# A Project Scheduling Game Equilibrium Problem Based on Dynamic Resource Supply
## 1 Introduction
Relevant research by [PERSON] [15] demonstrated that the simultaneous optimization of project scheduling and resource supply can improve the efficiency of project scheduling and reduce the overall cost. [PERSON] et al. [16] took the project duration and cost as the optimization objectives, considered the variable resource availability and expressed it by interval variables, and established a dual-objective optimization model of the MRCPSP under the constraint of variable resource availability. [PERSON] et al. [17] further expanded renewable resources into flexible resources with capacity differences, and established a problem model considering capacity differences in which the capacity level affects activity duration. [PERSON] and [PERSON] [18] considered the time-dependent resource capacity and divided the aggregate demand of intermediate and final products into batches in the batch production mode. [PERSON] et al. [19] proposed a two-stage optimization model based on constrained programming to address the bridge maintenance scheduling problem. Many scholars have proposed rich algorithms to solve the integrated system optimization problem of project scheduling and resource supply chains. [PERSON] et al. [20] designed a hybrid algorithm that combines Monte Carlo and hyper-heuristic methods to solve this problem. [PERSON] et al. [21] studied MRCPSP under the condition of uncertain activity duration and designed an approximate dynamic programming algorithm based on the rollout to solve it. [PERSON] et al. [22] studied MRCPSP with resource preemption characteristics, introduced an extended serial scheduling generation scheme to improve mode selection, and designed a two-population genetic algorithm. Furthermore, many studies have proven that GA and PSO are more effective and have different advantages in solving such problems [23; 24; 25; 26; 27]. GA was first proposed by [PERSON] in 1975. It is a random search algorithm that draws on natural selection and genetic mechanisms in the biological world and follows the principle of \"survival of the fittest\" [28]. Its basic idea is to imitate the natural evolution process through genetic manipulation of individuals with certain structural forms in the population, so as to generate a new population and gradually approach the optimal solution. PSO was proposed by [PERSON] and [PERSON] in 1995 [29]. It is a random search algorithm based on group cooperation, developed by simulating the foraging behavior of birds. It finds the global optimum by following the currently searched optimum. The existing research has made important achievements in project scheduling problems and algorithm designs. However, when constructing the model, the interaction between decision makers is ignored. Secondly, the project scheduling problem from the perspective of the engineering supply chain is a multi-objective and multi-stage complex decision problem; previous studies [26; 27] have shown that using the bi-level programming method can generate better results. The innovation of this paper is that the project scheduling problem and resource supply problem are regarded as an integrated system of a dynamic game, involving interactive influences and constraints. Moreover, a two-level multi-objective programming method is adopted, which organizes the whole process of \"objective--modeling--algorithm--optimization--decision.\" A large hydropower construction project is taken as an example to prove the scientificity and feasibility of the method.