On private property, including your driveway or a fenced job site, Miamisburg requires no placement permit for a container.
The right-of-way is a hard no. The City's encroachment rules say that all encroachments on public rights of way made after the section took effect are illegal, that the City Manager may require the owner to remove them, and that the removal cost falls on that owner. There is no permit limb to lift it. The City's other right-of-way instruments are a registration and street-opening regime for utility work and an excavation permit, neither of which reaches a placed object. So in Miamisburg the container goes on your own ground.
On the collection side, the City declares an exclusive right to perform refuse and recyclable collection, then says in the same section that private waste collectors may collect for residential apartments and for commercial and industrial establishments the City does not serve. More usefully, the City's own definition of refuse expressly excludes construction material, naming earth, gravel, brick, mortar, stone, wood, lime, plaster, cement, paint and roofing shingles. The chapter has no hauler license section at all. Read together, a container of construction debris sits outside the City's collection chapter. The caveat is that the City Manager may designate material as recyclable, and the recyclable definition is broad, so we treat this as a legal reading rather than a settled answer and we say so.
There is also a county layer. Montgomery County's health district operates a registration covering solid waste and trash-hauling vehicles, which not every Ohio county does, and that is a supplier-side requirement rather than something you file. Your account manager confirms it is in order before a delivery.
For city questions, ask for the City of Miamisburg Service Department, and for anything about the receiving site, the Montgomery County Solid Waste District. Your account manager will get you the current direct number for either.