Project scheduling is an important management task in many companies across different industries. Generally, projects require resources, such as personnel or funds, whose availabilities are limited, giving rise to the challenging problem of resource-constrained project scheduling. In this paper, we consider the scheduling of a project consisting of precedence-related activities that require time and two types of resources for execution: storage resources representing, e.g., the project budget; and renewable resources representing, e.g., personnel or equipment. Storage resources are consumed by activities at their start or produced upon their completion, while renewable resources are allocated to activities at their start and released upon their completion. The resource-constrained project scheduling problem with consumption and production of resources (RCPSP-CPR) consists of determining a minimum-makespan schedule such that all precedence relations are respected, the demand for each renewable resource never exceeds its capacity, and the stock level of each storage resource never falls below a prescribed minimum. Due to the consideration of storage resources, the feasibility variant of this problem is NP-complete. We propose a novel compact mixed-integer linear programming (MILP) model based on a novel type of sequencing variables. These variables enable us to identify which activities are processed in parallel and whether a sequencing of activities is necessary to respect the resource capacities. Our computational results indicate that our novel model significantly outperforms state-of-the-art MILP models for all considered scarcity settings of the storage resources. Additionally, our results indicate a superior performance for instances of the well-known resource-constrained project scheduling problem (RCPSP).

中文翻译：

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各种资源约束下项目调度的混合整数线性规划


项目调度是不同行业的许多公司的一项重要管理任务。一般来说，项目需要资源，例如人员或资金，但其可用性是有限的，从而导致资源受限的项目调度问题。在本文中，我们考虑一个项目的调度，该项目由与优先级相关的活动组成，这些活动需要时间和两种类型的资源来执行：代表项目预算的存储资源；可再生资源，例如人员或设备。存储资源由活动在开始时消耗或在活动完成时产生，而可再生资源在活动开始时分配给活动并在活动完成时释放。资源消耗和生产的资源受限项目调度问题 (RCPSP-CPR) 包括确定一个最小竣工进度表，以便尊重所有优先关系、对每种可再生资源的需求永远不会超过其容量以及库存水平每个存储资源永远不会低于规定的最小值。由于存储资源的考虑，该问题的可行性变体是NP完全的。我们提出了一种基于新型排序变量的新颖紧凑混合整数线性规划（MILP）模型。这些变量使我们能够确定哪些活动是并行处理的，以及是否需要对活动进行排序以尊重资源容量。我们的计算结果表明，对于所有考虑的存储资源稀缺设置，我们的新模型显着优于最先进的 MILP 模型。 此外，我们的结果表明，对于众所周知的资源受限项目调度问题 (RCPSP) 实例，我们具有卓越的性能。