Enabling Higher Dimensionality of Temporal-Spatial Analysis Applied to Linear Scheduling of Construction Operations Based on Singularity Functions in Structural Engineering

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The objective of this project is to investigate how construction and other industries can move beyond the current conceptual limitations of the critical path method algorithm for scheduling and better integrate their project information in two dimensions. The existing linear scheduling method thus far has remained an essentially graphical representation for lack of a comprehensive underlying mathematical basis that would allow applying an analytical algorithm at such higher dimensionality. To address this issue, the research will utilize the inherent versatility of the mathematical class of singularity functions and develop a self-contained new method of analyzing and optimizing linear and repetitive project schedules. The feasibility of this project is rooted in the discrete geometry-based activity description in linear schedules, in the valuable mathematical properties of singularity functions, and in their existing application to beams under various loads in structural analysis. Singularity functions are very desirable as they present a flexible means of modeling a phenomenon of interest in a single mathematical expression that may contain numerous components of different degree of complexity, but can still be solved manually with basic geometry and algebra skills to verify computer calculations.Real-world case studies with detailed schedule analyses of major projects in the national capital region will serve for verification and validation. An IT tool and associated educational materials will bring the expanded analytical capabilities to current project managers in the field, to future project managers and their educators in the classroom, and to other researchers. The PI will bring the fruits of this research to the Career Opportunities in Architecture, Construction, and Engineering mentoring program and to various pre-engineering summer programs at The Catholic University of America (CUA) to actively involve their constituents, including youth, women, and minorities, in educational outreach activities that will help building their skills and confidence in their abilities. The PI will share outcomes of the research with the professional and academic communities by publishing in scholarly publications, presenting the progress and results at premier conferences, and using the educational materials in continuing education training for industry professionals to facilitate the adoption of the new method. The materials will be integrated into the comprehensive practice-oriented construction curriculum at CUA. All materials will be housed on a website for timely dissemination. The new schedule analysis laboratory will become an incubator that can lead to further innovations toward the long-term vision of a fully information-integrated and information-driven project management and will give its graduate students valuable research experience.Overall, this project will generate a deeper understanding of the informational content of construction projects in their interplay between the temporal and spatial dimensions and will lead to improved planning, analysis, and execution of creating the infrastructure and the capital constructed facilities that sustain the high quality of modern life. The stakeholders of projects of linear or repetitive nature in the construction industry and in other industries will be able to benefit economically from improved resource utilization, more efficient site layout, safer workplaces through better interference detection, reduced rework, and optimized sequencing of operations. The anticipated contributions of this project to society's welfare will be (a) facilitating better decision making that can yield cost and time savings, (b) grooming young engineers into highly qualified entrants into academia and construction, and (c) developing the PI's research, teaching, and service areas for a productive future.