A container on private property, in a driveway or inside a job-site boundary, is the normal arrangement on the Arkansas side of Texarkana and it is how nearly every job here is served.
The written position on hauling is genuinely split, and the useful thing we can do is show you both halves rather than pick one. The city's licensing rule makes it unlawful to engage in the business of collecting and removing what the code calls garbage and refuse, or to operate a garbage or refuse truck over the city streets, without a city license. The same article then defines refuse as a closed list of six things: garbage, household trash, yard trash, brush, dead animals and business trash. Building materials are defined separately in that list of definitions, as lumber, brick, plaster, gutters and similar material from repairs, additions, new building or demolition, and they are not one of the six. The article goes further and says in terms that rock, scrap building material and other trash from construction or major remodeling is not classified as garbage, and that removing it is the responsibility of the owner or the contractor rather than the city.
Against that, the chapter's commercial collection article speaks throughout of garbage, trash or other solid waste from commercial premises, which is wider language, and it sends its own licensing requirement back to the same city license. The two halves have not been written to agree with each other. So the honest answer for a commercial job in Texarkana, Arkansas is that the city should confirm which reading it applies, and your account manager raises exactly that with the city before a commercial booking. For ordinary residential renovation the construction-waste wording is about as clear as it gets.
Two placement points are settled and worth knowing. The city's streets chapter contains no container permit of any kind; its permitting runs to excavation, and its street-closing rule applies only to work being done under an excavation permit. What does reach a container sits in the solid waste chapter instead, and it reaches further than people expect: depositing construction waste along a gutter, alley, sidewalk, street, vacant lot or any public or private premises inside the city limits is an offence, so a container has to hold its contents and the ground around it has to stay clear. The same chapter requires any vehicle cargo moving over city streets to be contained or covered.