A heavy hydrocarbon oil is mixed with one or more disulfide oil compounds and/or one or more oxidized disulfide oil compounds and, optionally, a homogeneous catalyst includes dissolved hydrogen, and the mixture is subjected to a delayed coking process to produce a liquid coking unit product stream for recovery and further processing, with the delayed coking being completed in a reduced residence time as compared to the delayed coking of the heavy hydrocarbon oil without the DSO and/or ODSO compounds.