Integrated production and job delivery scheduling with an availability constraint

In this paper we study the scheduling problem that considers both production and job delivery at the same time with machine availability considerations. There are two parallel machines, where one machine is not available during a time period. Only one vehicle is available to deliver jobs in a fixed transportation time to a distribution center. The vehicle can load at most c jobs as a delivery batch in one shipment due to the vehicle capacity constraint. The objective is to minimize the time by which all jobs are delivered. We consider both resumable and nonresumable cases. For each case, we propose an approximation algorithm with a worst case ratio of 3/2.