3.1. Baseline Network and Demand Portrait
The baseline network and demand portrait were established by merging redeemed e-prescription data from the reimbursement program (2022–2025) with the registry of dispensing locations under NHSU contracts, using the division_id as the primary key. This approach provides both a measurable demand proxy (the number of redeemed e-prescriptions) and the geocoded node addresses required for subsequent accessibility calculations [
21,
22].
Between 2022 and 2025, 3,060,522 e-prescriptions were redeemed in Kyiv and 1,147,424 in Lviv. The network of dispensing nodes in Kyiv was larger (1826 unique division_id entries compared to 492 in Lviv), consistent with the higher number of participating legal entities (178 vs. 62). Compared to 2022, the annual volume of redemptions in 2025 increased by 75.4% in Kyiv and 32.6% in Lviv, confirming an upward demand trend in both metropolitan areas [
21].
The distribution of demand among nodes is asymmetric in both cities. Using a standardized measurement approach (total redemptions per division_id), the share of the top 10 nodes in total demand is 14.2% in Kyiv and 29.7% in Lviv. In comparison, the top 50 nodes account for 35.0% and 61.4%, respectively, indicating a higher concentration of flow in Lviv. The median flow per node is also higher in Lviv (708 vs. 451), as is the mean (2332.2 vs. 1676.1), consistent with the observed concentration profile. Based on the Gini coefficient of flow distribution among nodes, both networks are highly concentrated (Kyiv: 0.750; Lviv: 0.737) [
21].
In terms of network structure, pharmacies (where division_type is “Pharmacy”) dominate, accounting for the majority of redemption volumes, while pharmacy points represent a smaller share. For spatial analysis, it is important to note that the registry [
22] does not contain coordinates for all nodes present in the time series [
21] (likely due to contract changes or closures). In Kyiv, coordinates are available for 79.0% of nodes, covering 94.9% of demand; in Lviv, coordinates are available for 89.2% of nodes, covering 94.5% of demand [
21,
22].
As shown in
Table 2, although the Kyiv network has more nodes, Lviv exhibits a higher concentration of demand across fewer dispensing points. This indicates that in Lviv, the failure of a small group of core network nodes could result in disproportionately large coverage losses, even without any change in total demand.
Table 2 summarizes the baseline network size, demand concentration, and geocoding coverage for Kyiv and Lviv.
Table 3 reports the demand composition by program groups for the two metropolitan areas.
The demand structure by program groups is similar across both metropolitan areas and is primarily driven by chronic nosology. This reinforces the argument for prioritizing continuity of access as a key metric of resilience. At the same time, differences in the proportions of specific groups signal varying levels of sensitivity in each city to shortages of categories of medicinal products.
Figure 2 presents monthly redeemed e-prescription dynamics in Kyiv and Lviv for 2022–2025.
Redemption dynamics show an upward trend between 2022 and 2025 in both cities, with distinct seasonal fluctuations. This observation is critical for subsequent scenario analysis: a fixed percentage shortage applied across different months can yield significantly different absolute impacts on unmet demand.
Figure 3 and
Figure 4 identify potential demand concentration hubs as the top-performing nodes by dispensing volume. For subsequent failure scenarios, these nodes represent natural points of risk; conversely, for response policies, they serve as natural points of intervention (flow redirection, inventory reinforcement, and prioritized service restoration).
To evaluate spatial accessibility within a coordinate-based proxy metric, the geodesic distance to the nearest node was calculated for a regular grid of points within the urban coordinate coverage. Based on this proxy, the mean distance to the nearest node is 2.265 km in Kyiv and 0.994 km in Lviv; the 95th percentile is 6.625 km and 2.804 km, respectively. The difference between the cities is primarily evident in the tails of the distribution: for Kyiv, the 95th percentile distance is 2.36 times higher than for Lviv (6.625 km vs. 2.804 km). This indicates significantly greater peripheral fragmentation of the baseline spatial coverage, which is vital for interpreting DSS effects: even with similar flow concentration among nodes (flow Gini of 0.750 and 0.737), the spatial accessibility profiles may respond differently. This metric is considered an indicative measure of accessibility. It should be interpreted as a proximity-based open-data proxy rather than as a full FCA/2SFCA accessibility score. FCA/2SFCA studies are used here as a reference point for future extensions based on network travel-time catchments and explicit demand–supply ratios [
31,
32,
33].
Table 4 reports the resulting coordinate-based proxy accessibility indicators.
The proxy assessment of accessibility (geodesic distance to the nearest node) does not replace network travel-time analysis; however, it allows for a baseline comparison of coverage geometry and the localization of potential service coverage gaps. For Lviv, given the concentration of demand in a small number of nodes, the failure or restoration of the network core has a disproportionate impact on the spatial distribution of coverage, even despite the relatively dense node geometry.
Figure 5 and
Figure 6 visualize the 6 × 6 nearest-node distance grids for Kyiv and Lviv.
The Kyiv grid shows a strongly uneven proximity profile. The lowest nearest-node distances are concentrated in the inner and central-eastern part of the coordinate grid, where values fall below 1 km in several cells. This indicates a dense dispensing-node geometry and a lower baseline risk of spatial access gaps. By contrast, the western, south-western and north-eastern edge cells show substantially higher nearest-node distances, including values above 5 km and one extreme value above 10 km. These cells should not be interpreted as specific administrative districts, because the grid is coordinate-based; however, they indicate peripheral sectors where the dispensing-node network is spatially thinner and where node failures or supply shocks may translate into larger service-coverage gaps. For Kyiv, the heatmap therefore explains why the DSS effect is not only a function of demand concentration but also of peripheral coverage geometry.
The Lviv grid shows a more compact proximity structure. Most cells are located within approximately 0–2 km of the nearest dispensing node, and the minimum values are concentrated around the central part of the coordinate grid. Higher values appear mainly at the western, north-western and south-eastern edges, but their absolute level remains lower than the most peripheral Kyiv cells. This means that Lviv’s baseline spatial geometry is comparatively denser, while its vulnerability arises primarily from demand concentration in a smaller number of high-load nodes rather than from long nearest-node distances. The heatmap therefore complements the node-concentration results: Lviv is less fragmented spatially, but more sensitive to the failure of core dispensing points.
3.2. Disruption Impact Without Optimization (Status Quo Policy)
The impact of disruptions without optimization is presented as the status quo policy, which performs no adaptive redistribution between nodes and introduces no additional hubs. In this formulation, capacity losses or supply deficits are translated into unmet demand in proportion to the scale of the shock, establishing a baseline benchmark for comparison with the DSS policy discussed in
Section 3.3. The node-failure component is calculated from redeemed e-prescription volumes [
21], while the broader scenario logic is consistent with disrupted-supply and resilient-inventory studies [
34,
35,
36].
A structural test was employed to assess node failures: the removal of the top-k nodes ranked by redemption volume (2022–2025). In this case, unmet demand equals the share of demand associated with the failed nodes. The results reveal a significant disparity between the metropolitan areas: the loss of the top 10 nodes corresponds to a 14.2% increase in demand at risk in Kyiv and a 29.7% increase in demand at risk in Lviv. In comparison, the top 20 nodes correspond to 21.7% and 42.1%, respectively. This aligns with the higher flow concentration in Lviv and signifies greater sensitivity to local failures of high-load nodes [
21].
For a supply shock in the status quo regime, a proportional limitation of the available volume is assumed: under a 20% supply deficit, unmet demand is 20% in each city. In the combined scenario (20% deficit + loss of the top 10 nodes), unmet demand increases to 31.4% in Kyiv and 43.7% in Lviv, highlighting the asymmetry in risk across the same class of disruptions [
21,
34,
35].
The coordinate proxy metric (geodesic distance to the nearest node) indicates that removing the top 10 demand-concentration nodes (hub nodes) barely alters the coverage geometry for Kyiv and has a limited effect on Lviv. This reflects the distinction between nodes with high flow and those that define the network’s spatial density. Given that the metric does not account for the road network or traffic regimes, this conclusion should be treated as indicative [
31,
32,
33].
Table 5 demonstrates that vulnerability in node-failure scenarios is determined not by the absolute number of nodes, but rather by the concentration of demand within the network core. This structural parameter explains why the Hub10/Hub20 scenarios are significantly more severe for Lviv than for Kyiv.
Figure 7 summarizes unmet demand and coverage under the status quo disruption scenarios.
In the status quo regime, a supply deficit results in a proportional decline in coverage. Conversely, node failure creates a disproportionate effect in cities with high concentrations. This motivates DSS policies: even without increasing total resources, it is possible to reduce losses in the lower tail of the coverage distribution through controlled redistribution.
Figure 8 shows the proxy spatial effect of top-10 hub removal on nearest-node distance.
Proxy spatial diagnostics following the removal of top hubs demonstrate that coverage geometry shifts unevenly: while some zones remain proximal to alternative nodes, they become potential service coverage gaps. The equity parameter within the DSS policy subsequently manages this nonuniformity.
3.3. Decision-Support Outcomes (Accessibility-First DSS with Equity Constraints)
The effects of the DSS policy were evaluated within a zonal, accessibility-first framework, and a regular 6 × 6 grid within each city’s dispensing nodes’ coverage area served as the spatial unit of analysis. Demand within each zone was defined as the aggregate of redeemed e-prescriptions from nodes located within that zone [
21]. At the same time, the network geometry was derived from node coordinates in the NHSU registry [
22]. The DSS policy applies to the redistribution rules defined in
Section 2.5: resources are iteratively reallocated from donor zones to deficit zones to raise the lower tail of coverage and reduce the number of areas falling below the service threshold (deserts), while adhering to the equity floor and the ε-budget for transport intensity.
Two policy regimes were compared: the status quo (absence of adaptive redistribution between zones) and DSS (redistribution constrained by the requirement that donor zones not fall below a specified minimum coverage level). The scenarios correspond to
Section 2.4: Def20 (a proportional 20% deficit in available volume); Hub10/Hub20 (failure of the top 10/20 nodes by redemption volume); and combined scenarios (Def20 + Hub). The scenario metrics are calculated consistently across all scenarios. Unmet demand is the share of the demand proxy not covered by the available volume. Coverage is the ratio between available volume and demand within a zone. p10 coverage captures the lower tail of the zonal coverage distribution. The Gini coefficient measures inequality in coverage across grid cells. Entropy describes the evenness of spatial coverage distribution. Desert cells are grid cells whose coverage falls below the equity floor τ. Redistribution intensity is reported as a normalized distance-budget proxy and is not interpreted as a direct estimate of CO
2e emissions.
Table 6 compares the status quo and DSS outcomes under the disruption scenarios.
The results in
Table 6 demonstrate that under a uniform deficit (Def20), the DSS does not change the 10th percentile (p10) of coverage (0.800 → 0.800) or the number of risk zones (3 → 3), which is consistent with a fixed total resource pool. Conversely, in structural node-failure scenarios, the DSS significantly improves the lower tail of the distribution: in Kyiv, under Hub20, the p10 coverage increases from 0.487 to 0.750, coverage inequality (Gini) drops from 0.142 to 0.012, and the number of deserts is reduced from 9 to 3. For Lviv, under Hub10, the p10 increases from 0.450 to 0.579, and the number of deserts decreases from 8 to 6. Notably, the total share of unmet demand does not change significantly, as the redistribution policy affects the geography of the deficit rather than the total resource volume. Entropy also increases under the DSS policy in several structural failure scenarios, indicating a more even distribution of coverage across zones. This result should be read as a concentration diagnostic that complements the Gini, p10 coverage, and desert-cell indicators. It does not by itself validate systemic resilience, but it helps identify whether redistribution reduces dependence on a small number of high-demand zones.
These results should be interpreted as spatial redistribution effects rather than as supply-generation effects. The DSS does not increase the total available volume of medicines. Its contribution is to reallocate the shortage burden across zones, improve lower-tail coverage, and reduce the number of cells below the equity threshold where feasible. Therefore, a scenario may show unchanged total unmet demand while still improving the spatial distribution of service coverage.
Table 7 reports an iteration-level zonal redistribution trace for the Kyiv Hub20 scenario. The trace is reconstructed at the same spatial level as the DSS itself: transfers are reported between 6 × 6 grid zones rather than between individual pharmacies. Each iteration reports the donor zone, shortage zone, transferred redeemed-prescription-equivalent volume, centroid distance, cumulative Redistribution Distance Index (RDI), and post-transfer coverage of the shortage zone. The example is not a vehicle-routing plan; it is a calculation trace of the zonal redistribution heuristic used to obtain the DSS scenario indicators.
The coverage distributions for the Hub20 scenario are presented in
Figure 9.
The distance-budget values should be interpreted as a secondary constraint on the intensity of redistribution rather than as a separate efficiency ranking of the two cities. They show that similar DSS rules may require different redistribution burdens depending on the spatial configuration of demand and available nodes.