On-line integrated production–distribution scheduling problems with capacitated deliveries

In on-line integrated production–distribution problems, customers release jobs to a manufacturer that has to process the jobs and deliver them to the customers. The jobs are released on-line, that is, at any time there is no information about future jobs. Processed jobs are grouped into batches, which are delivered to the customers as single shipments. The total cost (to be minimized) is the sum of the total weighted flow time and the total delivery cost. Such on-line integrated production–distribution problems have been studied for the case of uncapacitated batches. We consider the capacitated case with an upper bound on the size of a batch. For several versions of the problem, we present efficient on-line algorithms, and use competitive analysis to study their worst-case performance.