基于柔性资源约束的前摄性项目调度优化研究

Proactive Project Scheduling Optimization Based on Flexible Resource Constraint

不确定环境中,项目进度计划鲁棒性的高低直接影响项目能否顺利实施。本文研究了具有随机活动工期的柔性资源约束下的前摄性项目调度优化问题,目标是在柔性资源和项目工期的约束下,借助对活动开始时间合理的进行安排进而得到拥有最大鲁棒性的进度计划。首先对研究问题进行界定;随后构建优化模型,并根据问题NP-hard属性和模型特点设计了双层嵌套禁忌搜索启发式算法,通过内外两层交互搜索寻找满意解;最后通过一个实际案例对本文研究进行说明,并分析关键参数对进度计划鲁棒性的影响,得到如下结论:相对于资源无柔性情况下的项目进度计划而言,资源具备柔性后得到的项目进度计划的鲁棒性更高,具有更强的抗干扰能力,能够保证项目稳定执行;同时,项目进度计划鲁棒性分别随着项目工期的延长、资源可用量的增加或资源柔性的提高而上升。

With the increasingly fierce market competition and diversified customer needs,in order to quickly adapt to market changes,companies need to complete customized production and provide personalized services within a certain period of time.This requires the ability of companies to achieve smart manufacturing and resource flexibility plays an important role in it.Two typical examples of flexible resources are industrial robots and multi-skilled human resources.At the same time,projects are executed in a complex and dynamic environment,facing considerable uncertainties:activities may take more or less time than originally estimated,resource may become unavailable,etc.These uncertainties may lead to schedule disruptions or even failures.Therefore,it is important to develop a schedule that is protected as well as possible against schedule disruptions caused by uncertainties.Based on the above theory and facts,this paper studies the proactive project scheduling problem with stochastic activity durations and flexible resource constraints.The objective is to schedule the starting times of the activities in a reasonable way so as to maximize the robustness of the project schedule under the constraints of precedence,flexible resources and project deadline.Firstly,the research problem is defined,where the activity duration is a random variable with known mean value and standard deviation.Flexible resources are defined as renewable resources with multiple skills,but only one skill can be selected for use before project execution and each resource must be used as a whole.The robustness of the project schedule is defined as the sum of the products of time buffers and the weight coefficients of all the activities.Then the optimization model is constructed.Based on the NP-hardness attribute of the problem and the characteristics of the model,a two-layer nested tabu search heuristic algorithm is developed to obtain satisfactory solutions.The outer loop of the algorithm aims to find a feasible resource skill allocation plan and the inner loop searches for the project schedule with maximum robustness under the constraint of resource skill allocation plan.At last,a practical project is introduced to illustrate the research problem,for which the satisfactory solutions obtained under the constraints of inflexible resources and flexible resources are compared and analyzed.The research results indicate that,compared with the project schedule developed under the condition of inflexible resources,the robustness of the project schedule obtained with flexible resources has increased from 3.76 to 7.42,i.e.,an increase of 97.34%,which improves the anti-interference ability of the project and ensures a more stable project implementation.Besides,the influences of the key parameters,including project deadline,resource availability and resources flexibility,on the robustness of the project schedule,are analyzed.The following conclusions are drawn:with the extension of project deadline,the increase of resource availability or resource flexibility,the robustness of the project schedule increases respectively.The research in this paper extends the flexible resource constrained project scheduling to the robust project scheduling field,which can provide reference for relevant research.