关键词: 前摄性项目调度, 优化模型, 禁忌搜索算法, 柔性资源, 随机工期

Abstract: 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.

Key words: proactive project scheduling, optimization model, tabu search algorithm, flexible resource, stochastic activity duration