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Equity-aware stochastic optimization of mammography screening facility location under demand and capacity uncertainty

This study presents an equity-aware stochastic optimization framework for Texas that identifies optimal locations for new mammography facilities to significantly increase screening coverage and reduce racial and geographic disparities by strategically targeting underserved communities while explicitly accounting for demand and capacity uncertainties.

Original authors: Mahboubeh Madadi, Caroline Wilson, Cici Bauer, Shayan Shams

Published 2026-10-13

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Mahboubeh Madadi, Caroline Wilson, Cici Bauer, Shayan Shams

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Breast cancer remains one of the most common and deadly diseases affecting women in the United States, but early detection through screening mammography can save lives by catching the disease while it is still treatable. For these screenings to work, however, women must be able to physically reach a facility that has the right equipment and staff. In many parts of the country, particularly in rural areas or communities with fewer resources, the journey to a screening center is long, difficult, or simply impossible. This uneven distribution of healthcare services creates a gap where some women get the care they need while others do not, often based on where they live or their background. To fix this, planners need more than just a list of where clinics are; they need a way to decide where to build new ones when they cannot be certain exactly how many women will need them or how busy the existing clinics will be.

A team of researchers at the University of Texas Health Science Center at Houston has developed a new way to solve this puzzle. They created a computer model designed to find the best places to open new mammography screening facilities across the entire state of Texas. The goal was not just to help as many women as possible, but to do so in a way that treats every racial and ethnic group fairly. The researchers faced a difficult challenge: they had to make decisions about where to build before knowing exactly how many women would show up for screenings or how many appointments the current clinics could handle. To handle this uncertainty, they used a method called stochastic optimization, which essentially runs thousands of different "what-if" scenarios to find a plan that works well no matter how the future unfolds.

The study focused on more than 5.5 million women in Texas between the ages of 40 and 74, the group recommended for regular screening. The researchers started by mapping out the 615 existing mammography facilities and estimating how many women they could serve. They then identified thousands of potential spots where a new clinic could be built, focusing on areas where women currently had to travel too far or where the local clinics were already overwhelmed. Using their model, they tested which combination of new locations would provide the best coverage for the entire state while also ensuring that no specific group of people was left behind.

The results showed that opening 62 new facilities in carefully chosen locations could dramatically improve access. Under the current system, about 92 percent of eligible women were expected to have access to screening within a reasonable travel time. With the new plan, that number would rise to nearly 98 percent. More importantly, the plan significantly reduced the gap in access between different racial and ethnic groups. Before the new facilities, women in rural areas, particularly those who were White, Native American, or Pacific Islander, had the hardest time reaching a clinic. The new locations were placed specifically to help these underserved populations, raising their access levels to match those of women in more urban areas. The model ensured that every group saw an improvement, with the most disadvantaged groups gaining the most ground.

The researchers found that the new facilities would be distributed across the state, with nearly half of them located in non-metropolitan counties. In fact, 39 percent of the new sites would be the very first mammography facility in their respective counties, effectively ending the status of those areas as "mammography deserts." The study also revealed that simply building more clinics in cities would not solve the problem. The most effective strategy was to place facilities where the need was greatest, even if those areas had lower population numbers. This approach meant that the new clinics would be located in places where women currently lived, rather than just where the highest volume of patients was already gathering.

However, the study also highlighted the limits of what fixed buildings can achieve. In the most remote and sparsely populated parts of West Texas, even the best plan for new permanent clinics could not reach every woman within a sixty-minute drive. In these specific areas, the researchers noted that mobile screening units would likely be a better solution than building more permanent sites. The model also proved that accounting for uncertainty was crucial. If the planners had ignored the possibility of fluctuating demand and capacity and simply built based on average numbers, the result would have left nearly 30,000 more women without access each year. By planning for the unknown, the model secured access for those extra women.

Ultimately, the study demonstrates that a modest expansion of screening capacity, when guided by data and a commitment to fairness, can close significant gaps in healthcare. The researchers showed that it is possible to increase the number of women who can get screened while simultaneously making the system more equitable for everyone. The findings suggest that by placing facilities where under-served populations live, rather than just where the most people are, health systems can narrow the divide between rural and urban access and between different racial groups. While no single plan can solve every geographic challenge, this approach offers a clear, evidence-based path forward for making life-saving screenings available to more women, regardless of their zip code or background.

Technical Summary: Equity-aware Stochastic Optimization of Mammography Screening Facility Location

Problem Statement
Uneven geographic access to mammography screening limits participation in breast cancer prevention, particularly affecting rural and underserved communities in Texas. While existing Geographic Information Systems (GIS) analyses can describe current access disparities, they often fail to determine optimal locations for new facilities under conditions of uncertainty. Prior studies have frequently been descriptive, limited to single metropolitan areas, or relied on deterministic assumptions regarding demand and facility capacity. In a state like Texas, characterized by vast rural areas and large metropolitan centers, planning must account for competition for shared facilities, capacity constraints, and the risk that optimizing for average access may inadvertently worsen outcomes for groups already facing barriers. The core problem addressed is how to select a finite set of new mammography facility locations from a candidate pool to maximize screening coverage and minimize racial/ethnic disparities in access, while explicitly modeling uncertainty in both screening demand and the operational capacity of existing facilities.

Methodology
The authors developed a statewide, two-stage stochastic facility-location model with a lexicographic (prioritized) objective function.

Data and Inputs: The study utilized data for 5.58 million eligible women (aged 40–74) across 254 Texas counties and 6,896 census tracts. The existing supply network consisted of 615 FDA-certified facilities. Since facility-level capacity is not publicly reported, the authors estimated annual screening capacity for existing facilities using observed procedure volumes from the Texas Health Care Information Collection (THCIC) and facility-class priors.
Candidate Generation: A set of 222 candidate locations was generated by identifying "access-gap" census tracts where potential access (measured via Enhanced Two-Step Floating Catchment Area, E2SFCA) fell below 0.80 effective screening slots per eligible woman. Candidates were clustered by population-weighted spatial gaps, capped at six per county, and required a minimum population of 2,500 eligible women within a 60-km radius.
Stochastic Optimization Framework:
- Uncertainty Modeling: The model incorporates nine scenarios combining three demand multipliers (0.9, 1.0, 1.1) and three capacity-utilization states (utilization factors $\rho$ of 1.0, 0.8, and 0.6).
- Two-Stage Structure:
  - Stage 1 (First-stage decisions): Binary decisions ( $y_j$ ) to open candidate facilities are made before the realization of demand and capacity scenarios.
  - Stage 2 (Second-stage recourse): Patient allocation ( $x_{ij}^s$ ) and unmet demand ( $u_i^s$ ) adapt to the specific realized scenario $s$ .
- Lexicographic Objectives: The model is solved in two phases. Phase 1 minimizes expected unmet demand (maximizing coverage). Phase 2 minimizes the population-weighted between-group variance (BGV) of potential access across eight race and ethnicity groups, subject to a "coverage lock" that ensures the solution does not sacrifice near-optimal coverage to achieve equity.
- Accessibility Metrics: The optimization uses county-level drive times (60-minute threshold) calculated via Open-Source Routing Machine (OSRM). Tract-level straight-line distances were used for candidate generation and visualization but were noted to be optimistic compared to drive times.

Key Results

Coverage Gains: Opening 62 new facilities across 58 counties increased expected screening coverage from 92.47% (baseline) to 98.09%, reducing annual unmet demand from approximately 420,089 to 106,822 women.
Equity Improvements: The population-weighted between-group variance (BGV) in access decreased by 32%. Crucially, access improved for all eight race and ethnicity groups. The group with the lowest baseline access (non-Hispanic White, largely rural) saw access rise from 0.858 to 0.953 effective slots per woman, while the highest-baseline group (non-Hispanic Asian) saw a smaller gain, effectively compressing the disparity distribution without "leveling down" any group.
Geographic Distribution: The selected sites were need-driven rather than volume-driven. All 62 facilities were placed in tracts with baseline access below 0.80. Notably, 44% of the new facilities were in non-metropolitan counties, and 39% established the first mammography facility in their respective counties ("mammography deserts").
Value of Stochasticity: Explicitly modeling uncertainty provided significant value. The stochastic plan left 29,643 fewer women unserved annually compared to a deterministic mean-value plan (Value of Stochastic Solution, VSS = 29,643). The Expected Value of Perfect Information (EVPI) was relatively low (6,453 women), suggesting the stochastic solution captures most of the potential benefit even without perfect foresight.
Limitations of Fixed Sites: The analysis identified a structural limit for fixed facilities in remote, sparsely populated areas (e.g., Brewster, Jeff Davis, and Presidio counties in far-West Texas). In these regions, no single fixed site could serve the dispersed demand within a 60-minute travel limit, indicating that mobile screening is a necessary complementary strategy for these specific gaps.

Significance and Claims
The paper claims to advance the literature by integrating empirically derived capacity estimates, statewide candidate generation, and uncertainty modeling into a lexicographic optimization framework that prioritizes coverage before equity. Unlike models that rely on centrally imposed patient-routing patterns to achieve equity, this study demonstrates that reducing disparity can be achieved directly through strategic facility placement.

The authors assert that their results show a "modest, equity-aware expansion" of fixed capacity can substantially widen access and narrow racial and geographic disparities by placing facilities where under-served populations live, rather than where volume is highest. They emphasize that the residual disparities are primarily geographic (distance to care in rural areas) rather than a function of race or social vulnerability, as the model did not explicitly weight social vulnerability indices (SVI) in the objective function. The study concludes that while fixed-site expansion is highly effective for the majority of the state, the most remote communities require complementary mobile screening strategies, a distinction that deterministic planning might fail to capture.

Technical Summary: Equity-aware Stochastic Optimization of Mammography Screening Facility Location

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