How did the roman armies stay supplied with food and equipment while on campaigns far from Rome?

In Early Roman history, Roman armies would carry around their supply wagons, and use supply routes, much like the tribes of Gaul would for the entirety of their tribe (which is why it after losing one battle, a lot of Gallic tribes were out of it if they lost their tribal supply wagon, or if it was destroyed). After the Marian reforms, however, Marian forced his troops to each carry around small 'backpacks' filled with survivalist essential items; hence their nickname 'Marian's Mules'. Roman armies also had something called Sedes Belli, which were areas completely set up prior to battles and wars, meant as resupplying stations, or a place to fall back should things go bad for Roman armies. Generally, it was either a small outpost built quickly with the sole intention of harboring foods and water, as in the case of stations in Germania, where Roman civilization was afar, or it was an actual city/port that would be stocked with foods and other provisions, such as in the case of the city Antioch, when Rome would conduct campaigns against Parthia. If Roman armies were truly far away from anything, which was almost a nonexistent problem after the death of Trajan, then the armies would resort to local foraging if necessary. Small parties of men to search local fauna and flora, then take what could be found or was needed quickly, is an effective doctrine as long as the local environment can provide it, and you don't get caught.

Also, Roman military organization within ranks was completely set up by emperor Augustus to be convenient towards both the governments budget and the armies stomachs; From Jonathan Roth's 'The Logistics of the Roman Army at War': "As the soldier’s daily grain ration was two sextarii, the eight-man contubernium established by Augustus would, conveniently, have required exactly one modius. From this it is concluded that the principle rationale behind the organisation of the imperial legion was ease of ration calculations: ten modii per century, sixty modii per cohort, and so on." Very clever, Rome.