Chapter 23: The Classic Business Modeling Problem

When Liu Xiangping saw the two people in the classroom, he smiled and said, “There are only two people here? I heard there’s another one.”

“… I’ll call her and ask,” said Wang Xiaodong. Embarrassed, he walked outside with his phone.

The professor was not in a rush. He opened his vacuum flask and sipped some hot water. He then casually sat next to Lu Zhou and asked with a smile, “What’s the current situation on your team’s configuration?”

Lu Zhou put down his phone and replied with a smile, “I’m responsible for building the model, Wang Xiaodong is responsible for programming it, and Lin Yuxiang is responsible for writing the thesis and presenting.”

“Modeling, coding, and writing. The standard configuration I see,” said Professor Liu. He laughed and continued to say, “Speaking of which, you’re the undergraduate student Lu Zhou, right? I’ve read your thesis and it was really good.”

Lu Zhou eyes lit up, “Professor, you’re in mathematics?”

“You could say so, but I research physics side of things and I don’t publish mathematics theses much,” said Teacher Liu. As he squinted his eyes and looked at the classroom door, he said, “Your female teammate seems to be quite unreliable.”

Lu Zhou felt awkward and could only smile out of politeness.

Teacher Liu smiled as well and left the issue alone. He paused before saying, “As for your team configuration, let me suggest some slight changes. Making the model and thesis should be done by one person, the two other people should program the model. The advantage of this is that the person writing the model would have a strong grasp of the topic, and thus, the process of writing the thesis would be much smoother. Of course, the downside is that the person would be under a lot of pressure. The competition is only three days long. It means that when the person finished writing the model, he or she would have to immediately start writing the thesis.”

Lu Zhou asked thoughtfully, “Two people for coding?”

Teacher Liu sipped his tea and replied slowly, “That’s right.”

Lu Zhou laughed and did not give an answer yet, “I’ll think about it. After all, I should discuss this with my teammates.”

At the same time, the sound of footsteps came from outside the corridor. The last teammate had finally arrived.

“My apologies, I’m slightly late. I’m really sorry!” said Lin Yuxiang as she walked into the classroom with Wang Xiaodong. She looked down at the professor with an apologetic expression.

“It’s okay. Since everyone is here, let’s begin,” said Professor Liu Xiangping as he smiled casually. He did not blame her for being late. He turned around and walked to the podium, plugged a USB into the computer, turned on the projector, and pulled out his PowerPoint presentation.

“Before I present, I want to first ask you guys a question. This question isn’t very hard in itself, but it’s an example of a mathematics modeling question. I hope you guys can understand what exactly is mathematical modeling by doing this question.”

He pressed the mouse and turned the PowerPoint to the next page.

“Three businessmen, each carry a passenger on a boat to cross the river. The boat can only accommodate two people. The passengers secretly decided that if there are more passengers than businessmen on either side of the river, they’ll kill the businessmen. However, the method of taking the boat is determined by the businessmen. Question. How can the businessmen cross the bridge safely?”

In reality, this question was not difficult at all.

Lu Zhou did not even use the power of the system to find an answer. He replied.

“First round, two passengers go, one passenger comes back.”

“Second round, two passengers go again, one passenger comes back.”

“Third round, two businessmen go, one businessman and one passenger comes back.”

“Fourth round, two businessmen go, one passenger comes back.”

“Fifth round, two passengers go, one passenger comes back.”

“Sixth round, the last two passengers go and they would successfully cross the river!”

Clap, Clap, Clap!

Lin Yuxiang started clapping with her tiny hands and her face was filled with an expression of being awed.

Wang Xiaodong’s expressions did not change one bit. He looked like a worldly man.

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From his perspective, this question was not that difficult. Although he did not try to solve it himself, he believed that his IQ was high enough to solve it in the same amount of time.

“Completely correct,” laughed Professor Liu. He continued to say, “Even without any mathematical knowledge, this problem can be solved simply by logical analysis. What if we expanded this question into N businessmen?”

This question was slightly harder. However, while the mathematical side was easy, the hard part was abstracting this problem into a mathematical problem.

Lu Zhou gave it a serious thought for a moment. He already had a general outline in his brain.

“Can I use the blackboard?”

“Of course, you can,” said Professor Liu Xiangping while he waved his hand as an invitation.

Lu Zhou walked up to the blackboard and started to write with a chalk.

[Let the number of businessmen before crossing the river as Xk. Let the number of passengers be Yk. k = 1, 2…, Xk. Yk = 0, 1, 2, 3. Let the two dimensional vector Sk = (Xk, Yk). A successful crossing condition is recorded as S.]

Therefore S={(X,Y)|X=0,Y=0,1,2,3;X=3,Y=0,1,2,3;X=Y=1,2}

2. The number of businessmen on the kth ferry is 2 Uk, and the number of followers is Vk. The two-dimensional vector Dk=(Uk, Vk) is defined as a decision. Allow the decision set to be recorded as D, which is known by the boat capacity: D={(U,V)|1≤U+V≤V, U, V=0,1,2}

3 Combining the above conclusions, the variation law of state Sk with Dk is: S(k+1)=Sk+(-1)^k*Dk

]

“Amazing…” gaped Lin Yuxiang as she looked at the blackboard with a blank face. Her mouth was slightly wide opened. She watched Lu Zhou walked down the podium and she asked in surprise, “You don’t even need to write down your calculations?”

“I can just calculate it in my head,” said Lu Zhou while laughing.

Wang Xiaodong still remained silent.

From looking at his expression, the arrogant genius was thoroughly convinced by Lu Zhou’s mathematics ability.

Professor Liu looked at the steps on the blackboard and nodded his head, “Perfectly correct! But from a mathematical model perspective, you only completed half of the work. After building at the model, there’s still one more step. Implementation of the model. Of course, this model is very simple and I trust that Student Wong can definitely use his programming skills to build this. So, we won’t waste our precious time.”

Wang Xiaodong pushed his glasses. The expression on his face remained the same as it portrayed a sense of confidence.

Given that there was no chance for him to show off his programming skills, he was a bit disappointed.

After a pause, Professor Liu continued to say, “Data modeling is actually a process of simplifying a practical problem into a problem that can be expressed in terms of data and simple sentences. Then, solve the problem through mathematical tools.”

“So, the key is, what actual problems are your team going to solve?”

“Building a model isn’t testing your programming abilities or your mathematical abilities. It is actually testing your ability to translate real life problems into data and find a way to solve it. You guys have to remember this.”

“As for building the model, I don’t have much advice. There is no shortcut other than to practice and broaden your knowledge. As for programming, I can give some advice.”

“There are four types of commonly used software. Matlab, Mathematica, Lingo, and SAS. You don’t need to master all of them but you have to at least master one of them. The key is to use the software that suits you to solve the actual problem,” said Professor Liu Xiangping while he looked at Wang Xiaodong.

This was because he was mainly talking to him.

Wang Xiaodong pushed his glasses, nodded his head, and said, “I’ve used Matlab and SAS so there’s no problem.”

Professor Liu nodded, “Knowing these two are enough. You guys have to learn this by yourself. I can only help you when you are stuck.”

“The last point is regarding textbooks. I recommend that you read some books on mathematical modeling such as Mathematical Models, Mathematical Modeling Algorithms and Applications, and Mathematical Modeling Basics.”

“I still have some handouts and materials from the university. You can copy them and look at them at home but remember not to pass them out or upload it online. Understood?”

The three students replied at the same time: “Understood!”

Professor Liu laughed and said, “Okay, that’s it for today. I don’t have much else to say. It’s all up to you guys now. Come download the material from me if you need it. After you’re done, go and study English.”