Abstract: In traditional management of prefabricated building (PB) construction, project scheduling plans are critical to management performance. However, with the increasing applicability of PB projects, the scale and complexity of the projects continue to expand, resulting in a great rise in the demand for prefabricated components. At this point, a reliable and stable component ordering scheme plays an increasingly important role in project scheduling and optimal management. Moreover, in the real PB construction, the component ordering scheme and the project scheduling plan affect each other. On the one hand, the scheduling process inevitably involves the component assembly program, which means that a timely and reasonable component ordering scheme is conducive to the smooth progress of scheduling. On the other hand, the arrangement of resources and activities in the project scheduling determines the ordering time of components, which in turn affects the component ordering. Therefore, in order to improve the project management performance and better reduce the risk of project delays and cost overruns, a joint consideration of project scheduling and component ordering (PSCO) problems in PB projects is considered.
In this work, we firstly define the PSCO problem and propose an ordering strategy that integrates the consideration of ordering lead time and component consumption. Since the lead time is a key factor influencing the material ordering plan, i.e., different values of the lead time will have a different impact on the start time of the activity, which further affects the project schedule. Additionally, the start time and material ordering quantity also affect the project scheduling plan. Thus, we take these three variables as the decision variables in this paper and construct a time-cost trade-off model with limited resources. We define it as the PSCO model. It aims to study when the project is scheduled to start, as well as when and how many components are to be ordered, which can enable the duration and cost of the project to be minimized at the same time.
Then, we design an improved non-dominated sorting genetic algorithm-II (INSGA-II) which is suitable for solving projects with complex multi-paths. By analyzing the construction characteristics of PB projects, we conclude that the increasing scale and complexity of projects lead to higher amounts of activities. Traditional multi-objective algorithms may not be suitable for solving such projects. As a result, we design the INSGA-II algorithm where the probability of generating a feasible solution population is improved by adding path identification and judgment operations to the initialization population process in the preliminary stage of this algorithm. In addition, in order to improve the optimization efficiency of this algorithm, further optimization is made by using the multi-objective particle swarm optimization (MOPSO) algorithm after obtaining the optimal solution by the INSGA-II algorithm.
In the end, a case study is utilized to illustrate the efficiency of the model and algorithm. The simulation case is taken from previous literature. By analyzing the solution results, it can be found that considering the impact of the lead time on project schedule is beneficial to reducing the project cost within the duration threshold. Namely, with the same parameters, the ordering strategy that takes into account the lead time reduces the cost by 28.43% compared to the strategy with no such consideration. Moreover, the number of component ordering times has an impact on the PSCO model, i.e., the higher the number of component ordering times, the larger the corresponding project duration and the smaller the project cost. Meanwhile, we compare the comprehensive performance of the INSGA-II algorithm proposed in this paper with the multi-objective genetic algorithm (MOGA) and the MOPSO algorithm. It can be found that, with an increase in the number of iterations, the INSGA-II algorithm basically outperforms the traditional MOGA and MOPSO algorithms in terms of the optimization ability for multi-path complex projects. Moreover, by using multi-objective evaluation metrics of hypervolume (HV), inverted generational distance (IGD) and spacing (SP), the results also illustrate that the INSGA-II algorithm has better performance in diversity, convergence and distribution of solutions.
From the research results, we can see that this model and algorithm are effective and also efficient for solving the joint optimal model of PB project scheduling and component ordering problem. It not only improves the stability and reliability of PSCO plans in real project management, but also provides a powerful solution tool for project managers to reduce the risk of project delay and cost overrun, and further make better decisions for projects with complex multi-paths under uncertain environments.

Key words: prefabricated building construction, stochastic scheduling optimization, components ordering, lead time, improved NSGA-II algorithm

摘要： 装配式建筑项目规模与复杂性的不断提高,推动项目预制构件需求持续上涨,可靠稳定的构件订购计划对项目调度及最优化管理作用日益凸显。通过运用最优化原理和项目调度方法研究了不确定条件下装配式建筑项目调度与构件订购联合优化问题。针对项目活动工期及构件需求随机的情况,提出了集成考虑项目订货提前期与构件消耗量的订货策略,建立了带有资源约束的装配式建筑项目工期—成本权衡模型;其次根据实际项目特征设计了适应于求解具有复杂多路径项目的改进NSGA-II算法;最后展开了对案例模型的Pareto最优前沿求解,分析了不同订货策略下项目工期和成本变化,并将改进NSGA-II算法与多目标遗传算法和多目标粒子群算法进行了性能比较和指标评价。研究结果验证了所构建模型和算法的有效性,可为项目管理者在不确定环境下更好地降低项目延期及超支风险、制定项目最优决策提供参考。

关键词: 装配式建筑, 随机调度优化, 构件订购, 订货提前期, 改进NSGA-II算法