# Balancing Project Schedule, Cost, and Value under Uncertainty: A Reinforcement Learning Approach
## 2 Literature Review
### Project Value Management  
Value management is a common theme in LPM research. Some researchers use qualitative methods to explore various aspects of value, such as frameworks for defining and measuring value [7; 8; 9; 10; 11], mechanisms for creating value [12], challenges for decommissioning projects [13], and implications of offshore projects [14].  
Other researchers use quantitative methods to assess value in terms of stakeholder preferences and attributes [4; 15; 16]. Some of them apply quality function deployment (QFD), a technique that translates customer needs into engineering requirements [17], to project management [18; 19; 20]. We use QFD to determine project value by using value parameters in the activity modes, as shown in an example in Section 6.  
Another line of research in project value integrates the project scope and the product scope by extending the concept of activity modes to include value parameters in addition to cost and duration. The mode selection affects the project value. [PERSON] and [PERSON] [21] propose to maximize the ratio of effectiveness to cost, while [22] aligns the activity modes with the architectural components. Some studies also demonstrate the use of simulation-based training for LPM implementation [23; 24]. [PERSON] et al. [5] develop and solve an MIP that maximizes the project value in a deterministic multimode project scheduling problem. We build on their work by modeling and solving the problem with stochastic activity durations, which is more realistic but also more challenging, as uncertainty can lead to delays and overruns that affect the optimal mode selection.  
LPM suggests using schedule buffers to prevent schedule overruns [25], but it does not recommend any specific buffering methods (we review the literature on this topic in the next section). Previous studies on project scheduling with robustness or stability, however, have not considered project value. In this study, we develop and solve a new LPM model that maximizes project value and avoids cost and schedule overruns. We create a stable project plan that keeps the probabilities of violating the schedule and budget below a desired level.  
Our method for achieving stability is similar to the buffer scheduling framework because, when we select activity modes, we create a time gap between the baseline project duration and its due date. This time gap will cushion activity delays to meet the on-schedule and on-budget probabilities set by the decision makers. [PERSON] and [PERSON] [26] suggest using Monte Carlo simulation to set the size of a baseline schedule's buffer. We advance their work by directly searching for a baseline schedule that gives us the highest value under the desired on-schedule and on-budget probabilities. Our solution method is based on simulation, which supports our approach.  
Project scheduling and its solutions, both exact, using MILP, and heuristic, using methods such as genetic algorithms (GAs), have been extensively studied in the literature. Value functions in project scheduling are a novel concept, introduced by [5]. No one has ever shown the combination of value functions and chance constraints.