Scheduling under nonrenewable resources is one of the challenging issues in project scheduling problems. There are many cases where the projects are subject to some nonrenewable resources. In most of the literature, nonrenewable resources are assumed to be available in full amount at the beginning of the project. However, in practice, it is prevalent that these resources are procured along the project horizon. This paper studies the generalized resource-constrained project scheduling problem (RCPSP) where, in addition to renewable resources, nonrenewable resources are considered, such as budget or consuming materials by the project activities. As the problem is NP-hard, some sub-algorithm elements are developed, which can be used in the structure of inexact approaches for solving the problem. These elements include constraint propagation, priority rules, schedule generation schemes, and local search improvement procedures. Also, a lower bounding algorithm is developed based on the Lagrangian Relaxation (LR) approach, and the problem is optimized by the Genetic Algorithm (GA). The hybrid GA–LR​ algorithm produces a result reasonably near to optimum solutions. Comprehensive computational experiments based on standard project scheduling problems are performed to evaluate these developments. The experiments showed the performance and robustness of the proposed algorithm.

在不可调度资源下进行调度是项目调度问题中具有挑战性的问题之一。在许多情况下，项目需要使用一些不可再生资源。在大多数文献中，假定不可再生资源在项目开始时就可以全部使用。但是，实际上，这些资源是沿着项目范围进行采购的。本文研究了广义的资源受限项目计划问题（RCPSP），该问题中除了可再生资源外，还考虑了不可再生资源，例如项目活动的预算或消耗材料。由于问题是NP问题，因此开发了一些子算法元素，可将其用于解决问题的不精确方法的结构中。这些要素包括约束传播，优先规则，时间表生成方案和本地搜索改进程序。此外，基于拉格朗日松弛（LR）方法开发了一个下界算法，并通过遗传算法（GA）对问题进行了优化。混合GA-LR算法产生的结果合理接近最佳解。进行了基于标准项目计划问题的综合计算实验，以评估这些进展。实验表明了该算法的性能和鲁棒性。进行了基于标准项目计划问题的综合计算实验，以评估这些进展。实验表明了该算法的性能和鲁棒性。进行了基于标准项目计划问题的综合计算实验，以评估这些进展。实验表明了该算法的性能和鲁棒性。