无限制公共交货期排序问题的优势不等式
Dominance inequalities for scheduling around an unrestrictive common due date
摘要：
在这项工作中考虑的问题包括在一台机器上调度一组任务，在一个无限制的共同的截止日期，以尽量减少提前和拖期的加权和。这个问题可以用一个紧凑的混合整数规划（MIP）来表示。在这篇文章中，我们专注于基于邻域的优势属性，其中邻域与插入和交换操作相关联。我们从这些属性的本地搜索程序提供了一个很好的启发式解决方案。这项工作的主要贡献站在一个确切的解决方案的背景下：我们得到的限制，消除非局部最优解的插入和交换操作。我们提出了线性不等式翻译这些约束，以加强MIP紧凑的制定。这些不等式称为优势不等式，与标准的强化不等式不同。我们提供了一个数值分析表明，增加这些不等式显着减少了使用标准求解器解决调度问题所需的计算时间。
英文摘要：
The problem considered in this work consists in scheduling a set of tasks on a single machine, around an unrestrictive common due date to minimize the weighted sum of earliness and tardiness. This problem can be formulated as a compact mixed integer program (MIP). In this article, we focus on neighborhood-based dominance properties, where the neighborhood is associated to insert and swap operations. We derive from these properties a local search procedure providing a very good heuristic solution. The main contribution of this work stands in an exact solving context: we derive constraints eliminating the non locally optimal solutions with respect to the insert and swap operations. We propose linear inequalities translating these constraints to strengthen the MIP compact formulation. These inequalities, called dominance inequalities, are different from standard reinforcement inequalities. We provide a numerical analysis which shows that adding these inequalities significantly reduces the computation time required for solving the scheduling problem using a standard solver.
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。
