具有不同工件尺寸和不兼容工件族的单机调度问题
Scheduling a single parallel-batching machine with non-identical job sizes and incompatible job families
摘要：
研究了工件尺寸不同且工件族不兼容的单机上工件调度问题。来自同一系列的工件具有相同的处理时间，并且可以装入一个批，只要批大小符合机器的能力。目标是最小化总加权完工时间。该问题结合了两个经典的组合问题，即装箱问题和单机排序问题。我们开发了三个新的混合整数线性规划配方，即基于分配的配方，时间索引配方（TIF），集分割配方（SPF）。我们还提出了一个列生成（CG）算法的SPF，这是一个分支和价格（B&P）算法和CG为基础的启发式的基础。我们开发了一种预处理方法，以减少配方的大小。一个启发式框架的基础上邻近搜索也使用TIF开发。SPF和B&P可以在合理的运行时间限制内分别解决具有非单位和单位作业持续时间的实例，最多可以解决80个和150个作业。所提出的方法比文献中的方法性能更好。
英文摘要：
We study the scheduling of jobs on a single parallel-batching machine with non-identical job sizes and incompatible job families. Jobs from the same family have the same processing time and can be loaded into a batch, as long as the batch size respects the machine capacity. The objective is to minimize the total weighted completion time. The problem combines two classic combinatorial problems, namely bin packing and single machine scheduling. We develop three new mixed-integer linear-programming formulations, namely an assignment-based formulation, a time-indexed formulation (TIF), and a set-partitioning formulation (SPF). We also propose a column generation (CG) algorithm for the SPF, which is the basis for a branch-and-price (B&P) algorithm and a CG-based heuristic. We develop a preprocessing method to reduce the formulation size. A heuristic framework based on proximity search is also developed using the TIF. The SPF and B&P can solve instances with non-unit and unit job durations to optimality with up to 80 and 150 jobs within reasonable runtime limits, respectively. The proposed heuristics perform better than the methods from the literature.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
