Dual constrained single machine sequencing to minimize total weighted completion time

We study a single-machine sequencing problem with both release dates and deadlines to minimize the total weighted completion time. We propose a branch-and-bound algorithm for this problem. The algorithm exploits an effective lower bound and a dynamic programming dominance technique. As a byproduct of the lower bound, we have developed a new algorithm for the generalized isotonic regression problem; the algorithm can also be used as an O(nlogn)-time timetabling routine in earliness-tardiness scheduling. Extensive computational experiments indicate that the proposed branch-and-bound algorithm competes favorably with a dynamic programming procedure. Note to Practitioners-Real-life production systems usually involve multiple machines and resources. The configurations of such systems may be complex and subject to change over time. Therefore, model-based solution approaches, which aim to solve scheduling problems for specific configurations, will inevitably run into difficulties. By contrast, decomposition methods are much more expressive and extensible. The single-machine problem and its solution procedure studied in this paper will prove useful to a decomposition method that decomposes multiple-machine, multiple-resource scheduling problems into a number of single-machine problems. The total weighted completion time objective is relevant to production environments where inventory levels and manufacturing cycle times are key concerns. Future research can be pursued along two directions. First, it seems to be necessary to further generalize the problem to consider also negative job weights. Second, the solution procedure developed here is ready to be incorporated into a machine-oriented decomposition method such as the shifting bottleneck procedure.