So I got from Wikipedia that the Roman army reached its peak in term of size in approx. 211 AD with a force of 450 000 men. Even considering that not all of that was regular legions, the magnitude of this number just makes me wonder about the underlying logistics.
Did all of these soldiers have the same uniformized equipment? If so, do we have records of how this feat was achieved ? (Or maybe there was differences between legions on that matter?) It seems that the only way to accomplish this is by having some sort of proto mass production capabilities. What kind of company/organization/person would have been in charge of this?
Sorry if something is unclear with my English, I'm more than willing to further explain what I'm trying to find out if necessary.
Most of the legionary in 211 CE would have roughly the same equipment: a gladius (sword), two or more pila (throwing spears), a galea (helmet), a medium or heavy armor of some sort, and a scutum (shield). This was the basic armament of a Roman soldier for hundreds of years. In 211 there was some variation in the equipment, probably driven by local taste or the circumstances of geography. Hardly ever do we find two gladii that are exactly alike, even from the same area.
In the Republic, soldiers were traditionally expected to equip themselves. Nevertheless, the basics listed above were (we think) mostly manufactured in central and western Italia, and were about as uniform as one might expect. The swords were generally the gladius type, and the shields were generally the same weight and dimension. All of this is assuming the same time period, and the same force. Soldiers who could not equip themselves were given loaner items, but all of it (the nice stuff and the crap stuff) was manufactured in workshops (fabricae) employed via contracts. The publicani often bid for and executed such contracts (e.g., "I need 2000 shields and 2500 swords delivered to the Campus Martius by the end of the Winter").
In the Principate, production of armaments seems to shift away from Italy, at least partially. There is an abundance of archaeological evidence that arms were being manufactured at legionary bases in the provinces, especially the central and western provinces. In the East, we tend to find a lot of arms workshops that are called "civilian" for one reason or another. Either way, the site of production seems to become attached more directly to the legions' posts, not their point of origin. There is good evidence that equipment was issued and re-issued (some finds have three of four names inscribed on them in succession). This efforts kept all the soldiers at minimum levels of equipage. They were free, however, to purchase nicer items for themselves, and many probably did so. Items inlaid with tin and aniello (with a silverish sheen) were common. The basic sword you got from the fabricae could potentially be pretty shoddy, and the same for armor or helmet. Upgrading those items could help to keep you alive, and looking like a veteran instead of a fresh-faced recruit who just stumbled out of the armentaria (armory).
In the time you mention (the early 3rd century CE), there was no centralized production apparatus in the Empire. Each legion was responsible for keeping itself equipped over time, probably by a combination of the camp workshops and civilian smiths in the towns which invariably grew up around the camps. Later on, the production of arms would become centralized and organized into regional district armories.
For more, see Rathbone's detailed chapter on the subject in The Cambridge History of Greek and Roman Warfare, Vol 2: Rome from the late republic to the late empire (2008).