The Era of Survival for Companies with Data and Algorithm Competitiveness ~Transforming Social and Business Challenges into Mathematical Challenges~

Humans have contributed to the development of civilization by using mathematical methods to address many social and business challenges. This is a fact that many would agree.

Today, the world's proven mathematical wisdom is provided in excellent tools such as Python, R, MS Excel, and SAS, and Humanity is now able to solve more and more social and business challenges and problems in a very short time and with high quality.

What will happen in the future as the democratization of these analytical and analytical capabilities accelerates?

I have been reading a lot of literature on the future competitiveness of companies. One essence has emerged. The time has come for companies with data competitiveness and algorithmic competitiveness to survive.

AMAZON, NETFLIX, and UBER have data competitiveness and algorithmic competitiveness. They are not achieved through Nobel Prize-winning discoveries. They are the algorithmic implementation of a very simple essence into business.

Many business executives need to understand the "new essence" that will be the backbone of the next era.

We need to prepare for the next era by understanding that the mathematics that elementary and middle school students learn contains elements that will maximize corporate profits and bring about fairness.

Today I will address the following topic.

"Using a mathematical optimization approach to profit maximization planning."

Q: Raw materials are limited. Find the quantities of products X and Y that will maximize profit.

ANSWER: producing 18 kg of product X and 4 kg of product Y will maximize profit the most.

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A company's factory manufactures products X and Y. Product X has two raw materials, A and B. Product Y has two raw materials, A and B.

Product X requires raw materials A and B. Product Y also requires raw materials A and B.

Product Y also requires raw materials A and B.

Sales profit in one finished product

• X: 10,000 yen
• Y: 20000 yen

Raw materials required to manufacture 1 kg of product X

• A: 1kg
• B: 2kg
• 3kg in total

Raw materials required to manufacture 1 kg of product Y

• A: 3kg
• B: 1kg
• 4kg in total

Raw material inventory

• A: 30kg
• B: 40kg
• 70kg in total

<A>

• The amount of A required to make product X is three times the amount of A required to make product Y.
• The amount of A required to make product Y is one-third of the amount of B required to make product X.

<B>

• The amount of B required to make product X is half the amount of A required to make product Y.
• The amount of B required to make product Y is twice the amount of B required to make product X.

<C>

• The sales profit of one finished product is X: 10,000 yen and Y: 20,000 yen, so it is doubled.

Q: Raw materials are limited. Find the production volume of the X and Y products that maximize the profit.

What kind of approach do you guys take?

solution:

　Assumption:

• Profitable product X production volume x kg
• The production volume of the product Y that maximizes the profit is y kg
• Conditional expression:

Formulate the above <A> and <B>

• x + 3y ≦ 30
• 2x + y ≦ 40
• 0 ≦ x, 0 ≦ y,

Purpose:

• From the relationship of <C>
• Maximize x + 2y

Solution:

• x = 18
• y = 4

Manufacturing 18kg of product X and 4kg of product Y maximizes profits.

Let's implement these in Python. It can be implemented with just 12 lines of code. It doesn't even have to be calculated by humans every time. 24 hours 365 days This code can keep working.

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import pulp

problem = pulp.LpProblem('LP', pulp.LpMaximize)

x = pulp.LpVariable('x', cat='Continuous')

y = pulp.LpVariable('y', cat='Continuous')

problem += 1 * x + 3 * y <= 30

problem += 2 * x + 1 * y <= 40

problem += x >= 0

problem += y >= 0

problem.objective = x + 2 * y

status = problem.solve()

print('Status:', pulp.LpStatus[status])

print('x=', x.value(), 'y=', y.value(), 'obj=', problem.objective.value())

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Result:

• Status: Optimal
• x= 18.0 y= 4.0 obj= 26.0

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In other words, substituting 18 for x and 4 for y gives "x + 2y = 26".