Minimizing bicriteria scheduling of two-component jobson a bounded series-batching machine

Minimizing maximum cost and makespan simultaneously on a bounded series-batching machine is considered in the paper, in which each job contains a specific component and a standard component. Specific components are scheduled separately, while standard components are scheduled in batches. Completing a job means that its two components have been completed. Additionally, the two components of a job can be scheduled in any order. We present an O(n⁴)-time algorithm for the simultaneous optimization scheduling problem. When the maximum cost is the maximum lateness, time complexity of the algorithm is O(n³log n) time.