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Mathematical Programming

Mathematical programming is a method to find the most optimized solution for mathematical model.

We find the most optimized solution in other fields. For example,
Design of Experiments : To find the most preferred plan of experiment.
Quality Engineering : To find the most stable condition of quality.
Regression Analysis : To find the most likely function.

So, you may have the question, "What is Mathematical Programming?"

I think "Mathematical Programming" is that

• The purpose is to find the most optimized value (maximum, minimum).
• The study is to make method to find the solution.
• Mathematical model in mathematical programming is made in Operations Reserch.

"Problems" in Mathematical Programming

There are some "problems". Mathematical programming tries to solve those problems. Popular method is Linear Programming

• Production Planning Problem : To find the combination of materials to maximize the benefit
• Transport Problem : To find the route to minimize the cost
• Facility Arranging Problem : To find the arrangement go minimize the cost of transport
• Knapsack Problem : To find the most expensive combination under the condition of weight
• Salesman Problem : To find the shortest route to go around all points

Linear Programming

If there are several inequality, the range of solution is limited. Linear Programming is the method to find the optimized solution of linear inequalities.

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