HARP: Equitable Health Access Planner

• HARP is a framework for equitable health access planning that combines geospatial analysis, optimization, and multi-criteria resource allocation.
• It integrates methods such as travel-time modeling, access gap analysis, and sequential facility planning under budget uncertainty.
• The system translates fairness and universal health coverage goals into computable constraints and metrics for operational planning.

Searching arXiv for the specified HARP-related papers and closely related healthcare access planning work. Health Access Resource Planner (HARP) denotes a family of data-driven, optimization-based approaches for health access planning that integrate geospatial accessibility analysis, equity-sensitive resource allocation, service-area delineation, and sequential facility investment under budget uncertainty. In the recent literature, the term is used both for a South Asia–oriented operational blueprint that combines Earth-observation (EO), travel-time modeling, barrier indices, and optimization (Elahi et al., 2024), and for a mathematically explicit access-aware allocation methodology that models realized uptake under access gaps between disadvantaged and advantaged subpopulations (Andrews et al., 2024). Related work extends HARP to multi-year facility planning with persistent proportionality constraints in Ethiopia (Choo et al., 29 Aug 2025), while modularity-based delineation of hospital service areas and referral regions supplies a complementary catchment-construction layer for regional planning (Hu et al., 2020).

1. Definition and problem domain

HARP is designed to support equitable, timely, and operationally feasible allocation of health resources. Across the cited formulations, the recurring problem is that nominal resource availability does not imply realized access. Geographic separation, terrain, seasonality, infrastructure quality, facility hours, cold-chain limits, workforce shortages, financial barriers, and heterogeneous acquisition rates can all produce systematic divergence between planned provision and actual uptake (Elahi et al., 2024).

The South Asia blueprint identifies three intertwined gaps: facility accessibility, workforce availability, and service delivery capacity. Facility accessibility is framed through geographic and temporal obstacles, including travel-time thresholds such as populations beyond 30 minutes and localization of underserved areas using VIIRS nightlights and population density. Workforce availability concerns insufficient or imbalanced deployment of health workers, particularly in rural or remote low-NTL areas. Service delivery capacity includes hours, cold-chain, supply, and infrastructure constraints that reduce effective coverage (Elahi et al., 2024).

The access-aware allocation formulation studies a divisible health resource distributed across geographic units indexed by $j \in [k]$, with total supply $R$, local population $P_j$, and availability ratio $\alpha := R/P \in (0,1)$. Its decision variable is the allocation vector $x := (N_j)_{j \in [k]}$, subject to $N_j \ge 0$, $\sum_j N_j = R$, and no-waste constraints $N_j \le P_j$. At each location, the population is partitioned into disadvantaged and advantaged subpopulations, with disadvantaged share $\beta_j \in [0,1]$ and an access gap parameter $\eta \in [0,1]$ governing acquisition-rate slowdown for the disadvantaged (Andrews et al., 2024).

In the Ethiopian planning formulation, HARP is a decision-support tool for sequential facility planning. It selects binary investments $R$0 over a horizon $R$1, where candidate facility sites are indexed by $R$2, annual budgets are online and irrevocable, and each selected facility contributes persistent coverage in all later years. The objective is to maximize cumulative population coverage while satisfying fairness constraints across administrative units such as districts at every decision step (Choo et al., 29 Aug 2025).

A plausible implication is that HARP is best understood not as a single fixed software package, but as a planning architecture spanning static allocation, geospatial access modeling, facility siting, and sequential investment design.

2. Conceptual architecture and policy framing

In the South Asia formulation, HARP is explicitly aligned with Universal Health Coverage goals and the WHO health system framework pillars, with an added emphasis on Cross-Sectoral Linkages. The framework maps Health Financing, Service Delivery, Human Resources for Health, Health Information Systems, Governance, Essential Medicines and Technology, and Cross-Sectoral Linkages into spatially explicit indicators at 1 km or finer resolution (Elahi et al., 2024).

Its indicator families include access measures such as percent of population with $R$3 minutes, 2SFCA and gravity access scores, and seasonal drop in access; HRH measures such as $R$4 against targets and workforce equity indices; service-delivery measures such as throughput per hour or day, vaccine reach $R$5, stockouts, and hours open; financing measures such as cost-to-reach per household and budget allocation and execution by district; HIS measures such as facility geocode completeness and data latency; governance measures such as decision latency and coordination metrics; medicines and technology measures such as cold-chain uptime and transport fleet capacity; and cross-sectoral measures such as road class mix, telecom coverage, disaster hazard overlay, and seasonal accessibility loss (Elahi et al., 2024).

The access-aware allocation formulation introduces a distinct but complementary layer. It measures deviation from proportional geographic allocation using simplex distances,

$R$6

and

$R$7

where $R$8 and $R$9. This makes geographic parity an explicit constraint or penalty, rather than an implicit norm. HARP then minimizes disparity subject to parity headroom and feasibility, thereby formalizing the trade-off between equity-oriented reallocation and proportional distribution (Andrews et al., 2024).

The Ethiopian formulation adds a third policy principle: persistent proportionality. Let types or fairness groups be indexed by $P_j$0, with long-run proportionality targets $P_j$1. Because exact per-step proportionality may be infeasible under online budgets, HARP instead enforces the best achievable minimum satisfaction ratio at every time,

$P_j$2

with

$P_j$3

This converts fairness from an end-of-horizon aspiration into a prefix condition under uncertainty (Choo et al., 29 Aug 2025).

These formulations jointly show that HARP is not confined to travel-time analytics. It is equally a policy translation layer, converting high-level fairness, resilience, and UHC objectives into computable constraints, metrics, and prioritization rules.

3. Data model, geospatial engine, and accessibility estimation

The South Asia blueprint defines HARP’s data stack as a harmonized integration of EO, administrative, health-system, and infrastructure sources. The EO and ancillary layers include Sentinel-2, Landsat 8/9, ESA WorldCover, HRSL or GHSL, VIIRS V2.2 annual composites and monthly Black Marble, SRTM, ALOS PALSAR, Copernicus GLO-30 DEM, HydroSHEDS, CHIRPS, ERA5, Sentinel-1 flood extent, OSM and national road datasets, GPWv4, WorldPop, DHS/MICS, HMIS facility master lists, EVM assessments, and telecom coverage data. Data freshness is operationalized through reproducible ETL schedules such as VIIRS monthly, Sentinel-2 weekly, OSM weekly, HMIS monthly or quarterly, and DHS/MICS as available (Elahi et al., 2024).

The ETL layer performs deduplication and conflation of facility lists, using fuzzy matching on names and addresses, spatial clustering within 100–300 m, preference for HMIS identifiers, and confidence scoring. Geocoding stores precision and provenance; road data reconciliation marks seasonal edges; projections are standardized; and per-layer timeliness, completeness, and accuracy metrics are propagated downstream for uncertainty analysis (Elahi et al., 2024).

Accessibility modeling is based on friction and multimodal travel-time surfaces. For walking, slope-adjusted speed is defined through Tobler’s hiking function,

$P_j$4

Road and river edges receive context-specific speeds, seasonal multipliers, and closure flags, and ferry schedule penalties are incorporated into hybrid routing. Travel time from location $P_j$5 to facility $P_j$6 is then

$P_j$7

with the minimum computed via cost-distance or Dijkstra on a hybrid graph (Elahi et al., 2024).

Two principal accessibility families are then computed. The two-step floating catchment area method uses

$P_j$8

where $P_j$9 is service capacity and $\alpha := R/P \in (0,1)$0 is a travel-time threshold such as 60 minutes. Gravity-based accessibility uses

$\alpha := R/P \in (0,1)$1

with $\alpha := R/P \in (0,1)$2 or $\alpha := R/P \in (0,1)$3. Coverage gaps are summarized as

$\alpha := R/P \in (0,1)$4

and equity can be measured by a Lorenz/Gini expression over catchments or districts (Elahi et al., 2024).

Calibration is empirical rather than purely parametric. The South Asia blueprint specifies use of HMIS utilization versus modeled access, ground travel-time surveys, generalized linear models for catchment utilization decline versus $\alpha := R/P \in (0,1)$5, and sensitivity analysis over speed parameters, seasonal coefficients, and thresholds $\alpha := R/P \in (0,1)$6 minutes (Elahi et al., 2024). The Ethiopian implementation operationalizes a related coverage logic using 1 km population forecasts and 2-hour walking catchments derived from the global friction surface, with cumulative coverage

$\alpha := R/P \in (0,1)$7

and diminishing returns due to persistent submodular coverage (Choo et al., 29 Aug 2025).

A common misconception is that HARP equates access with Euclidean proximity. The cited formulations instead rely on friction-adjusted travel times, multimodal routing, service capacity, seasonality, and—in the access-aware model—subpopulation-specific realized uptake (Elahi et al., 2024, Andrews et al., 2024).

4. Equity, realized uptake, and access-aware allocation

The access-aware allocation model formalizes a distinction between allocated supply and realized acquisition. At location $\alpha := R/P \in (0,1)$8, acquisition by disadvantaged and advantaged groups is modeled via independent Poisson acquisition processes. Without saturation, disadvantaged and advantaged base rates are $\alpha := R/P \in (0,1)$9 and $x := (N_j)_{j \in [k]}$0, producing the naïve disadvantaged acquisition fraction

$x := (N_j)_{j \in [k]}$1

Realized uptake under the naïve model is

$x := (N_j)_{j \in [k]}$2

The exact model adds saturation and exhaustion through stopped Poisson processes and Binomial CDF terms, while a tractable approximation defines

$x := (N_j)_{j \in [k]}$3

which yields a saturation-aware approximation to realized uptake (Andrews et al., 2024).

Disparity is then defined through per-capita acquisition rates:

$x := (N_j)_{j \in [k]}$4

and resource disparity is

$x := (N_j)_{j \in [k]}$5

The paper interprets $x := (N_j)_{j \in [k]}$6 as a proxy for downstream inequity. Under an outcome model with elevated baseline disadvantage risk factor $x := (N_j)_{j \in [k]}$7 and resource effects $x := (N_j)_{j \in [k]}$8 and $x := (N_j)_{j \in [k]}$9, expected adverse outcomes are linear in $N_j \ge 0$0 with positive slope when

$N_j \ge 0$1

For COVID-19 hospitalization data from 10/2021–2/2022, the reported values $N_j \ge 0$2 for advantaged and $N_j \ge 0$3 for disadvantaged yield a very small threshold, and observed $N_j \ge 0$4 values such as $N_j \ge 0$5 for ages 65+ versus 18–64 exceed it, so reducing $N_j \ge 0$6 reduces expected hospitalizations (Andrews et al., 2024).

Optimization proceeds by minimizing disparity subject to geographic parity and feasibility. Under the naïve model, HARP solves a linear program with either $N_j \ge 0$7 or relative-$N_j \ge 0$8 deviation constraints; under the saturation-aware approximation, $N_j \ge 0$9 becomes piecewise-linear concave and is handled through an iterative reweighting heuristic that repeatedly updates $\sum_j N_j = R$0 and re-solves the LP. The methodology can also incorporate capacity limits $\sum_j N_j = R$1, vulnerability floors $\sum_j N_j = R$2, and logistics budgets $\sum_j N_j = R$3 if data permit (Andrews et al., 2024).

A central empirical result is that precise knowledge of the access gap $\sum_j N_j = R$4 is often unnecessary. The coefficient vector $\sum_j N_j = R$5 rotates within a narrow cone, so the same minimizing vertex of the feasible polytope may remain optimal across a range of $\sum_j N_j = R$6 values. The paper formalizes this as an $\sum_j N_j = R$7-robust optimizer proposition and gives a three-location example with

$\sum_j N_j = R$8

for which the optimal allocation

$\sum_j N_j = R$9

is identical for all $N_j \le P_j$0, shifting allocation toward the highly disadvantaged location (Andrews et al., 2024).

This suggests that HARP’s equity logic is not limited to identifying underserved places. It can also prescribe intentionally non-proportional allocations when proportionality would amplify access-induced disparity.

5. Optimization modules, service areas, and sequential planning

The South Asia blueprint specifies several optimization modules. For facility placement, it uses a $N_j \le P_j$1-median formulation:

$N_j \le P_j$2

subject to

$N_j \le P_j$3

Capacity-constrained assignment adds budget and capacity constraints, workforce balancing minimizes

$N_j \le P_j$4

and vaccination access under cold-chain constraints maximizes $N_j \le P_j$5 subject to session, storage, and route feasibility. Exact solvers include CBC, Gurobi, and CPLEX; heuristics include greedy add/drop, local search, Teitz-Bart, Lagrangian relaxation, and simulated annealing. Scenario analysis spans normal conditions, monsoon, flood events, and conflict access reductions (Elahi et al., 2024).

The Ethiopian facility-planning formulation addresses a different optimization regime: sequential planning under online budgets. HARP models cumulative coverage as monotone submodular, with site selections persisting once made. Its multi-step algorithm computes per-type quotas from a min-ratio type sequence, imposes them through a partition matroid

$N_j \le P_j$6

and performs greedy marginal-gain selection under that constraint. The resulting planner has a worst-case per-step guarantee

$N_j \le P_j$7

for monotone submodular $N_j \le P_j$8 and a single matroid constraint per round (Choo et al., 29 Aug 2025).

The same work also introduces a learning-augmented single-step selector. Given a budget-$N_j \le P_j$9 advice set $\beta_j \in [0,1]$0, HARP considers advice prefixes $\beta_j \in [0,1]$1, greedily completes each to a full solution $\beta_j \in [0,1]$2, and returns the best $\beta_j \in [0,1]$3. This yields robustness and consistency: it never underperforms the greedy baseline, and if advice is optimal then HARP returns the advised solution. Under pure cardinality constraints, the baseline greedy guarantee is $\beta_j \in [0,1]$4; under a partition matroid, it becomes $\beta_j \in [0,1]$5 (Choo et al., 29 Aug 2025).

A further structural layer arises from modularity-based delineation of service areas. Using all-payer inpatient flows in Florida, the modularity optimization paper constructs HSAs and HRRs from a weighted undirected bipartite network between residence ZIPs and hospital ZIPs, with weighted modularity

$\beta_j \in [0,1]$6

Louvain optimization maximizes within-community patient flows relative to random expectation, thereby improving localization of catchments for planning (Hu et al., 2020). This catchment-construction problem is orthogonal to allocation, but it is operationally complementary: HARP requires coherent spatial units for workforce ratios, referral leakage, and region-level capacity comparisons.

The paper reports that Florida’s Dartmouth-comparable partitions achieved $\beta_j \in [0,1]$7 for HSAs and $\beta_j \in [0,1]$8 for HRRs, while global-optimal partitions yielded 17 HSAs with $\beta_j \in [0,1]$9 and 16 HRRs with $\eta \in [0,1]$0. Mean localization index for HSAs rose from $\eta \in [0,1]$1 in Dartmouth units to $\eta \in [0,1]$2 in the global-optimal partition, MSI fell to $\eta \in [0,1]$3, and HHI for global-optimal HSAs was $\eta \in [0,1]$4 (Hu et al., 2020). A plausible implication is that a HARP deployment operating on outdated or poorly localized service areas may misestimate catchments, leakage, and comparative need.

6. Operational deployments, empirical findings, and limitations

The South Asia blueprint presents case-study illustrations rather than a single deployed system. In urban slums such as Dhaka and Karachi, it combines high population density with low NTL pockets, congestion, and hours-of-operation barriers; modeled interventions include extended clinic hours with $\eta \in [0,1]$5 throughput and micro-sites in slum clusters, reducing the percent beyond 30 minutes from $\eta \in [0,1]$6 to $\eta \in [0,1]$7 and decreasing the Gini of access from $\eta \in [0,1]$8 to $\eta \in [0,1]$9. In remote mountainous areas of Northern Pakistan and Nepal, mobile clinics sited via $R$00-median and footbridge upgrades reduce median $R$01 from $R$02 to $R$03 minutes, increase 2SFCA $R$04 by $R$05, and decrease coverage gap $R$06 by $R$07 on average. In Bangladesh chars and Assam floodplains, seasonal friction surfaces indicate $R$08–$R$09 speed reductions, and pre-positioned boats and floating clinics increase $R$10 by $R$11 in high-hazard chars while maintaining at least $R$12 of sessions during monsoon. Cross-border catchment analysis in the Indo-Nepal Terai and Punjab-Sindh border is described as reducing average $R$13 by $R$14 and bringing workforce ratio $R$15 closer to $R$16 with $R$17 fewer new posts via redistribution (Elahi et al., 2024).

The access-aware allocation paper reports empirical validation of the access model across California, Illinois, Ohio, and Pennsylvania counties and globally across 142 countries. Observed uptake declines approximately linearly with vulnerability share $R$18, supporting the relation $R$19. Access-aware allocations under both $R$20 and relative-$R$21 headroom reduce $R$22 substantially relative to proportional allocation. Under moderate availability $R$23, $R$24 shifts downward across $R$25; under high availability $R$26, improvements are relatively larger because saturation would otherwise favor the advantaged subpopulation (Andrews et al., 2024).

In Ethiopia, HARP was co-developed with the Ethiopian Public Health Institute and Ministry of Health and evaluated on Afar, Benishangul Gumuz, and Somali, with Sidama in the appendix. Candidate sites are 1 km grid cells, coverage uses 2-hour walking time, and proportionality targets are specified as DP0 with $R$27, DP1 proportional to unassisted home birth rates, and DP2 inversely proportional to postnatal care coverage. Annual budgets were 12 facilities for Afar, 10 for Benishangul Gumuz, 30 for Somali, and 12 for Sidama. Reported results include roughly linear coverage growth with annual budget, shrinking efficiency loss of fairness at higher budgets, $R$28 under DP0, and stronger fairness compliance under DP1 or DP2. In retrospective district-level analysis, the advice-augmented selector outperformed both expert and greedy baselines in 25 districts; in a representative district, $R$29 exceeded $R$30 by approximately $R$31 and $R$32 by approximately $R$33. In Sidama, HARP outperformed both baselines in 11 districts, although coverage gains were smaller due to high existing coverage (Choo et al., 29 Aug 2025).

The limitations documented across these works are consequential. The access-aware allocation model assumes infinite-horizon acquisition and static allocation, omits dynamic behavioral responses such as hesitancy and trust, and uses a single $R$34 unless extended to $R$35 (Andrews et al., 2024). The South Asia blueprint notes the need for uncertainty propagation by Monte Carlo, confidence scoring, active correction for under-mapped roads and facilities in low-NTL zones, and aggregation of personally identifiable data to grids (Elahi et al., 2024). The Ethiopian sequential planner does not explicitly model facility readiness, lead times, or staffing and supply constraints, and recognizes that persistent proportionality can reduce short-term coverage gains even while improving fairness (Choo et al., 29 Aug 2025). The modularity-based service-area method does not impose hard spatial contiguity during optimization, treats each admission separately, and relies on inpatient flows that may not generalize to outpatient or ED patterns without extension (Hu et al., 2020).

Taken together, these limitations clarify the status of HARP in the literature. It is a rigorous planning framework with explicit mathematical objectives, empirical calibration pathways, and operational case studies, but it is not a complete substitute for policy judgment, local validation, or domain-specific system constraints. Its technical significance lies in making access, disparity, fairness, and spatial organization jointly computable within a reproducible planning pipeline.