Abstract: In the realm of project scheduling, the increasing prevalence of intelligent manufacturing and advanced technologies has led to a growing emphasis on project integration and systematization. However, this rise in complexity and uncertainty is particularly pronounced in R&D projects, which often involve numerous innovative and unique activities, resulting in limited historical data. Consequently, decision-makers must heavily rely on expert judgment to assess activity uncertainty. Fuzzy logic has emerged as a powerful tool for expressing expert information, as it allows data to be derived from expert estimates while aligning with their preferences. It proves especially valuable in handling R&D projects characterized by difficult-to-predict task complexities and unclear partner needs. Meanwhile, the high uncertainty associated with the innovative nature of R&D project activities makes project execution highly susceptible to external disruptions. To enhance project stability and mitigate the impact of activity disturbances, decision-makers need to consider project robustness carefully. This entails accurate estimation of uncertain activity durations and the rational arrangement of project plans to minimize time and resource conflicts during execution. Hence, the challenge of how decision-makers can effectively use expert fuzzy information for robust project scheduling in the absence of historical data is of paramount importance.
It is essential to recognize that in the context of fuzzy robust project scheduling, decision-makers exhibit diverse risk preferences. When formulating plans, decision-makers often introduce varying time slacks between activities to safeguard the stable execution of tasks based on each activity's potential impact on time and resource conflicts. These differing risk preferences lead to distinct judgments regarding the possibility of conflicts between activities, resulting in the incorporation of time slacks of different sizes between activities and, consequently, the creation of project schedules with varying levels of robustness. The decision-maker's risk preference significantly influences the schedule generation process. If the consideration of conflicts is too conservative or too aggressive, the project may not align with the decision-maker's expectations, leading to time delays and resource wastage. Therefore, generating a reasonable and satisfactory project schedule according to different risk preferences of decision-makers holds substantial practical value.
Existing research on robust project scheduling typically assumes that the duration of uncertain activities follows a random distribution. However, there has been limited investigation into the fuzzy robust project scheduling problem. Additionally, few scholars have considered the risk preferences of decision-makers in the field of project scheduling. Previous literature has primarily focused on comparing project scheduling optimization results under different risk preferences, without incorporating risk preference into the optimization model. To the best of our knowledge, there are no studies that have considered the risk preference of decision-makers in the fuzzy robust scheduling problem. Therefore, this paper holds unique research value.
Therefore, this paper addresses the fuzzy robust project scheduling problem considering the decision-makers' risk preferences. The objective is to arrange the start time of each activity in the project constrained by the renewable resources and project plan duration. The objective is to maximize the robustness of the project schedule under the specified preference, ensuring stable project execution in an uncertain environment, while meeting the decision-maker's satisfaction criteria.
Firstly, to aid decision-makers in formulating optimal project schedules in the scenarios lacking historical data, this paper introduces a proactive fuzzy project scheduling optimization model that incorporates decision-makers' risk preferences. The uncertain activity durations are described by the six-point fuzzy numbers. By employing possibility theory to express the credible function of these fuzzy numbers, the paper identifies potential time conflicts between activities with precedence relationship constraints, and possible resource conflicts arising from activities executed simultaneously and utilizing the same resource. The proposed “fuzzy overlap” serves as a surrogate measure to evaluate schedule robustness, capturing the potential conflict areas between related activities. Additionally, the weight parameters of the credibility function represent the risk preference factors of project decision-makers.
Secondly, a complexity analysis of the model reveals its NP-hard property, indicating the need for a heuristic approach. Hence, the paper adopts an alternate tabu search algorithm tailored for solving robust project scheduling problems with high initial solution quality. The algorithm employs decoding of the activity list and the time slack list to generate the schedule. Subsequently, it refines the solution through alternating iterations, considering the respective neighbors of the two lists.
Finally, the proposed tabu search method is validated and evaluated using an actual project case, XHQMGZ, with 40 activities. The research makes a sensitivity analysis of key parameters, namely the risk preference value, project deadline, and resource availability. The obtained results demonstrate a significant improvement in the robustness of the project schedule generated by the fuzzy-overlap based research method when compared to the practical project schedule. The overall fuzzy overlap value of the project is notably reduced, leading to a considerable reduction in activity conflicts. Moreover, as decision-makers' risk preferences move from the conservative to the optimistic, the possibility of conflicts between activities in the schedule increases, thereby increasing the sum of project conflict intervals. When deadlines and resource availability are tightly constrained, variations in decision-makers' risk preferences have a more pronounced impact on changes in the sum of project conflict intervals, especially in scenarios where decision-makers exhibit risk-averse preference. Additionally, when decision-makers hold risk-optimistic preferences, an increase in deadlines has a greater influence on the sum of project conflict intervals than an increase in resource availability.
This research incorporates the risk preference factor of decision-makers into the fuzzy robust value project scheduling approach, resulting in an enhanced understanding and control of project execution. As a future direction, it is worth exploring different reactive scheduling strategies of decision-makers under risk preferences, which could enable finer project control and management before and during project execution. This would further contribute to the optimization of project outcomes in uncertain and complex environments.

Key words: project scheduling, optimization model, heuristic algorithm, fuzzy activity duration, risk preference

摘要： 不确定条件下模糊鲁棒性项目调度计划的生成受决策者风险偏好影响。本文研究模糊活动工期下考虑决策者风险偏好的鲁棒性项目调度优化问题,目标是合理安排活动开始时间,生成特定风险偏好下鲁棒性最大的进度计划。首先界定问题,构建优化模型;随后针对问题NP-hard属性和模型特点设计交替禁忌搜索启发式算法,求解得到不同风险偏好下满意的进度计划;最后用实例验证说明,并分析关键参数影响。结论如下:决策者风险偏好由规避转乐观时,项目冲突区间总和增多;截止日期、资源可用量较紧张时,风险偏好变化对冲突区间总和变化影响更大;风险偏好乐观时,截止日期变化对冲突区间总和变化影响更大。研究成果可为不同风险偏好决策者在不具历史数据的高不确定环境中制定合理前摄性计划提供决策支持。

关键词: 项目调度, 优化模型, 启发式算法, 模糊活动工期, 风险偏好