Faculty Mentor Information
Dr. Paul Bodily, Idaho State University
Additional Funding Sources
This material is based upon work supported by the National Science Foundation under EPSCoR Award OIA2242769.
Presentation Date
7-16-2026
Abstract
Energy and water problems have a prevalence of optimization solutions. Yet operators, educators, and students working in these systems frequently lack tools that make the underlying optimization problems visible, tractable, or teachable. It has been noted that Dr. Bruce Savage, Chair of the Civil and Environmental Engineering Department at Idaho State University, has identified this gap directly, specifically noting that visualization and interactive learning tools of this kind could be transformative not only for K-12 students but for collegiate education as well. This research responds to that need by developing interactive, visualization-driven software that maps real-world energy-water challenges onto canonical problems in computational theory, making both the solutions and the reasoning behind them accessible across a wide range of audiences.
Pump scheduling serves as the central demonstration problem. The task of selecting which pumps to operate during which hours of a 24-hour cycle (subject to storage constraints, demand requirements, and time-of-use electricity pricing) is NP-Hard in its general form, placing it among the most computationally difficult classes of optimization problems. This research implements a dynamic-programming solution over a directed acyclic graph (DAG) representation of the decision space, recovering an exact optimal schedule efficiently by exploiting the problem's inherent temporal structure. The result is surfaced through two complementary interfaces: a K-12 module that builds intuition through simplified, animated pump and delivery scenarios, and a full algorithmic workspace that exposes cost trajectories, pump state matrices, and step-by-step solution traces for professional and research audiences.
The impact of this work is threefold. Practically, it demonstrates that rigorous algorithmic methods can produce exact, interpretable solutions to scheduling problems that practitioners often address only with heuristics. Pedagogically, it provides a concrete bridge between K-12 exploration and college-level engineering analysis. Meaning the same problem, rendered at the right level of abstraction, can meet students where they are and grow with them. More broadly, it offers evidence that computational theory is not merely an academic formalism but a broadly applicable lens for reasoning about critical infrastructure decisions across the energy-water nexus.
Applied Computational Models and Algorithmic Solutions to Common Optimization Problems in Energy-Water Systems
Energy and water problems have a prevalence of optimization solutions. Yet operators, educators, and students working in these systems frequently lack tools that make the underlying optimization problems visible, tractable, or teachable. It has been noted that Dr. Bruce Savage, Chair of the Civil and Environmental Engineering Department at Idaho State University, has identified this gap directly, specifically noting that visualization and interactive learning tools of this kind could be transformative not only for K-12 students but for collegiate education as well. This research responds to that need by developing interactive, visualization-driven software that maps real-world energy-water challenges onto canonical problems in computational theory, making both the solutions and the reasoning behind them accessible across a wide range of audiences.
Pump scheduling serves as the central demonstration problem. The task of selecting which pumps to operate during which hours of a 24-hour cycle (subject to storage constraints, demand requirements, and time-of-use electricity pricing) is NP-Hard in its general form, placing it among the most computationally difficult classes of optimization problems. This research implements a dynamic-programming solution over a directed acyclic graph (DAG) representation of the decision space, recovering an exact optimal schedule efficiently by exploiting the problem's inherent temporal structure. The result is surfaced through two complementary interfaces: a K-12 module that builds intuition through simplified, animated pump and delivery scenarios, and a full algorithmic workspace that exposes cost trajectories, pump state matrices, and step-by-step solution traces for professional and research audiences.
The impact of this work is threefold. Practically, it demonstrates that rigorous algorithmic methods can produce exact, interpretable solutions to scheduling problems that practitioners often address only with heuristics. Pedagogically, it provides a concrete bridge between K-12 exploration and college-level engineering analysis. Meaning the same problem, rendered at the right level of abstraction, can meet students where they are and grow with them. More broadly, it offers evidence that computational theory is not merely an academic formalism but a broadly applicable lens for reasoning about critical infrastructure decisions across the energy-water nexus.