In a flow-shop problem with transportation times and a single robot n jobs consisting of m operations have to be processed in the same order on m machines. Additionally, transportation times are considered if a job changes from one machine to another. We assume that unlimited buffer space exists between the machines and all transportations have to be done by a single robot. The objective is to determine a feasible schedule with minimal makespan. New complexity results are derived for special cases where the processing or transportation times are constant values. Some of these may also be interpreted as new results for special cases of the classical 3-machine flow-shop F3||Cmax with constant processing times at certain stages.