The routing open shop problem: new approximation algorithms

We consider the routing open shop problem being a generalization of the open shop and the metric travelling salesman problems. The jobs are located at nodes of some transportation network, and the machines travel on the network to execute the jobs in the open shop environment. The machines are initially located at the same node (depot) and must return to the depot after completing all the jobs. It is required to find a non-preemptive schedule that minimizes the makespan. The problem is NP-hard even on a two-node network with two machines. We present new polynomial-time approximation algorithms with worst-case performance guarantees.