Bicriteria fabrication scheduling of two-component jobs on a single machine

This paper studies the bicriteria problem of non-preemptively scheduling n jobs, each of which is associated with a due date and comprises a standard and a specific component, on a single fabrication machine to minimize makespan and maximum lateness simultaneously. The specific components are processed individually and the standard components are grouped into batches for processing. A setup time is required before each batch of standard components is processed. A standard component is available (i.e., ready for delivery to the next production stage) only when the batch it belongs to is totally completed, whereas a specific component is available on completion of its processing. The completion time of a job is defined as the moment when both its two components have been processed and are available. An O(n^2log n) -time algorithm with linear memory requirements is presented which can generate all Pareto optimal points and find a corresponding Pareto optimal schedule for each Pareto optimal point.