# A Project Scheduling Game Equilibrium Problem Based on Dynamic Resource Supply
## 6 Conclusions and Future Research  
This study investigated the integration of multimode project scheduling and resource supply in an engineering supply chain. Resource constraint is not only a constraint condition of the engineering supply chain, but is often a separate optimization problem. Therefore, integrating resource supply into project scheduling is an MRCPSP-MPSCP integrated system with multi-agent decision-making characteristics and a hierarchical decision-making structure. Resolving conflicts in this integrated system helps ensure that the project runs successfully at an acceptable cost and is completed on time. On this basis, a Stackelberg dynamic game model was established, and a two-level multi-objective programming method was designed to further solve internal conflicts. Subsequently, a two-layer GADS/DIWPSO hybrid algorithm with an interactive evolution mechanism was proposed to solve the new Stackelberg model, and a satisfactory Stackelberg-Nash equilibrium solution was determined through a repeated dynamic interaction process. This provides theoretical significance for solving related problems of engineering supply chain. In the context of the global impact of COVID-19, coordinated optimization and sustainable operation of the engineering supply chain play an important role in the recovery of the industrial economy. This study provides a theoretical basis and algorithm support for how engineering and construction departments and resource suppliers in the supply chain promote the optimization of overall benefits. For the engineering construction department, considering the limitation of resource supply, more thought is devoted to the project scheduling problem to ensure the overall operation of the project. For resource suppliers, considering the characteristics of master-slave decision-making, this study provides a reference for the formulation of a resource transportation strategy, and finally promotes mutual benefit on both sides to achieve better cooperation results. After discussion and analysis, it can be discovered that in the engineering supply chain, the multi-period resource supply problem does have an impact on the project scheduling. Therefore, the dynamic game model for the MRCPSP-MPSCP integrated system is more realistic, and the proposed two-level multi-objective programming method and GADS/DIWPSO hybrid algorithm can solve the conflicts between stakeholders, and finally realize the Stackelberg-Nash equilibrium strategy. In conclusion, when solving similar problems, researchers should start from reality, fully consider the conflicts of interest among participants, and make reasonable assumptions. Only in this way can a better decision plan be generated. However, there are still some limitations in this study: 1 he scheduling problem of multiple projects is not considered; 2 the mixed transportation of multi-type vehicles is not considered in terms of resource transportation; and 3 more participants can be considered in a large engineering supply chain, such as material manufacturers and transportation agents. These limitations will form the basis for future research. Conceptualization, C.F. ; methodology, C.F. and S.H. ; data analysis, C.F., S.H. ; and Y.M. ; writing--original draft preparation, C.F. and S.H. ; writing--review and editing, Z.L. ; supervision, Z.L. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was supported by the National Natural Science Foundation of China (No. 71702167 and No. 72202056). **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** All processed data used in the study have been shown in the article. **Acknowledgments:** The authors gratefully acknowledge the funding and support provided by the National Natural Science Foundation of China (No. 71702167 and No. 72202056) and are grateful to the editors and the reviewers for their insightful comments and suggestions.