Correct me if I am wrong,but your post seems to be written with the implicit assumption that there needs to be some kind of central planner, or at least an administration regulating production and redistributing goods.

Therefore, the distribution of goods among different classes of people should be done in such a way that the social welfare is maximized.

I see two classes of people: the productive class in the market economy, and the political class of bureaucrats and administrators feeding parasitically off the productive.

The same quantity of goods can be produced with the help of different production techniques.

Yes. And the prices of the various inputs combined with the prices for the products tend to signal the most effective way to produce a given good or service in a complex economy while simultaneously informing consumers and producers of supply and demand. None of this requires a decision-maker.

...the producer has to face the problem of scarcity and selection at the same time. [...] This can be analyzed with the help of Production Possibility Curve.

People don't think in terms of abstract mathematical graphs in the real world. Supply, demand, risk, reward, price, and prejudice all come into play. You can use data to describe what factors likely influenced people after the fact, and you can use data to estimate future outcomes, but good economic analysis is merely descriptive, not prescriptive.