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Madison Railroad is owned by the City of Madison Port Authority.
The railroad runs a short line of track which runs between Madison, Indiana and North Vernon, Indiana. The majority of their traffic is for the Sonoco plastics plant in North Vernon. Most of this traffic only runs the short distance from the plant to downtown North Vernon.
To my knowledge, Madison Railroad only owns two locomotives (3634 and 2013).
Their biggest claim to fame is that the steepest mainline grade in the country (5.8) is on the Madison Railroad where it goes down the hill in Madison to travel down to the Ohio River.
Of historic significance, the route that CMPA uses is part of the Madison & Indianapolis RR. Construction of this line was started in 1836 to connect Madison, Columbus, Indianapolis and Lafayette. The track carried the first steam locomotive in the state of Indiana in 1838.
After the Madison & Indianapolis RR's bankrupcy, the line was taken over by a subsidiary of the Pennsylvania RR.