This paper considers the problem of minimizing the schedule length of a two
-machine shop in which not only can a job be assigned any of the two possib
le routes, but also the processing times depend on the chosen route. This p
roblem is known to be NP-hard. We describe a simple approximation algorithm
that guarantees a worst-case performance ratio of 2. We also present some
modifications to this algorithm that improve its performance and guarantee
a worst-case performance ratio of 3/2.