This paper studies a due-window assignment scheduling problem with deterioration effects on a single-machine. Under different due-window assignment, i.e., the due-window of a job without any restriction, our goal is to make a decision on the optimal due-window and sequence of all jobs to minimize the weighted sum of earliness and tardiness, number of early and delayed, due-window starting time and size. We present properties of the optimal solutions, for some special cases, we prove that the problem can be solved in polynomial time. For the general case, we present a lower bound and an upper bound (i.e., a heuristic algorithm), then a branch-and-bound algorithm is proposed.

本文研究了单机上具有劣化效应的到期窗口分配调度问题。在不同的到期窗口分配下，即没有任何限制的作业的到期窗口，我们的目标是决定所有作业的最佳到期窗口和顺序，以最小化早到和迟到的加权和延迟、到期窗口开始时间和大小。我们提出了最优解的性质，对于一些特殊情况，我们证明了该问题可以在多项式时间内解决。对于一般情况，我们提出了一个下限和一个上限（即启发式算法），然后提出了一个分支定界算法。