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Mathematical Model of Bus Scheduling Problem.
It is known that a given bus line has 14 stops, 13 off-line stations, a running speed of 20 kilometers per hour, and a full load of 100 people. The normal waiting time should not exceed 10 minutes, and the peak hours in the morning and evening should not exceed 5 minutes. The interests of the bus company, the bus company proposes to control the full load rate between 50% and 120%;
Please combine the above information to determine an easy-to-operate model, how many vehicles are required to run the resulting line, and the operating schedule.
Chen Nuo read the questions and thought for a while.
假设早高峰为6：40-9：40，晚高峰为16：30-19：30，其余时间为正常时间
Assuming normal driving, each car has to wait for 10 minutes
The bus travels at a speed of 20 kilometers per hour and travels 10 kilometers in 3.3 minutes
Based on the above, 22 uplink and downlink vehicles are required.
After ten minutes of talking, Chen Nuo came to the conclusion of the required vehicle.
Zhao Yuan was stunned, Ye Xinran and several other students were also at a loss.
They could understand what Chen Nuo said earlier, but as they talked, they forgot the former, and the latter was naturally the same as listening to heavenly scriptures.
Professor, is the answer wrong?
After waiting for a few seconds, without Zhao Yuan's response, Chen Nuo couldn't help but speak.
Yes, you are quite right.
Zhao Yuan, who woke up like a dream, looked at Chen Nuo, as if he was looking at a monster, and his mental arithmetic ability was so good.
Is this difficult?It's hard to say, it's hard to say it's not hard.
Even if you don't use mathematical thinking, you can calculate it with logical reasoning, but it's a little more troublesome.
Chen Nuo, you are reasoning. If there are dozens of lines, you will be exhausted if you do this.And in the competition, there needs to be a calculation process and a paper. You have to build a model.
Chen Nuo didn't speak, but got up and walked towards the whiteboard.
(1) Known data, station mark: j=1, 2, 3n;
Visitor density: uj(t), j=1, 2n;
Relevant variables: the moment when the kth car leaves station j: Tk1=Tk, Tkj=Tk1+
After writing for half an hour, Chen Nuo stopped after finishing all the writing on the whiteboard in the research room.
pop, pop, pop
Zhao Yuan looked at the whiteboard and clapped vigorously.
Ye Xinran and others also applauded, and the way they looked at Chen Nuo changed, they were astonished.
After reading the topic only once, you can reason and build models without even calculations, all in one go.
Chen Nuo, you are the most talented student among all the modeling competition students I have taken, and your mathematical talent definitely surpasses mine
Zhao Yuan praised Chen Nuo without hesitation.
Hua Luogeng was alive, comparable to Qiu Chengtong's gorgeous rhetoric and exaggerated metaphors, Chen Nuo blushed when he heard it.
The corners of Ye Xinran and the others' mouths twitched violently. They had never seen Professor Zhao Yuan talk so much and still praise a student.
Keer, can you type out the model code?how much time is required?
While Zhao Yuan was drinking water, Chen Nuo looked at Chen Ke'er.
If Chen Ke'er can write the code of this model, then this year's National One will be stable.
Chen Ke'er stared at the whiteboard, thought for a while, and said in a low voice: "It's not a big problem. It may take a day. If you can help, it will take half a day."
Chen Nuo heaved a sigh of relief, this time was within his controllable range.
Chen Nuo, the difficulty of the questions in the modeling competition over the years is similar to this one. Now you are all good at solving problems, modeling and programming. If you write better papers, you will definitely have a seat in this year's National One.
What Zhao Yuan said made the three girls in the other group envious.
The gold content of Guoyi is still very high, whether it is the postgraduate entrance examination or the postgraduate entrance examination, you can get extra points, and the tutor will also give priority to such students with modeling thinking.
With this national first award, even if Ye Xinran and Chen Ke'er can't get into the graduate students of Professor Zhao Yuan, they can still study with other professors.
Ye Xinran couldn't believe it.
She hasn't come to her senses yet, Guoyi got it so easily?
who I am?Where am I?What should I do?
Chapter 17 Hey! 119 Well, someone used biochemical weapons
Hey, wake up, it's time to get up cough, it's time to work!
Chen Nuo patted Ye Xinran on the shoulder.
Ye Xinran woke up from the surprise, and gave Chen Nuo a hard look with her big watery eyes.
Ke'er and the other girls secretly laughed, Chen Nuo is really too straight.
Are you writing a thesis?Me and Kerr programming?
Row!
Ye Xinran smiled happily, and she really had a place to use her skills.
Then he secretly scolded himself for not living up to expectations, but he was a top student, so he was actually happy about this little thing.
The problem was solved, and the model was built. Although Chen Nuo couldn't write code, but with his mathematical thinking, coupled with Keer's programming level, the programming was completed by lunch time.
It was originally a happy ending, but Ye Xinran's thesis turned out to be a problem.
In one morning, Ye Xinran only wrote a letter of commitment and a summary, with almost zero text.
If it's just that, Chen Nuo took it over and read it, and the summary was full of loopholes.
Senior sister, are you really a top student?
Chen Nuo sighed, no matter how you look at it, it's two gods leading one pit, maybe the official competition will be one god leading two pits.
This kind of mathematical modeling paper is the simplest, which is to write down the entire answering process and add text expressions.
The difficulty lies in the abstract part, which is the core part of the whole paper, because the professors will make a preliminary screening based on the structure and overview of the paper during the selection process.
After recalling the requirements of the thesis, Chen Nuo picked up the computer and started typing.
With professor-level university mathematics skills and specialized modeling skills, the text part can be written with flying colors.
Everyone saw that Chen Nuo's hands were flying like flying, and he didn't even need to think.
Rows of formulas and numbers appear.
fill out the form
In just over an hour, the seven-page text was written, followed by another crackling operation, and the thesis was completed.
There was no more than two hours before and after.
Professor, would you like to see?
Zhao Yuan took the paper that Chen Nuo had printed out, and slowly flipped through it, revising it with a pen while reading it.
An hour later, Zhao Yuan put down his pen and handed the thesis to Chen Nuo who was reading the materials.
I go, this is what I wrote?What did you write?
After seeing the revised thesis, Chen Nuo was confused for the first time in front of Zhao Yuan and everyone.
Seven or eight pages of papers, each page is densely packed with red annotations.
Except for the formula that has not been changed, the text and layout have all been changed.
It's not a grammar problem, it's a title problem, and then it's a problem of title symbols and sentence segmentation.
Chen Nuo looked at the revised paper word by word, and slowly fell into deep thought.
It has to be said that Professor Zhao Yuan's thesis is comparable to a textbook, with concise and accurate words, and all expressions are clear at a glance.
Great job, Professor!
Hahaha
Zhao Yuan smiled happily, and finally won the round in front of this kid.
He has published more than a hundred papers, and he has corrected nearly a thousand papers in pieces. It is not easy to keep a young boy in check.
Chen Nuo, don't make up words and sentences. This is only a Chinese paper. If you need to publish a foreign journal for your research in the future, any ambiguity will lead to the failure of the paper. Be sure to remember!
Chen Nuo nodded and said: Give me ten days, I can do it too!
With the system in hand, I own the world, that's how domineering.
Me too!
Well, cooking is fine!
Chen Nuo, this girl is fighting with you!
Xinran, you are the school belle, pay attention to the influence!
Chen Ke'er hugged Ye Xinran who was flaring her teeth and claws, and the research room was full of joy.
Chen Nuo didn't know what was going on, and always liked to bicker with Ye Xinran.
Maybe it's the self-confidence after having the system!
After the first cooperation, Professor Zhao Yuan gave several questions, such as: train operation mobilization and section traffic safety issues;
Monitoring and control of coal mine gas and coal dust;
Evaluation and prediction of water quality in the Yangtze River;
After reading these questions, Chen Nuo doubted whether the major companies gave gifts to the modeling committee.
Especially the problem of train scheduling, can this be done by one person?
Xia Guo has [-] passenger trains and [-] freight trains operating on the railway every day, which involves train running time, stop time at each station, and interval time.
It is unbelievable that the number of student tickets, elderly tickets, standing tickets, and sitting tickets is huge.
During peak hours, 150 billion visits are received every day. Double Eleven is in front of 12306, which is the gap between babies and adults.
Even if he can make a model of this thing, even if he gathers all the programming power of Huaqing, he will definitely not be able to make it in a short time.
After everyone diverged their thinking, Professor Zhao Yuan talked about modeling thinking for another hour, and after sending out a lot of materials.
It was agreed to do running-in training from [-]:[-] am to [-]:[-] am every day, and everyone dispersed.
A quarter of an hour later, at the takeaway station, Chen Nuo cut straight to the point: Brother Da, what is the maximum amount I can change to my back order?
If you don't follow the two professors to do research, what kind of trouble will you make?
Zhang Da looked at Chen Nuo who hadn't appeared for three or four days, and was a little surprised.
See all kinds of things in the world, experience the vicissitudes of life, taste all kinds of flavors of life, and taste the coolness of the world!
speak English!
Work out and challenge yourself!
Fuck, your skin is itchy, right?
Well, I have a showdown, I want to brush skills!
Fuck off!
Naogui Nao, Zhang Da took a look at the backstage and said: My maximum authority is twelve orders per hour!
so low?
Chen Nuo was a little dissatisfied. He also wanted to use Zhang Da's relationship to increase the amount of takeaway orders to the highest and complete the task of [-] orders in seven days.
One thousand orders, seven days, an average of 143 orders a day, according to this amount of orders, it takes twelve hours a day.
This is an impossible task, at least not during the summer vacation.
Forget it, let's honestly deliver food and see luck.
Chen Nuo gave up the task after making some calculations.
You have a new takeaway order, please process it in time!