2026 ASEE Annual Conference & Exposition

Linking Risk and Scheduling through Unit-Price Equations: A Pedagogical Framework for Construction Students

Presented at Architectural Engineering Division (ARCHE) Technical Session 2

Traditional approaches to teaching risk and scheduling in construction education often rely on qualitative risk matrices and deterministic activity durations, limiting students’ understanding of how time and cost emerge from field operations. This paper presents a procedural, equation-based pedagogical framework that links scheduling and risk reasoning to unit-price formulations grounded in productivity. The framework decomposes a main construction activity into elemental activities and expresses each cost component through explicit material, labor, logistics, and equipment terms. Activity durations are derived consistently from the same productivity assumptions embedded in the unit-price equations. To introduce uncertainty, variability in operational parameters (e.g., productivity rates and consumption quantities) is modeled through simple stochastic formulations and propagated via simulation to obtain probabilistic cost and duration outcomes. The approach is illustrated using a worked construction example with documented deterministic inputs (Appendix A) and a focused stochastic demonstration on a selected elemental-activity branch (Appendix B), supported by a reference implementation (Appendix C). Learning objectives emphasize (1) causal understanding of productivity-driven cost–time relationships, (2) formulation of transparent unit-price equations, and (3) interpretation of probabilistic outputs. Results show that the framework supports these objectives within a controlled instructional setting, shifting instruction from tool execution toward procedural reasoning.

Authors

Prof. Jose Guadalupe Rangel-Ramírez http://orcid.org/0000-0003-1044-4687 Tecnologico de Monterrey, School of Engineering and Sciences [biography]

Dr. José Guadalupe Rangel-Ramírez is a civil engineer and academic specializing in the risk, safety, and reliability of engineering systems. He has over 15 years of international research, teaching, and consultancy experience. He holds a Ph.D. in Civil Engineering from Aalborg University, Denmark, where his doctoral work focused on reliability-based inspection and maintenance of offshore wind turbines. He also earned a Master’s in Structural Engineering from the National University of Mexico and a civil engineering degree from the Autonomous University of Tamaulipas.
Currently a full-time professor at Tecnológico de Monterrey (Puebla campus), Dr. Rangel-Ramírez leads educational and research initiatives in structural design, construction management, and engineering risk analysis. He has also served as an assistant professor and postdoctoral fellow at Aalborg University, contributing to EU-supported research projects involving fire protection engineering, offshore energy infrastructure, and evacuation modeling.
Dr. Rangel-Ramírez has supervised over 40 theses across undergraduate, master’s, and PhD levels and had collaborated with industry partners such as TotalEnergies and COWI. His technical contributions include probabilistic modeling in earthquake engineering, agent-based modeling for public safety, probabilistic risk frameworks, and simulation tools for seismic and fire risk scenarios. He has published widely in international journals and conferences and is recognized as one of the most highly evaluated professors in his field.
With expertise spanning earthquake engineering, structural reliability, and renewable energy systems, he is committed to applying cutting-edge research to practical challenges in civil infrastructure. He is fluent in Spanish and English, and is proficient in numerous programming languages and structural engineering software. Dr. Rangel-Ramírez is an active member of several professional organizations and continues to foster interdisciplinary collaborations that push the boundaries of resilient and sustainable civil engineering.
Prof. Miguel X. Rodriguez-Paz http://orcid.org/0000-0002-9975-9847 Tecnologico de Monterrey (ITESM) [biography]

Prof. RodrÃguez-Paz got his B.Sc. In Civil Engineering from Tecnologico de Oaxaca in 1993. He studied a M.Sc. In Structural Engineering at Tecnologico de Monterrey and got his Ph.D. from the University of Wales at Swansea in 2003 where he did research on
Ing. Luis Horacio Hernandez Carrasco P.E. Tecnologico de Monterrey (ITESM) [biography]

Civil Engineer
Master degree in Structural Engineering
Master in Business Administration
Full time professor at (Tec de Monterrey) ITESM
Professional Registered Engineer in Structural Design
Juan Gutiérrez

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