应威廉希尔中文官方网站的邀请，英国谢菲尔德大学威廉希尔中文官方网站Francisco Saldanha-da-Gama教授于2025 年 4 月 8 日下午 2 点在中关村校区主楼317会议室做了题为《Project Scheduling with Flexible Resources》的学术报告。报告会由郭思尼老师主持，学院众多师生参加了本次报告会。
Francisco Saldanha-da-Gama教授围绕多技能资源约束项目调度问题（MS-RCPSP）展开深入讲解。他首先介绍了项目调度问题的基本构成，包括任务、任务间优先关系和执行时间，而目标是优化绩效指标。当引入资源限制时，形成资源约束项目调度问题（RCPSP），进一步考虑资源的多技能特性则发展为 MS-RCPSP。教授通过咨询公司分配团队、软件开发团队组建以及评估团队组织等实际案例，生动阐释了MS-RCPSP在现实中的应用场景。
Francisco Saldanha-da-Gama教授重点介绍了针对MS-RCPSP的不同建模框架，涵盖连续时间模型和离散时间模型。连续时间模型采用连续时间变量表示活动开始时间，其优点是整数变量较少，但线性松弛边界较弱；离散时间模型将时间离散化，划分为多个时间单元，虽属于大规模整数规划模型，但线性松弛边界更精确。教授还详细讲解了基于序列的模型和时间索引决策变量相关模型，并对不同模型的线性规划松弛边界进行了理论比较和实证分析。
在实证分析环节，Francisco Saldanha-da-Gama教授介绍了研究中使用的基准实例，这些实例通过技能因子（SF）、网络复杂度（NC）和修正资源强度（MRS）等特征进行分类。所有模型使用C++结合IBM、ILOG、CPLEX进行编码，设置5小时的CPU时间限制进行实验。实验结果显示，连续时间模型在求解到最优性方面表现最佳，找到的最优解数量最多，计算时间最短，且找不到可行解的实例最少；而离散时间模型在提供线性规划松弛边界方面表现更优，但在求解最优解时存在一定局限性。
报告结束后， Francisco Saldanha-da-Gama教授和与会师生展开了积极的讨论交流。师生们就研究中的疑问、模型应用前景等问题积极提问，教授耐心解答，现场学术氛围浓厚。此次报告不仅让师生们对多技能资源约束项目调度问题有了更深入的理解，也为相关领域的研究提供了新的思路和方法，受到了师生们的一致好评。
汇报人简介：
Professor Francisco Saldanha-da-Gama serves as the Chair of Supply Chain Management at the Management School of the University of Sheffield and heads its Center for Applied Research in Supply Chain, Operations, and Logistics. Specializing in operations research, supply chain management, logistics, decision-making under uncertainty, facility location, and project scheduling, he has amassed profound academic insights through three decades of teaching in operations management, operations research, applied probability, and statistics. A prolific scholar, he has led/co-led numerous domestic and international research projects, guided over 20 doctoral and postdoctoral researchers, and secured over ten academic awards—including the 2024 “Best Paper Award” from Omega: The International Journal of Management Science. Actively involved in international academic circles, he is a member of the EURO Working Group on Locational Analysis. He also acts as Editor-in-Chief of Computers & Operations Research, consulting editor for Social Sciences & Humanities Open, and sits on the editorial advisory boards of journals like Journal of the Operational Research Society, Omega, and Operations Research Perspectives, fostering academic advancement.
In academic research and practical application, Professor Francisco Saldanha-da-Gama focuses on developing innovative optimization models to tackle core challenges in supply chain resilience and dynamic resource allocation. For instance, in project scheduling, he proposed hybrid continuous-discrete time models for the Multi-Skilled Resource-Constrained Project Scheduling Problem (MS-RCPSP), balancing computational efficiency and solution accuracy. Empirical studies validate that continuous-time models outperform discrete ones in solving large-scale MS-RCPSP instances, especially under tight time limits. His research integrates benchmark dataset analysis with real-world scenarios like software development and consulting to highlight methodological practicality. Moreover, he collaborates with industry partners to apply findings in optimizing healthcare logistics, energy distribution, and disaster response networks, merging theoretical innovation with practical use. As a prominent speaker at international academic conferences, he bridges operations research theory and practice through sustainable, adaptive systems, driving the field’s ongoing progress.
