The resource allocation problem (RAP) determines a solution to optimally allocate limited resources to several activities or tasks. In this study, we propose a novel resource allocation problem referred to as multi-period non-shareable resource allocation problem (MNRAP), which is motivated by the characteristics of resources considered in the stem cell culture process for producing stem cell therapeutics. A resource considered in the MNRAP has the following three characteristics: (i) resource consumption required to perform an activity and available resource capacity may change over time; (ii) multiple activities cannot share one resource; and (iii) resource requirements can be satisfied through the combination of different types of resources. The MNRAP selects some of the given activities to maximize the overall profit under limited resources with these characteristics. To address this problem, pattern-based integer programming formulations based on the concept of resource patterns are proposed. These formulations attempt to overcome the limitations of a compact integer programming formulation, the utilization of which is challenging for large-scale problems owing to their complexity. Further, based on a branch-and-price approach to solving pattern-based formulations, effective heuristic algorithms are proposed to provide high-quality solutions for large instances. Moreover, through computational experiments on a wide range of instances, including real-world instances, the superiority of the proposed formulations and heuristic algorithms is demonstrated.

中文翻译：

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多周期不可共享资源分配问题的整数优化模型与算法

资源分配问题 (RAP) 确定将有限资源最佳地分配给多个活动或任务的解决方案。在本研究中，我们提出了一种新的资源分配问题，称为多周期不可共享资源分配问题（MNRAP），该问题是由用于生产干细胞疗法的干细胞培养过程中考虑的资源特征所激发的。 MNRAP 中考虑的资源具有以下三个特征： (i) 执行某项活动所需的资源消耗和可用资源容量可能随时间而变化； (ii) 多项活动不能共享一种资源； (iii) 资源需求可以通过不同类型资源的组合来满足。 MNRAP 选择一些给定的活动，以在具有这些特征的有限资源下实现总体利润最大化。为了解决这个问题，提出了基于资源模式概念的基于模式的整数规划公式。这些公式试图克服紧凑整数规划公式的局限性，由于其复杂性，该公式的使用对于大规模问题具有挑战性。此外，基于分支和价格方法来解决基于模式的公式，提出了有效的启发式算法，为大型实例提供高质量的解决方案。此外，通过对包括现实世界实例在内的广泛实例的计算实验，证明了所提出的公式和启发式算法的优越性。