Financial Analysis and Optimization for Linear Scheduling Model of Construction Projects with Integrated Singularity Functions

该项目的目标是研究一种新的规划建设项目的方法，通过建模、分析和支持使用称为奇点函数的独特类型的数学表达式来优化建设项目的现金流。这些多功能函数定义了感兴趣变量的顺序范围，其可以是任何顺序。它们在工程上被用来描述和解决各种加载到结构构件上的情况，根据先前的一项研究，新的研究被应用于线性时间表，即关于所消耗时间的工作进度的二维计划，在时间部分方面创造了更好的分析能力。然而，成本的核心要素，例如材料、设备和劳动力的流出与业主进度付款的流入，仍然没有解决。其复杂的行为受到活动和付款请求和收据的时间安排的影响，而这些时间安排又受到各种限制，例如融资条款和条件。管理这些要素的能力直接影响到任何建筑公司的盈利能力，并最终决定其经济生存。尽管有这种基本重要性，但人们一直认为现金流很难用一个全面的模型来描述，通常只是近似甚至平均。该项目将弥补知识体系中的这一概念空白，这也将在项目管理的日程安排和预算编制职能之间建立直接联系。为了确保这项研究的实际适用性，该项目将包括与建筑行业的合作伙伴公司合作，这些公司同意为新方法的验证提供真实的项目数据。这些项目将作为案例研究，以测试算法和新功能，这些功能将表示例如一次性或重复付款、本金和利息，以及可能的特殊规定，例如在完成之前扣留的所有者保留金。他们详细的注释分析将与这些公司分享，并将在项目经理研讨会上分享。研究工作将与校园计划、学生组织和围绕建筑职业的高中指导计划中的教育推广活动交织在一起。国际和平协会将向其少数族裔青年群体提供一个关于财务规划基础知识的游戏式练习，并将通过国家导师组织进行传播。这个项目的学生可以在他们公开展示的团队项目中使用这些新发现的知识，并可能在他们的个人生活中受益。PI所在机构的学生将接受关于新财务规划的课程模块，其有效性将得到衡量。研究生研究助理将参加一个精心设计的计划，该计划将包括一系列研究、教学和服务方面的培训元素，为学术生涯做准备。总体而言，该项目有可能成为建筑业和其他行业项目经理工具箱的重要补充，通过提供一种在实践中有用且极具可教性的综合现金流建模、分析和优化方法。它将通过以下方式对社会作出贡献：(A)提高承包公司的财务规划能力，以支持他们的盈利能力；(B)对研究生助理进行广泛的教育；(C)让专业人员参与一个融合研究、教学和服务工作的项目；(D)提高未被充分代表的青年对财务规划和建筑业职业的认识；以及(E)为进一步推动项目规划的创新建模奠定基础。

The objective of this project is to investigate a novel approach for planning construction projects by modeling, analyzing, and supporting the optimization of their cash flows with a unique type of mathematical expressions called singularity functions. These versatile functions define sequential ranges for the variable of interest, which can be of any order. They had been used in engineering to describe and solve varied loading scenarios onto structural elements and under a prior research study were newly applied to linear schedules, i.e. two-dimensional plans for work progress over consumed time that created improved analytical capabilities in terms of the time component. However, the central element of cost, which occurs as outflows for e.g. materials, equipment, and labor versus inflows from owner's progress payments, remained unsolved. Its complex behavior is impacted by the timing of activities and payment requests and receipts, which in turn are subject to various constraints, e.g. financing terms and conditions. The ability to manage these elements impacts the profitability of any construction firm directly and ultimately determines its economic survival. Despite this fundamental importance, cash flows have been viewed as being difficult to describe in one comprehensive model and were typically merely approximated or even averaged. This project will remedy this conceptual gap in the body of knowledge that will also build a direct link between the scheduling and budgeting functions of project management. The resulting method will function in synergy with linear schedules and also as a stand-alone solution.To ensure the practical applicability of this research, the project will include a collaboration with partners companies from the construction industry who have agreed to provide real project data for validation of the new approach. These projects will serve as case studies to test the algorithm and the new functions that will express e.g. one-time or repeated payments, principal and interest, and possible special provisions, e.g. owner's retainage that is withheld until completion. Their detailed annotated analysis will be shared with the firms and in a seminar for project managers. The research work will be interwoven with educational outreach activities in campus programs of student organizations and at a high school mentoring program that revolves around construction careers. The PI will contribute a game-style exercise on basics of financial planning to its group of minority youth, which will be disseminated through the national mentor organization. Students in this program can use this newfound knowledge when working on their publicly presented team project and may also benefit from it for their personal lives. Students at the PI's institution will receive course modules on the new financial planning, whose effectiveness will be measured. The graduate research assistant will participate in a carefully designed program that will encompass a series of training elements in research, teaching, and service to prepare for an academic career. Overall, this project bears the potential to become an important addition to the toolkit of project managers in construction and other industries by providing an methodology for integrated cash flow modeling, analysis, and optimization that is both useful in practice and eminently teachable. It will contribute to society by (a) improving the financial planning capabilities of contracting firms to support their profitability, (b) broadly educating the graduate assistant, (c) engaging the PI in a project that fuses research, teaching, and service work, (d) increasing the awareness of underrepresented youth with respect to financial planning and careers in the construction industry in, and (e) laying the foundation for further innovative modeling that advances project planning.