Scheduling parallel machines with single vehicle delivery

We investigate the integrated production and distribution scheduling problem in a supply chain. The manufacturer’s production environment is modeled as a parallel machine system. A single capacitated vehicle is employed to deliver products in batches to multiple customers. The scheduling problem can also be viewed as either parallel machines with delivery considerations or a flexible flowshop. Different inventory holding costs, job sizes (volume or storage space required in the transportation unit), and job priorities are taken into account. Efficient mathematical modeling and near-optimal heuristic approaches are presented for minimizing total weighted completion time.