Abstract: To achieve schedule stability of a project plan in the presence of activity duration variabilities,an integrated optimization method of robust project scheduling and resource allocation was proposed considering resource transfer times.Three kinds of surrogate measures of solution robustness were designed from three different perspectives: resource transfer relations,activity slacks and random activity durations.Then,two mixed integer programming models(MinEA,MaxPF)as well as a stochastic programming model(MinTPC)were constructed and solved by using exact methods and a tailored tabu search algorithm.On this basis,a hybrid optimization strategy(MinTPC+MaxPF)was suggested which determined the start times of project activities in the first stage and further optimizes the resource transferring decisions in the second stage.The simulation experiment results showed that the MinTPC+MaxPF method could achieve the best performance regarding both solution robustness and quality robustness.Besides,solution robustness of the MinEA method was greater than that of MinTPC,while the latter had an edge over the former in terms of quality robustness.The proposed models and methods could provide guidance for coordinating activity scheduling and resource transferring under activity duration uncertainty,which helps to improve schedule robustness of real-life projects and to enhance economic benefits of enterprises.

Key words: resource-constrained project scheduling problem, resource transfer time, robustness, duration uncertainty, resource flow network

摘要： 为使项目在面临活动工期扰动时尽可能按照基准调度计划稳定执行,针对带转移时间的资源受限项目调度问题提出鲁棒调度与资源分配集成优化方法。分别从资源转移关系、活动时差、随机活动工期三个不同角度设计三种解鲁棒性代理指标,构建了两个混合整数规划模型(MinEA,MaxPF)和一个随机规划模型(MinTPC),并分别采用精确方法和禁忌搜索启发式算法求解;在此基础上提出MinTPC+MaxPF混合优化策略。仿真实验结果表明,MinTPC+MaxPF方法在项目解鲁棒性和质鲁棒性两方面均能获得最优绩效;MinEA方法的解鲁棒性优于MinTPC,而后者的质鲁棒性优于前者。所研究的模型和方法,可以为项目决策者在工期不确定环境下协调活动进度安排和优化资源转移提供指导,提升项目计划鲁棒性,提高企业的经济效益。

关键词: 资源受限项目调度问题, 资源转移时间, 鲁棒性, 工期不确定, 资源流网络