# Project Robust Scheduling Based on the Scattered Buffer Technology
## 1 Introduction
among others comprehensively considered the metrics of _flexibility_ and _fluidity_, which they called _Pairwise Float_, and it was used as integer programming to establish the objective function of the robust scheduling. Similar to the chain method, the method mentioned above also uses fixed-time schedule to create a partial order schedule [18]. [PERSON] et al. put forward an index-\(stby(a)\) that is used to measure the stability of the solution scheme. In his paper, \(aslack(a_{i})\) is used to indicate the retardation value of activity \(a_{i}\)'s start time. In all the pairs of activities \(\left(a_{i},\,a_{j}\right)\), \(stby(a)\) denotes the average value of the retardation value of activity \(a_{i}\). Therefore, the smaller is the \(stby(a)\), the better the robustness of the schedule becomes [19]. [PERSON] and [PERSON] identified a series of criteria of evaluating resource flow network, and they compared that to the famous indicator _flexibility_ to realize a more accurate analysis of the resource flow network [20]. [PERSON] and [PERSON] developed a new procedure for generating a proactive baseline schedule for the resource-constrained project scheduling problem. The greatest advantage of this algorithm is that it is not bound by any reactive strategy in the future. Then, they defined a new robustness measure, and introduced a branch-and-cut method for solving a sample average approximation of the original problem [21]. [PERSON] proposed two new metrics to evaluate schedule robustness. Individual robustness measures the ability of trains to limit the adverse effects of their own primary delays. On the other hand, collective robustness measures the ability of the network as a whole to limit the knock-on effects of primary delays imposed on a small fraction of trains [22]. With the resource flow network becoming an important research approach used in the project scheduling, the research of the robust scheduling based on the resource flow network has gradually been carried out, making some research achievements. For example, [PERSON] and [PERSON] described different techniques involving the use of slack; the authors inserted the time buffers to establish the robust solution so the schedule could absorb the impact of some unpredicted events. The authors also presented time window slack (TWS) and focused time window slack (FTWS)--an approach for calculating the minimum value of the slack that can be added to each activity. A slack was added to each activity without redefining the duration of the activity to play a protective role during the project execution [23]. After proposing the resource flow network algorithm, [PERSON] et al. further researched the resource-constraint project scheduling problem under the static and dynamic condition. As for robust scheduling problem under dynamic conditions, they offered a new algorithm by polynomial insertion of the time buffer, and they applied it to robust rescheduling to check its robustness [24]. [PERSON] and [PERSON] discussed the robust time buffers allocation problem in RCPSP based on the fixed duration. They studied the scheduling model of the resource-constrained project, and also proposed a time buffer robust (Buf R) allocation algorithm [25]. [PERSON] et al. studied the adapted float factor (ADFF) heuristic, and modified the resource flow network based on the resource conflict problem in the ADFF heuristic. Then, they put forward three scattered buffer methods: the resource flow dependent float factor (RFDFF) heuristic, the virtual activity duration extension (VADE) heuristic and the starting time criticality (STC) heuristic. The resource flow network was introduced into all of these algorithms [26; 27]. Based on three heuristic algorithms, parametric heuristic (ParH), activity marginal stability (AMS) heuristic and activity stability contribution (ASC) heuristic, [PERSON] and [PERSON] assigned the buffers to the baseline scheduling. While achieving the robustness of scheduling, the completion date is another important indicator that needs to be balanced [28].