Why was there no solution found to Soviet famines and near-famines?

This is a question about economics, not history.

Feeding people is no easy task. The typical person can easily eat through a panel truck full of food every year. The cost of this includes not only producing the food, but transporting and distributing it. Growing food and getting it to market is hard work and the farmer will demand something in return or he will not act. If someone cannot give the farmer something he wants or convince someone else to pay in their stead, they will receive no food and starve.

People will also starve if the economic process is obstructed or interfered with. For example, if soldiers prevent a farmer from transporting his goods from one place to another freely, or from selling his goods, or if they steal his produce, then this will result in a lack of food trading in the area in which the soldiers are operating, thus producing starvation, even if the inhabitants have money to pay.

The large Soviet famines involved both of these factors: people having no wealth to buy food and military/police forces interfering with food production and trading.

A lot of the time it was the Soviet Union government deliberately trying to starve some of their people to get rid of the "undesirable" people.
Sometimes it was because the Soviet Union government didn't know how to properly feed their people, and when they did they chose to ignore the people.

The last major famine in the USSR happened mainly in 1947, because of collectivization, war damage, the severe drought in 1946 in over 50% of the grain-productive zone of the country and government social policy and mismanagement of grain reserves.

Also, some famines were not preventable, like the Great Famine of 1315–1317. Crops failed nation-wide and back then they did not have the technology to prevent such a catastrophe.

The same can be said for Russia, when Stalin was in power. Millions of his people died in Russia! Why? Because he didn't care to feed them.

You are making a number of assumptions here which are not correct. The basic mechnanism of the pre-war famines was this:

Stalin was pursuing a policy of rapid and extensive industrialization. This policy, which was not based on organic growth, necessitated the purchase on a huge scale of Western (largely American) technology and expertise. Whole factories were purchased in the US and installed in Russia under the supervision and guidance of American engineers.

This required in turn huge hard currency outlays which could only be built up quickly by exports. The sale of gold confiscated from wealthy citizens and objects of art (such as Russian icons) provided some currency but most came from the export of enormous quantities of grain.

This grain was forcibly extracted from peasants, with no concern at all whether they had enough - either to plant or to eat. Inevitably, they starved.

That's how it was.

So, as you see, the USSR in the relevant timeframe was not importing grain, it was exporting it big time. (The imports only started in 1962 or so, as a temporary expedient). But is was not exporting surplus, it was exporting its basic stock. Another point to correct is that the ultimate "end-users", the city dwellers, did not starve. It was the producers, the peasants, who did, as I have explained above. Finally, the Soviet citizens did not know anything about life in the West. They were fed propaganda to the effect that Western conditions were much worse for common folk and many of them sincerely believed their standard of life was higher than that of their Western counterparts.

A few points not covered in other excellent answers:

• Wealthy peasants, the Kulaks, were specifically targeted by Soviet regime. Whilst these peasants were comparably wealthy and resistant to land reform - they were also the farmers most likely to be literate, skilled and possessing efficient farming infrastructure. Killing these peasants reduced the agricultural output of the USSR.
• The political stranglehold that Trofim Lysenko and Lysenkoism had on Soviet agronomy. The guy was a political hack that basically undermined a generation of scientists.
• Some countries have less arable land than others and so trade other goods and services for food. The USSR had few healthy trade relationships outside of the Warsaw block.
• Meet the new boss, same as the old boss. Despite left-right hand wringing about the USSR, the attitude towards the common population has been remarkably consistent across various regimes from the Tsars to the Bolsheviks to today's oligarchic kleptocracy. Indeed, we can blame it on the one-two punch of the Mongol Invasion and the Black Death. The Mongols destroyed the Kievan Rus, the last democratically inclined nation in the region; replacing it with Tartar overlords. The Black Death altered the relationship between nobles and peasants due to skill shortages. In Western Europe the re-negotiation resulted increased autonomy and power to the people (or guilds), but in Eastern Europe the nobles tightened their hold on serfs and serfdom; an attitude shift that has lasted to this day.