时间受限项目调度中的热带优化问题
Tropical optimization problems in time-constrained project scheduling
AI总结：
本文研究时间受限项目调度中的优化问题，通过热带数学方法解决调度问题，提出紧凑向量形式的解法，用于进一步分析和实际应用。
摘要：
我们考虑由并行活动组成且受多种时间约束的项目，包括开始-开始、开始-完成和完成-开始 precedence 关系、释放时间、截止期和截止日期。调度问题被公式化为寻找最优调度方案，以最小化项目工期、最大偏差、最大流时间及最大完成时间偏差。我们将这些问题表示为热带数学中的优化问题，并通过应用热带优化的直接求解方法来解决。结果得到新的调度问题直接解法，以紧凑向量形式呈现，可用于进一步分析和实际实施。通过简单的数值示例展示了这些解法。
英文摘要：
We consider a project that consists of activities to be performed in parallel under various temporal constraints, which include start-start, start-finish and finish-start precedence relationships, release times, deadlines, and due dates. Scheduling problems are formulated to find optimal schedules for the project with respect to different objective functions to be minimized, such as the project makespan, the maximum deviation from the due dates, the maximum flow-time, and the maximum deviation of finish times. We represent these problems as optimization problems in terms of tropical mathematics, and then solve them by applying direct solution methods of tropical optimization. As a result, new direct solutions of the scheduling problems are obtained in a compact vector form, which is ready for further analysis and practical implementation. The solutions are illustrated by simple numerical examples.
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