多模式项目调度的连续时间公式
Continuous-Time Formulations for Multi-Mode Project Scheduling
摘要：
本文综述了多模式资源受限项目调度问题的紧致连续时间公式。具体来说，我们首先指出了一个严重的缺陷，在现有的开始结束事件为基础的配方，由于不一致的模式选择。我们提出了两种选择，制定失踪的约束，我们认为一个等价的重新稀疏的约束矩阵。其次，我们制定了一个现有的模型，依赖于开关事件的聚合变体，并澄清在这样的模型中的模式一致性问题的作用。第三，我们提出了现有的网络流配方的两个变种。我们通过调整以前使用的几种技术来增强我们的模型，例如，在仅具有单一模式的情况下。大量的基准实例从文献中提供了一个最新的和公平的计算研究与开箱即用的求解程序包的基础。我们将我们的模型与文献中的两种模型进行比较。我们的实验自信地断言，网络流公式在测试床中占主导地位，他们提供了一个提示，为什么基于事件的模型在多模式设置中变得不那么有竞争力。
英文摘要：
This paper reviews compact continuous-time formulations for the multi-mode resource-constrained project scheduling problem. Specifically, we first point out a serious flaw in an existing start-end-event-based formulation owing to inconsistent mode choices. We propose two options to formulate the missing constraints and we consider an equivalent reformulation with sparser constraint matrix. Second, we formulate an aggregate variant of an existing model that relies on on-off-events and clarify the role of mode consistency issues in such models. Third, we suggest two variants of an existing network flow formulation. We enhance our models by adapting several techniques that have been used previously, e.g., in cases with only a single mode. A large set of benchmark instances from the literature provides the basis for an up-to-date and fair computational study with an out-of-the-box solver package. We compare our models against two models from the literature. Our experiments assert confidently that network flow formulations prevail in the test bed, and they provide a hint on why event-based models become less competitive in multi-mode settings.
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