Approximation algorithm for minimizing total latency in machine scheduling with deliveries

We study the problem of minimizing total latency in machine scheduling with deliveries, which is defined as follows. There is a set of n jobs to be processed by a single machine at a plant, where job Ji is associated with its processing time and a customer i located at location i to which the job is to be delivered. In addition, there is a single uncapacitated delivery vehicle available. All jobs (vehicle) are available for processing (delivery) at time 0. Our aim is to determine the sequence in which the jobs should be processed in the plant, the departure times of the vehicle from the plant, and the routing of the vehicle, so as to minimize the total latency (job delivery time). We present a 6e ∼ 16.309691-approximation algorithm for the problem.