Construction spatial modeling and scheduling with three-dimensional singularity functions |
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| Affiliation: | 1. Construction Engineering and Management Program, Department of Civil Engineering, Catholic University of America, 620 Michigan Avenue NE, Washington, DC 20064, United States;2. Faculty of Engineering, Cairo University, Giza, Egypt;3. Department of Civil Engineering, 500 El Camino Real, Santa Clara University, Santa Clara, CA 95053, United States;4. Department of Mathematics, Campus Saint Jean, University of Alberta, 8406 Marie-Anne-Gaboury Street (91st Street), Edmonton, Alberta T6C 4G9, Canada;1. Department of Mechatronics & Control Engineering, University of Engineering & Technology, Lahore, Pakistan;2. Department of Industrial & Manufacturing Engineering, University of Engineering & Technology, Lahore, Pakistan;3. Department of Transportation Engineering & Management, University of Engineering & Technology, Lahore, Pakistan;1. School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, 639798, Singapore;2. School of Computer Engineering, Nanyang Technological University, Nanyang Avenue, 639798, Singapore;3. Institute for Media Innovation, Nanyang Technological University, 50 Nanyang Drive, Research Techno Plaza, 637553, Singapore;1. Department of Civil Engineering, Santa Clara University, Santa Clara, CA 95051, United States;2. Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, United States;3. Lecturer, Faculty of Engineering, Cairo University, Giza, Egypt;1. University of Alberta, Department of Civil & Environmental Engineering, Hole School of Construction, 4-110H Markin/CNRL Natural Resources Engineering Facility, Edmonton, Alberta T6G 2W2, Canada;2. Campus Saint Jean, University of Alberta, 8406-91 Street, Edmonton, Alberta, Canada |
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| Abstract: | Previous approaches for construction project scheduling have been limited to one dimension of time for bar charts and two dimensions for linear and repetitive scheduling approaches, which added a measure of work quantity. The question therefore arises if and how it is possible to derive a three-dimensional and ultimately multi-dimensional model. Reviewing mathematical theory finds that traditional functions lack the capability to express intervals for activities. Singularity functions are therefore chosen to newly derive stationary and directional activities in a Cartesian coordinate system, wherein the two dimensions of the floor plan area plus one dimension of time are explicitly modeled in an integrated manner. They are implemented into a conflict-avoiding heuristic scheduling algorithm that minimizes total project duration, which is computerized and validated with example calculations. |
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