I'm not quite sure who these Gulledges are - and I can find very little regarding Gulledge Brothers Lumber Co. and Railroad.
It looks like there were two companies of the same name in Arkansas, whether the first one was dissolved and another reformed afterward, I can't tell.
There are two entries in the Arkansas Logging Railroad List. 1) Gulledge Brothers Lumber Co. of White, Ashley Co. AR, was started in 1906 and ended in 1916. 2) Gulledge Brothers Lumber Co. of White, Ashley Co. AR, was started in 1907 and no end date is listed.
An early case in the State of Minnesota has been cited several times in various court decisions, and that case is:
Gulledge Brothers Lumber Co. vs. Wenatchee Land Co.
In the case, the Minnesota courts held the rule that courts of one state will not enforce the penal laws of another applied to suits for the recovery of revenue penalties.
Gulledge Brothers Lumber Co. is also listed under Mississippi Logging Railroads and Louisiana Logging Railroads - so it appears either this was quite a large operation or that there was more than one Gulledge family operating under the same or similar names.
The Louisiana concern was in Bastrou, Morehouse Parish. There was a description of it in the 1917 Southern Lumberman Sawmill Directory:
Bastrou. (Morhouse Parish, pop. 1,000) Gulledge Lumber and Stave Co., circular sawmill; capacity 30,000 ft. Equipment: planing mill (capacity 30,000 ft.), edgers, trimmers, dry kilns, logging road, 2 miles of track, 30-lb. rails, commissary. Output: cypress, red and sweet gum, hickory, red and white oak, shortleaf yellow pine; staves.
There is a litte more information available for this LA site. W. C. Shelton sold 60 acres of property to W. T. Gulledge in 1917 for $900 cash.
W. T. Gulledge and his brother L. E. Gulledge built a sawmill there and called it "Cornal Shelton". In 1922, the brothers sold the property to Frost Johnson Lumber Co. for $25,000 cash. After the sale, the Gulledge mill was replaced by a permanent steam-powered mill.
Those two sets of initials are the only ones I've found so far that reference a lumber co.
The Crossett Lumber Co. obtained properties once logged by the Gulledge Brothers near White, AR, in the 1920s.
You may try looking up a copy of the court case in Minnesota to see what names are listed there, if any.
In the meantime, I'll do some further digging to see if I can find out who these men are and how they fit into the family. If I find anything else, I'll post it here :)