How to Optimize Colorado River Water & Power Distribution for Five States

In the previous issue we discussed the importance of MCM O‑Award papers and introduced the A‑problem; this article focuses on the B‑problem, which addresses water and power allocation for five western U.S. states.

Problem

Background

For centuries, dams and reservoirs have been built on rivers to store water for agriculture, industry, residential use, recreation, flood control, and hydro‑electric generation. Climate change is reducing inflows, threatening both water supply and power generation at Glen Canyon (Lake Powell) and Hoover (Lake Mead) dams.

Natural‑resource officials from Arizona, California, Wyoming, New Mexico, and Colorado are negotiating a water‑sharing plan for the Colorado River basin. Historic agreements allocate more water than currently available, and prolonged drought may leave the basin unable to meet basic water and electricity needs.

The negotiation team asks your group to devise a defensible, adaptable allocation plan for the five states, considering reduced rainfall, high temperatures, and the need to balance agricultural, industrial, residential, and power‑generation demands.

Requirements

Develop a mathematical model that, given fixed water‑supply and demand conditions, determines how much water to draw from each reservoir (Lake Mead level M, Lake Powell level P) to satisfy all demands without additional inflow, and estimates the time required to deplete the supplies.

Recommend a method to resolve conflicts between general water use and hydro‑electric generation, stating explicit criteria.

Explain actions to take when water is insufficient to meet all demands.

Analyze model behavior under varying conditions, including: Changing population, agricultural, and industrial growth. Increased share of renewable‑energy technologies. Implementation of additional water‑ and energy‑saving measures, without relying on existing political agreements.

Prepare a one‑ to two‑page article for the journal Dryness and Thirst , aimed at water‑infrastructure managers in the U.S. Southwest.

Model Frameworks

Model 1 – Resource Allocation Network (RAN)

Simulates the entire water‑to‑power process and formulates the allocation as a linear programming problem when water is abundant but no extra inflow is available.

Results show the network can sustain 21 days without additional water under the five‑state allocation.

Model 2 – Marginal‑Utility Based IPV Model

Introduces marginal utility functions to quantify the scarcity of water for general use versus hydro‑electric generation, forming utility and value functions that assess trade‑offs.

By applying auction theory, the model seeks a Pareto‑optimal allocation.

Model 3 – Independent Private Value (IPV) Model

Solves the IPV model using a generalized backward‑search (BS) algorithm, yielding a more economical and sustainable allocation than Model 1.

Extended Analyses

Additional scenarios incorporate Mexico’s water rights, sensitivity analyses on population, agricultural, and industrial growth, renewable‑energy penetration, and water‑saving measures.

Key findings include:

The IPV auction increases equity among the five states, raising the overall value for Wyoming, New Mexico, and Colorado.

When water is scarce, a bidding system encourages higher‑price purchases, financing infrastructure to reduce long‑term dependence on Colorado River water.

Dynamic programming updates the allocation every 100 days to reflect cyclical reservoir fluctuations.

Conclusions

The multi‑model approach provides a robust decision‑support tool for allocating limited water and power resources across the Colorado River basin, balancing stakeholder interests while remaining adaptable to climate variability and policy changes.