Abstract: It has become a common practice to promote the implementation of mega projects through debt financing. However, the high financing costs brought by massive financing have pushed up the total cost of contractors and severely squeezed their profit margins. Contractors urgently need to optimize project cash flow, improve fund allocation efficiency, and reduce financing costs. Project scheduling can change the timing and magnitude of cash flow occurrence, thereby affecting cash flow gaps. Contractors can make financing decisions that are beneficial to themselves based on the financing rates of each period. In addition, contractors usually spend a certain amount of prior cost to add time buffer for activities to ensure the stability of the schedule, which can reduce the cost of changes and adjustments after the event. Obviously, adding a time buffer will further change the project funding gap and contractor financing arrangements.In summary, this study investigates the financing cost minimization project scheduling problem considering buffer costs and utility under random activity durations, which has strong practical value.
The research in the field of cash flow project scheduling mostly focuses on the maximization of net present value and cost minimization, and rarely considers the financing costs of project contractors. Although financing cost minimization scheduling can be nominally classified under the research branch of cost minimization project scheduling, the latter does not consider changes in cash inflows and the further financing changes. Therefore, this study has unique research value.
Firstly, we define the research problem and construct an optimization model. The objective function of the model is to minimize the financing costs of contractors during project implementation, taking into account the cost and utility of inserting time buffers for activities. It should be noted that there is no actual adjustment cost, since we only focus on generating the schedule in advance and does not involve the actual execution. Here, a virtual value is used to replace the actual adjustment cost. Because the post adjustment cost will decrease with the increase of time buffer insertion, the virtual adjustment cost of an activity can bedefined as the minus function of the activity time buffer. By optimizing the time buffer decision variables, the cost structure and cash flow of contractors can be optimized, ultimately reducing their financing costs.
Secondly, a hybrid algorithm VNTS is designed to solve the model. VNTS adopts the TS overall search framework. When a better solution cannot be found in the current neighborhood, the neighborhood transformation function of VNS is used to skip to the next neighborhood to improve search efficiency. It can be concluded that adding time buffers to activities with greater impact and higher risk coefficients can effectively improve the objective function value. Based on this, we propose improvement measures for neighboring point generation: for the time buffer list, evaluate the risk impact level of all activities, and sort the activities according to the value from highest to lowest. Select the activity with the highest value among the unselected activities and randomly change its value to another value on the neighborhood interval.
Then, we test the VNTS hybrid algorithm and improvement measures for neighboring point generation. The example library is obtained by the ProGen based on different parameter settings. The results show that the solution quality of VNTS is superior to the two independent algorithms TS and VNS, respectively, and the difference continues to expand with the increase of problem size.In terms of time efficiency, VNTS is significantly inferior to VNS and TS in all problem scales. After applying neighbor generation improvement measures in VNTS, the solution quality of the algorithm has significantly improved. This indicates that the search direction is determined based on the level of risk impact, which makes the search path more optimal, for taking into account both the variability level of activity duration and its impact on the overall project.
Finally, a case study is used to illustrate the research content of this article. Simulation analysis is conducted on three types of benchmark schedules. It is found that the actual total financing costs of the shortest benchmark schedule fluctuate the most severely. The fluctuation in the actual total financing costs of the benchmark schedule for minimizing financing costs considering buffering costs and their utility is much smaller than that without buffering costs and their utility. The results of the sensitivity analysis show that the contractor's financing cost first declines and then rises with the relaxation of the deadline, first declines and then rises with the expansion of the robustness threshold, increases with the increase of the financing rate, decreases with the increase of the payment proportion and payment times, increases with the expansion of marginal cost, and decreases with the increase of attenuation coefficient. The research results of this article can provide quantitative decision support for contractors to control financing costs under random activity durations.

Key words: financing cost, project scheduling, optimization model, hybrid algorithm VNTS, random activity duration

摘要： 巨额融资所带来的高昂融资费用,推高承包商的总成本,严重挤压其利润空间。承包商迫切需要对项目现金流进行优化,提高资金配置效率,降低融资费用。此外,为了应对不确定性干扰,承包商通常花费事前成本为活动添加时间缓冲,以保证进度计划稳定性,以减少事后变更和调整费用。因此,本文研究随机活动工期下考虑缓冲成本及效用的融资费用最小化项目调度优化研究,旨在为承包商生成具有一定鲁棒性的融资费用最小化基准进度。首先,界定研究问题并构建优化模型,在此考虑为活动插入时间缓冲所带来的成本及效用。其次,设计VNTS混合算法对模型进行求解,提炼相关性质以提高算法搜索效率,并在算例集合上进行算法测试。最后,通过案例对本文研究进行说明。研究结果可以为随机活动工期下承包商控制融资费用、提高项目收益,提供定量化决策支持。

关键词: 融资费用, 项目调度, 优化模型, 变邻域禁忌搜索混合算法, 随机活动工期