# Balancing Project Schedule, Cost, and Value under Uncertainty: A Reinforcement Learning Approach
## 2 Literature Review
### Ccbm  
There is a large body of literature on CCBM scheduling and buffer sizing methods for single-mode projects. Some studies use fuzzy numbers to model uncertainty. For example, ref. [27] uses fuzzy numbers to estimate the uncertainty of project resource usage and determine the size of the PB with resource constraints. [PERSON] et al. [28] used an uncertainty factor derived from fuzzy activity durations and other factors to calculate the PB. [PERSON] et al. [29] used fuzzy numbers to create a probability matrix with all possible combinations of realized activity durations. Other recent studies use probability density functions (PDFs) to represent uncertainty in activity duration. For instance, ref. [30] uses an approximation technique for the convolution to combine activity-level PDFs and model project-level variability. [PERSON] et al. [31] used classical methods for sizing the FBs and proposed a two-stage rescheduling approach to solve resource and precedence conflicts and prevent critical chain breakdown and non-critical chain overflow. [PERSON] et al. [32] extended the traditional root square error method (RSEM) [33] to develop a multi-attribute buffer sizing method. [PERSON] et al. [34] used goal programming to minimize duration and resource load variations and insert the PB and FBs using RSEM. [PERSON] and [PERSON] [35] showed that some multitasking can reduce buffer sizes by releasing resource capacity. [PERSON] et al. [36] considered a modified CCBM approach with two types of resources: regular resources available until a cutoff date and irregular emergency resources available after that date. [PERSON] et al. [37] focused on creating a new project schedule monitoring framework using a branch-and-bound algorithm and RSEM for scheduling and buffering. [PERSON] et al. [38] combined location-based management with CCBM in repetitive construction projects and introduced a new resource conflict buffer. [PERSON] et al. [39] calculated the PB using the duration rate and network complexity of each project phase and monitored the buffer dynamically for each phase. Some researchers also use information flow between project activities. For example, [PERSON] et al. [40] proposed optimal sequencing of the critical chain activities based on the information flow and the coordination cost, aiming to reduce duration fluctuation and buffering. [PERSON] et al. [41] used two factors to calculate the PB using the design structure matrix physical resource tightness and information flow between activities. Information flows are also used in [42], whose work is extended in [43]. In their studies, they considered rework risks and a rework buffer in scheduling. There are few publications on CCBM buffer sizing and scheduling for multimode projects. Some recent publications include [44], which uses work content in resource-time units to generate activity modes and compares two types of CCBM schedules. [PERSON] et al. [45] combined mode selection rules and activity priority rules (PRs) for scheduling multimode projects with CCBM. [PERSON] et al. [46] used three modes--urgent, normal, and deferred--to level multiple resources and add five metrics to the RSEM buffer calculation formula. Buffer management is also studied in contexts other than CCBM. A discussion of those methodologies falls outside the scope of this paper; some examples are [47; 48; 49; 50; 51; 52; 53; 54; 55]. Previous research has some drawbacks. Researchers mostly focused on using PDFs either to compute the buffers for a schedule that was already built based on fixed activity durations or to assess the buffered schedule using simulation, rather than finding a time-buffered schedule by solving the chance-constrained CCBM problem. Few researchers have explored RL applications in project scheduling, despite the proven effectiveness of RL-based methods in dealing with uncertain environments, as mentioned above. Lastly, there is little research on multimode CCBM problems. This study, hoping to address some of these gaps, focuses on solving the chance-constrained CCBM problem.