Abstract: The resources-constrained multi-project scheduling problem is constructing a schedule that projects can be executed in parallel if the resources and precedence constraints are not violated. The baseline schedule plays a crucial role in the multi-project scheduling. However, efficient multi-project scheduling becomes more challenging due to not only the complex resources constraints and inter-dependencies between projects but also the increasing size and complexity of projects. Moreover, in the real world, projects are subject to considerable uncertainty. Two types of uncertainty are always studied: duration uncertainties and renewable resources uncertainties. A multi-project scheduling plan should be not only robust, but also competitive in the market and in uncertain environments. There is sufficient research on robust optimization but little one on adjustable robust optimization, which is more applicable than the traditional robust optimization approach. As a new method that can solve uncertain optimization problems, adjustable robust optimization has improved its applicability compared to traditional robust optimization. The purpose is to determine multi-project scheduling schemes with different robustness levels.
In this paper, we propose the multi-project adjustable robust scheduling problem in uncertain environments, where local resources supply uncertainty and activity duration uncertainty are simultaneously considered. Multi-project management is divided into multi-project layer and project layer. A stochastic scheduling model and an adjustable robust optimization model based on resources flow are proposed. Unlike stochastic programming methods in multi-project scheduling, robust optimization does not require probabilistic information about uncertain parameters and assumes that the uncertain parameters lie in a given uncertainty set. We design a new adjustable robust optimization method to generate robust baseline schedules for multi-project. The first stage is project scheduling based on priority rules, which aims to find feasible scheduling schemes that satisfy local resources and activity order constraints. Each project is simulated in a different scenario under uncertain local resources and activity duration conditions. In the second stage, we propose a linear adjustable robust optimization model based on the global resources flow to decide the start time of these projects based on how long they may be delayed. Compared with existing adjustable robust optimization approaches, this approach not only performs robust optimization based on the risk attitude of the manager but also generates baseline schedules with different robustness levels under each risk attitude. Furthermore, unlike existing adjustable robust optimization methods that can only solve small-scale problems, this approach integrates heuristics and exact algorithms that can efficiently solve large-scale problems.
Finally, the numerical experiments are performed. Compared with the traditional robust optimization method, the two-stage adjustable robust optimization approach is more flexible, which can effectively avoid the over-conservative characteristic of traditional robust optimization methods. At the same time, it can provide different schedules according to the manager’s risk attitude. In addition, the parameter analysis shows that the change in local resources supply and order strengths between projects has a more significant impact on the optimization results. However, the change in stochastic activity duration has a relatively small impact on the optimization results. In multi-project scheduling in uncertain environments, although a robust baseline schedule can consider various uncertainties, it is difficult to completely resist the interference of uncertainties, such as global resources disruptions and project network relationship change. Therefore, future research also needs to design reactive scheduling methods to ensure that multi-projects are completed on time in uncertain environments.

Key words: multi-project scheduling, uncertain resource supply, stochastic activity duration, adjustable robust optimization

摘要： 针对多项目管理实践中面对的不确定性环境和激烈市场竞争,多项目调度方案既要充分考虑不确定因素的干扰,还要避免调度方案过于保守造成运营效率低下等问题。因此,在局部资源供应量和活动工期双重不确定的条件下,对多项目可调节的鲁棒优化问题进行了研究,目的是制定不同鲁棒性水平的多项目调度方案。首先,在项目层和多项目层分别设计随机调度模型和基于资源流的可调节鲁棒优化模型;其次,将项目层基于蒙特卡洛仿真的随机调度和多项目层的可调节鲁棒优化进行集成,设计了双层可调节鲁棒优化算法;最后,基于设计的多项目测试集进行数值实验。结果表明:双层可调节鲁棒优化算法可生成多个鲁棒性水平的调度方案,并且随着随机因素的不确定性增加和算例规模增大,可调节鲁棒优化范围逐步扩大。

关键词: 多项目调度, 资源供应量不确定, 随机活动工期, 可调节鲁棒优化