# Project Robust Scheduling Based on the Scattered Buffer Technology
## 1 Introduction
Because more and more people realize that the difference between the traditional deterministic project scheduling model and the practical one is the uncertainty in reality, the stochastic resource-constrained project scheduling problem is also widely concerned. To balance two goals of completion time and financial gain, [PERSON], [PERSON] and [PERSON] et al. solved the robust optimization model according to the uncertain level of parameters and the different scenarios of duration distribution [11; 12]. [PERSON] et al. balanced these two targets by determining the optimal delays, the safe floats and the release dates [13]. Based on the rollout algorithm, [PERSON] and [PERSON] put forward the hybrid algorithm ADP-HBA, which integrates the approximation architectures of the look-back and the look-ahead, thus updating the activity sequence step by step [14]. With the introduction of the resource flow network into the research of robust scheduling, many scholars pay much attention to this research field. The application of resource flow network has become an important method to study the robustness. The benefit of robust buffer schedule generated based on the resource flow network is to avoid the occurrence of resource conflict in the generation of buffer schedule. At the same time, the change of activity duration will not break the transmission of resources among activities, as long as the transfer relationship of resources is unchanged, no matter how the random duration of activity will change, which will not affect the precedence relationship of the schedule and the feasibility of resources. At present, the research method of robust scheduling for duration uncertainty is mainly the heuristic algorithm based on time buffers. As for the setting of time buffers, the earliest research is about inserting centrally the time buffer into a project chaining. Doing so can guarantee the project would be completed within the predicated time to improve the quality robustness of the schedule. This method is also called centralized buffer method. The most representative one of the centralized buffer method is the critical chain management method. Inserting centrally the time buffers to absorb the uncertainty of the project to protect the critical chain ensures that the project can be completed within the time limit. However, the centralized buffer can neither act on each activity nor ensure the stability of the schedule. Centralized buffer technology has been studied for a long time, and the research results are also rich, so the authors do not go into much detail here. With the in-depth research,to solve the problems of solution robustness in schedule, many scholars put forward scattered buffer technology. The scattered insertion of time buffers can reserve space for the time uncertainty of the activity that is caused by the disruption factors, and can absorb the disruption to prohibit the propagation of the disruption through the schedule, enhancing the solution robustness of the schedule. At present, the research of the scattered buffer technology is more active, and some achievements have been made in the measure of the solution robustness and the method of inserting time buffers. In aspect of the metric of the solution robustness, new metrics are constantly proposed to measure the stability of the schedule. [PERSON] et al. proposed the index RB (S), which is quoted by [PERSON] et al. as _fluidity_. It defines the number of all pairs of activities and the average width of the slack in due date. This value reflects the property of schedule to offset the time variability during the execution of activities. Higher values of fluidity indicate lower risks of a domino effect, thus higher probabilities of the local variability. Similar indicators are _flexibility_ and _disruptibility_, which are based on slack in scheduling and used to measure the possibility of resisting interference among activities [15; 16; 17]. [PERSON] et al.