资源可用量不确定和活动多模式情形下的随机项目调度问题  

Stochastic scheduling of projects with uncertain resource availabilities and multiple modes

作　　者：谢芳 徐哲[2] 于静[3] XIE Fang;XU Zhe;YU Jing(School of Finance,Shandong Technology and Business University/Collaborative Innovation Center for Financial Service Transformation and Upgrading,Yantai 264005,China;School of Economics and Management,Beihang University,Beijing 100191,China;School of Management,Tianjin University of Technology,Tianjin 300384,China)

机构地区：[1]山东工商学院金融学院金融服务转型升级协同创新中心,山东烟台264005 [2]北京航空航天大学经济管理学院,北京100191 [3]天津理工大学管理学院,天津300384

出　　处：《管理工程学报》2022年第3期170-178,共9页Journal of Industrial Engineering and Engineering Management

基　　金：教育部人文社会科学基金资助项目(17YJC630177、16YJC630159);国家自然科学基金资助项目(71571005、71771138)。

摘　　要：可更新资源可用量的不确定是项目调度中普遍面临的问题,本文在随机资源可用量和活动多模式的约束下,考虑到活动可中断的情形,基于马尔可夫决策过程理论构建以最小化项目期望工期为目标的随机调度模型,针对问题特征设计以动态活动-模式优先规则和串行调度生成机制相结合的启发式算法作为基准策略的Rollout算法,并针对PSLIB的J30算例集展开实验研究。研究发现:随着资源可用量变化波动的增大,项目工期、活动中断次数以及问题的求解难度也随之增加;虽然考虑活动中断的优先规则在解决确定型问题时的表现优于不考虑活动中断的优先规则,但对于随机问题的效果却相反;本文提出的算法对于资源需求小或资源供应充足的情形求解效果更佳。本研究可以有效利用项目进度信息为项目管理者提供高质量的动态决策依据。The multi-mode resource-constrained project scheduling problem(MRCPSP)has a strong application in construction engineering and software projects.It gives full consideration of the availabilities and optimization configuration of renewable resources.Solving the problem helps to provide decision support of schedule for the project manager before the start of project.The defect of MRCPSP is that various uncertainties in actual project scheduling have not been taken into consideration,such as the uncertain resource availabilities due to the maintenance of machines,employees′vacations,and the closure of work sites due to emergencies.Against this background,this paper discusses the stochastic scheduling of MRCPSP under uncertain resource availabilities with the objective of minimizing the expected project makespan.In the studied problem,we assume that the availabilities of uncertain renewable resources are stochastic variables.Under the constraints of precedence relationships among activities,the selection of activity modes,stochastic resource availabilities and activities′preemption,the starting activities together with their execution modes are dynamically decided until all activities are completed.Then a high-quality solution is obtained.Using the project data which is generated continuously,our paper aims to give a dynamic decision-making basis for project scheduling under the uncertain environment,which is of great significance for guiding project practice.Based on the problem description,a Markov decision process(MDP)model is established in the first part according to the problem characteristics.It consists of five parts:decision stage,state space,decision space,state transition function and objective function.The moment when some renewable resource is not sufficient or the unoccupied availability of some resource increases(including the moments when an activity is completed and the actual availability of some resource increases)is the decision time.At each decision time,the state space is composed of the com

关 键 词：资源不确定 多模式 随机调度 马尔可夫决策过程 ROLLOUT算法 

分 类 号：C935[经济管理—管理学]