*Article* **A Project Scheduling Game Equilibrium Problem Based on Dynamic Resource Supply**

**Cuiying Feng 1,2,3, Shengsheng Hu 1,\*, Yanfang Ma <sup>4</sup> and Zongmin Li <sup>2</sup>**


**Abstract:** In a resource-constrained project scheduling problem, most studies ignore that resource supply is a separate optimization problem, which is not in line with the actual situation. In this study, the project scheduling problem and the resource supply problem are regarded as a dynamic game system, with interactive influences and constraints. This study proposes a Stackelberg dynamic game model based on the engineering supply chain perspective. In this model, the inherent conflicts and complex interactions between the Multi-mode Resource-Constrained Project Scheduling Problem (MRCPSP) and the Multi-Period Supply Chain Problem (MPSCP) are studied to determine the optimal equilibrium strategy. A two-level multi-objective programming method is used to solve the problem. The MRCPSP is the upper-level planning used to optimize project scheduling and activity mode selection to minimize project cost and duration; MPSCP is a lower-level planning method that seeks to make resource transportation decisions at a lower cost. A two-layer hybrid algorithm, consisting of Genetic Algorithm (GA) and Particle Swarm Optimization (PSO), is proposed to determine the optimal equilibrium strategy. Finally, the applicability and effectiveness of the proposed optimization method are evaluated through a case study of a large hydropower construction project, and management suggestions for related departments are provided.

**Citation:** Feng, C.; Hu, S.; Ma, Y.; Li, Z. A Project Scheduling Game Equilibrium Problem Based on Dynamic Resource Supply. *Appl. Sci.* **2022**, *12*, 9062. https://doi.org/ 10.3390/app12189062

Academic Editor: Antonio J. Nebro

Received: 20 August 2022 Accepted: 6 September 2022 Published: 9 September 2022

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**Keywords:** multi-cycle supply chain; project scheduling; Stackelberg dynamic game; two-level multi-objective programming; GA with double strings; particle swarm optimization
