use only

T1 _______________

F1 _______________

T2 _______________

F2 _______________

T3 _______________

F3 _______________

T4 _______________

Problem Chosen

F4 _______________

2018 Mathematical Contest in Modeling (MCM) Summary Sheet

Languages in global: Where to go ?

What are the factors of language development in current interconnected world? Our

mission is to investigate trends of worldwide languages and select locations for some new

international offices of a major multinational service company.

First, based on the Gray Model (GM) and the Autoregressive Integrated Moving Average

Model(ARIMA), we proposed a predictive model. Two steps were divided in this part: Step

1.we predicted the 15-year quantity-trends of native speakers and the total speakers by using

the GM. Step 2.the forecasting values during the coming 35 years were obtained through the

ARIMA. As a result, we found Russian would be replaced by Malay. And Persian, kicking

French out, would squeeze in the top 10 list ranked by total speakers’ amount.

Then we created the Language Geography Model by using Agent-based Model. During

the modeling process, we have divided the floating population into returnees and non-

returnees. At last, we took India and Canada as 2 samples and finally extended the model to

other countries. Results show that linguistic-geographical changes of Chinese, English, Hindi,

Arabic and Russian will occur at the same time, while Spanish, French, Punjabi and Japanese

will change meanwhile.

Finally, we set up an Office Locations Model which applied Analytic Hierarchy Process

(AHP). Relevant functions can be listed according to the relationship between speakers’

number and geographic area. Considering distance weight obtained and other comprehensive

factors, a AHP model can be established, and the city with the highest weight is the target

office location. Eventually, we determined offices should be set up in Washington, New Delhi,

Kuala Lumpur, Beijing and Cairo, respectively related to English, Hindi, Malay, Chinese and

Arabic. Another point should be noticed is that the total influence-index of top 3 languages of

50 years later is larger than that of the top 6 languages today, which tell us 3 offices are

enough for the company half-century later.

Keyword: Gray Prediction; ARIMA; Agent; Analytic Hierarchy Process;

Team #72416

Page 1 of 20

1. Introduction

1.1 Background

According to the UNESCO’s survey, there are 6,900 languages available worldwide,such as

Mandarin (including standard Chinese), Spanish, English, Hindi, Arabic, Bengali, Portuguese,

Russian, Punjabi and Japanese. About half of the world's population speaks one of the ten

languages above.With the integration of the world economy, we gradually learn to speak a second

language in our lives. When considering the total number of speakers of a certain language

(native speakers, second or third language users), the total speakers may increase or decrease

over time.

Trends on the world languages are influenced by various factors. Our mission is to

investigate trends of languages in globalization and select several new international offices for a

major multinational service company.

1.2 Restatement

To do the investigation and find appropriate offices’ positions, we should consider and

address the following questions.

 Combine a wide range of influences and factors to analyze the speakers' distribution.

 Predict what will happen to the number of native speakers and total speakers in the next 50

years and analyze whether any one of the current top-ten language lists will be replaced by

another or not.

 Analyze whether the migration of migrants in the next 50 years will affect the geographical

distribution of languages.

 Choose the locations for 6 new international offices for a large multinational service

company, then, analyze short-term and long-term changes.

 Given the changing nature of global communications, can it be advisable for companies to

establish fewer than six international offices.

2. Assumptions

 There are no drastic changes on international stability, economy and foreign policy.

 Population migration and the general speakers are not affected by any unpredictable or high-

impact, low probability events longtime, such as natural disasters and state coup.

 As for geographical location, in spite of altitude, horizontal straight distance is the only thing

concerned.

 There are only 2 kinds of native languages in each country.

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