Heuristics for parallel-machine scheduling with job class setups and delivery to multiple customers

We consider the identical parallel-machine scheduling problem in which both job class setups for job processing and product delivery are required. A setup time is incurred for a job if it is the first job to be processed on a machine or its processing on a machine follows a job that belongs to another class. Processed jobs are delivered in batches to their respective customers. The batch size is limited by the capacity of the delivery vehicles and each shipment incurs a delivery (transportation) cost and takes a fixed amount of time. The objective is to minimize the weighted sum of the last arrival time of the jobs to the customers and the delivery cost. We develop heuristics for the problem and analyse their performance bounds.