In a flow-shop problem with transportation times and a single robot additionally transportation times are considered which arise when a job changes from one machine to another. These transportations are all done by a single robot, i.e. conflicts between different transport operations may arise.
If job i changes from machine Mk to Mk+1,
a job- and machine-dependent transportation time
t ik
occurs. If these times are job-independent or
machine-independent, we write
t k
or
t i.
Constant tranportation times are denoted by
t ik=T
and
t i
{T 1,T 2}
means that the transportation times may take only two values.