Hierarchical minimization of two maximum costs on a bounded serial-batching machine

This paper studies a hierarchical optimization problem of scheduling $n$ jobs on a serial-batching machine, in which two objective functions are maximum costs. By a hierarchical optimization problem, we mean the problem of optimizing the secondary criterion under the constraint that the primary criterion is optimized. A serial-batching machine is a machine that can handle up to $b$ jobs in a batch and jobs in a batch start and complete respectively at the same time and the processing time of a batch is equal to the sum of the processing times of jobs in the batch. When a new batch starts, a constant setup time $s$ occurs. We confine ourselves to the bounded model, where $b<n$. We present an $O(n^4)$-time algorithm for this hierarchical optimization problem. For the special case where two objective functions are maximum lateness, we give an $O(n^3\log n)$-time algorithm.

SOME IMPROVED ALGORITHMS ON THE SINGLE MACHINE HIERARCHICAL SCHEDULING WITH TOTAL TARDINESS AS THE PRIMARY CRITERION

It is well-known that a single machine scheduling problem of minimizing the total tardiness is NP-hard. Recently, Liu, Ng and Cheng solved some special hierarchical minimization problems with total tardiness as the primary criterion by the Algorithm TAP (Two Assignment Problems) in O(n3) time. And in this paper we present some algorithms for these problems with running time O(n log n).