In the distributed management environment, multiple projects may be located in different regions, so the global resource transfer times cannot be neglected when making multi-project scheduling plans. Besides, activity durations may be affected by various uncertain factors (e.g., breakdown of production equipment) in the actual scheduling, resulting in deterioration or even infeasibility of the pre-determined scheduling plans. A distributed multi-project scheduling problem considering resource transfer times and uncertain activity durations is studied. Robust project scheduling is employed to tackle uncertainty. It is named as the robust distributed resource-constrained multi-project scheduling problem with transfer times (robust DRCMPSP-TT). In the robust DRCMPSP-TT, consider the parallel execution of multiple projects in a distributed decision-making environment. The duration of the activities is uncertain, and the execution of the activities requires both local and global resources. Obtain the multi-project baseline scheduling and global resource transfer plans through problem-solving.
To formulate this problem, a two-stage model containing local scheduling and global coordination decision-making is established based on the multi-agent system. In the local scheduling optimization model, each PA focuses on the robustness of the single-project baseline scheduling plan, while in the global coordination decision-making model, the CA is concerned with the robustness of the multi-project scheduling plan. Moreover, a two-stage algorithm integrating time buffer addition and resource flow network construction is designed to solve the problem. In the first stage, the local scheduling problem is solved by the deeply optimized branch-and-bound algorithm to generate local baseline schedules with insertion time buffers. In the second stage, based on the local baseline schedules, a heuristic resource allocation algorithm is developed to optimize additional resource arcs to coordinate global resource allocation and transfer effectively.
The experimental research is executed based on 24 instances generated by RanGen1 software. According to the number of projects and activities in each multi-project, these instances are divided into 4 problem subsets, denoted 2_10, 2_30, 5_10, and 5_30. Each problem subset contains 6 multi-project instances with different problem parameters. Experimental results show that variations in the problem size and the degree of duration uncertainty have an impact on the robustness of the baseline schedule. Compared with the existing branch-and-bound algorithms and various heuristic algorithms, the proposed two-stage algorithm can effectively improve the robustness of the baseline schedule and is more suitable for solving the studied problem. The experimental results further verified that the timely project completion probability increases with the increase of the deadline and approach 1 at different speeds under different duration variability levels. In addition, by analyzing the relationship between project deadlines and the timely project completion probability, quantitative reference opinions are provided for managers to determine reasonable deadlines.
It makes up for the vacancy of the DRCMPSP and opens the door to further study the DRCMPSP with resource transfer and uncertain activity durations in this study. It mainly adopts the proactive scheduling strategy to solve robust DRCMPSP-TT, while combining proactive scheduling with reactive scheduling to solve this problem can be a topic for future research. In addition, the global resource availability is often uncertain due to various unexpected and uncontrollable conditions such as equipment failure, and DRCMPSP-TT under uncertain global resource availability can be further investigated.