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

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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.