Risk-Informed Data Analytics for Sustainable Pharmaceutical Supply: A Governance Framework for Public Oncology Hospitals

Abstract

Ensuring uninterrupted access to essential medicines in public healthcare systems is a persistent challenge with clinical, economic, and environmental implications. Oncology services are particularly vulnerable to stockouts, which compromise therapeutic continuity and increase reliance on urgent procurement with high carbon and waste footprints. This study proposes a risk-informed, data-driven framework for pharmaceutical inventory governance in a high-complexity public oncology hospital in Chile, aligning with sustainability goals and green supply chain principles. Using operational data from 2023–2024, we integrate descriptive analytics, ABC–XYZ segmentation, and a continuous-review (s, Q) policy extended through a Logistic Risk Index (LRI) that consolidates demand variability, supply performance, and clinical-economic criticality. Empirical analysis reveals strong expenditure concentration in AX/AY segments and significant misalignment between institutional and analytically derived parameters. A Monte Carlo simulation N = 1000 runs per scenario) compares baseline, adjusted, and fully risk-informed policies under stochastic demand and lead-time conditions. Results show that the risk-informed configuration reduces stockout exposure by up to 46%, improves fill rates (93.1% → 96.4%), and shortens replenishment delays, while maintaining total logistic cost stability. Critically, urgent orders decrease from 27.4 to 14.8 per year, avoiding an estimated 630 kg CO₂ emissions and 25 kg of packaging waste annually. These findings demonstrate that resilience, efficiency, and sustainability are not competing objectives but can be jointly achieved through integrated analytics and governance. The proposed approach offers a scalable blueprint for public health systems seeking to transition from reactive inventory management toward anticipatory, transparent, and sustainability-oriented decision-making, contributing to SDG 3 (health and well-being) and SDG 12 (responsible consumption and production).

1. Introduction

Ensuring the uninterrupted availability of essential medicines is a persistent challenge in public healthcare systems, especially in oncology services, where stockouts have direct clinical, ethical, economic, and, increasingly, environmental consequences [1,2]. Emergency replenishment often involves expedited logistics and additional packaging, which amplify the carbon footprint and pharmaceutical waste associated with reactive supply practices [3]. Thus, inventory resilience is not only a matter of service continuity but also of sustainability in resource-constrained health systems [4].

Public hospitals operate under structural constraints—limited budgets, rigid public procurement, fragmented information systems, and heterogeneous demand—that elevate vulnerability and complicate resilient and environmentally responsible inventory management [1,5]. These constraints hinder the adoption of proactive strategies that could simultaneously improve therapeutic continuity and reduce environmental externalities, aligning with global sustainability goals such as SDG 3 and SDG 12 [6].

Recent advances in stochastic inventory management have emphasized the importance of explicitly modelling demand uncertainty, lead-time variability, and service-level trade-offs in healthcare supply chains. This body of work highlights the limitations of static policies and supports the adoption of adaptive, data-driven forecasting and inventory models [7].

In parallel, risk-aware supply chain research has incorporated multi-dimensional risk factors—such as demand variability, supply uncertainty, and large-scale disruption effects—into analytical decision-making frameworks. These approaches increasingly rely on probabilistic modelling and structured risk-assessment methodologies to prioritize critical items and enhance supply chain viability [8,9].

Furthermore, the growing literature on data-driven decision support systems in hospital operations has demonstrated the value of integrating operational data, analytical modelling, and simulation-based approaches to support real-time decision-making and improve resource allocation. Recent systematic reviews highlight how data exploitation and AI-enabled clinical decision support systems can enhance the quality, robustness, and responsiveness of healthcare operations [10,11].

Over the last decades, scholarship in healthcare supply chains has advanced inventory optimization, demand forecasting, and efficiency-oriented policies [12,13]. Yet, much of this evidence remains disconnected from public-sector institutional realities and regulatory constraints, particularly in Latin American contexts, and rarely addresses the environmental dimension of supply chain decisions [14]. This gap is consistent with prior work in Chilean hospital contexts, which shows the benefits and constraints of lot-sizing under stochastic demand [15]. Three gaps motivate this study.

First, there is a lack of end-to-end analytical approaches that explicitly integrate public procurement, inventory control, continuity of clinical care, and sustainability into a single operational governance framework. Studies typically treat inventory in isolation and overlook how procurement constraints, supplier performance, clinical risk, and environmental impact interact systemically [1,3,5]. We address this by proposing an integrated, governance-oriented framework that links purchasing mechanisms, inventory behaviour, therapeutic continuity, and environmental performance via unified metrics, dashboards, and scenario-based evaluation.

Second, empirical evidence from public hospitals with real operational data—particularly in oncology and Latin America—remains limited. Prior work often uses simulated or private-sector datasets, hindering external validity for public systems with budget rigidities, regulatory requirements, and demand variability. Moreover, the environmental implications of reactive inventory policies, such as increased transport emissions and waste from emergency orders, are seldom quantified [2,14]. We contribute evidence from a high-complexity public oncology hospital in Chile (2023–2024), identifying operational stockout drivers (e.g., delayed tenders, supplier non-compliance, emergency purchases) and classifying them by institutional origin [16,17].

Third, there is a persistent gap between descriptive analytics and actionable decision support. While ABC–XYZ classification is widely used to characterise consumption value and demand variability, it is seldom translated into dynamic operational rules [18,19]. In practice, this yields static parameterisation, uniform service levels, and limited responsiveness to shifting risk—including environmental risk from inefficient replenishment. We close this gap by operationalising risk-informed policies that transform descriptive analysis into action: adaptive reorder points, safety stock adjustments, and alert thresholds tied to explicit service-level, economic, and sustainability implications.

Building on these gaps, we propose a data-driven, risk-informed framework for pharmaceutical inventory management in a public oncology hospital. Methodologically, we integrate descriptive analytics and ABC–XYZ classification with a continuous-review policy (s, Q) extended through a dynamic risk-based approach [20,21]. We construct a Logistic Risk Index (LRI) that combines demand variability, supply performance, and clinical criticality proxies, so that inventory parameters adjust to systemic risk for each medicine rather than uniform service levels. Scenario-based analyses compare the baseline configuration versus the risk-informed policy, assessing impacts on stockout exposure, replenishment timeliness, operational efficiency, and estimated environmental benefits [5,11]. In parallel, we operationalise governance and decision support via actionable indicators, thresholds, and monitoring tools that strengthen coordination across clinical, logistical, and administrative teams [22,23].

In sum, the framework enables public health institutions to transition from reactive inventory management toward risk-aware, evidence-based governance, providing a transferable blueprint that supports service continuity, operational resilience, and sustainable resource allocation [1,4,5].

From a methodological perspective, the primary contribution of this study is not the introduction of new individual analytical techniques but the integration of established inventory management methods into a unified, risk-informed governance framework. This integration enables a direct operational linkage between descriptive analytics (ABC–XYZ), multi-dimensional risk assessment (LRI), and inventory policy parameterization ((s, Q)), which is rarely addressed in a coherent and empirically grounded manner in the healthcare supply chain literature. In this context, the Logistic Risk Index (LRI) represents the central innovative component of the framework. Unlike traditional multi-criteria risk scoring approaches, which often rely on extensive expert elicitation or complex weighting schemes, the LRI is designed as a data-driven, interpretable, and operationally implementable composite indicator. It translates multiple sources of logistical and clinical risk into actionable inventory decisions, thereby bridging the gap between analytical modelling and institutional governance in public healthcare systems.

1.1. System Boundaries and Governance Architecture

Consistent with core systems and socio-technical perspectives [24,25,26,27,28,29], we conceptualize pharmaceutical inventory management as an integrated ocio-technical system where analytical policies, institutional constraints, and governance routines interact within explicit operational boundaries.

1.1.1. System Boundary

The boundary of analysis includes: (i) Oncology Pharmacy (FO) and Central Pharmacy (FC) as operational nodes; (ii) procurement channels—CENABAST, public tender, and direct/urgent purchasing—with their lead-time distributions and service constraints; (iii) supplier performance under public procurement regulation; (iv) clinical demand patterns shaped by oncology protocols; and (v) environmental externalities associated with transport and packaging of replenishment orders. Following the systems canon, we emphasise feedback, stocks/flows, and decision rules as structural determinants of behaviour [25,26].

1.1.2. Information and Decision Flows

Information circulates bidirectionally among clinical services (treatment schedules), pharmacy operations (consumption, stock levels, reorder triggers), procurement (POs, supplier compliance), and administration (budget governance). Feedback loops are central: stockouts can trigger urgent purchasing, increasing carbon emissions and packaging waste and raising administrative burden, which tightens budget constraints and reinforces the need for proactive, risk-informed planning; conversely, improved visibility (ETL, dashboards) and differentiated service targets reduce stockout exposure and urgent orders, stabilising total logistics costs. This joint optimisation of the social and technical subsystems reflects sociotechnical design principles [27] and viable governance structures [28].

1.1.3. Governance and Analytics Layer

ABC–XYZ segmentation, the Logistic Risk Index (LRI), and continuous-review (s, Q) policies operate as decision rules within the governance layer: segmentation and LRI modulate service levels and alert thresholds; (s, Q) translates those targets into operational parameters per item and channel; and the dashboard provides continuous monitoring and auditability. This framing positions inventory decisions not as isolated calculations but as governance processes embedded in a system of interdependent clinical, logistical, administrative, and environmental objectives—coherent with systems thinking foundations and system safety/governance ideas in complex sociotechnical settings [24,29].

In this paper, the aim is to develop and empirically validate a data-driven, risk-informed governance framework for pharmaceutical inventory management in a public oncology hospital, explicitly linking inventory analytics, stochastic risk, and sustainability outcomes to the continuity of therapeutic service. The proposed approach integrates descriptive analytics, ABC–XYZ segmentation, a Logistic Risk Index (LRI), and a continuous-review inventory policy within a transparent decision-support and governance structure grounded in real operational data.

The remainder of the paper is organised as follows. Section 2 presents the Materials and Methods, distinguishing between the empirical study design and data architecture (Section 2.1) and the simulation-based evaluation framework (Section 2.3). The empirical subsection details the institutional context, data sources, variable construction, ABC–XYZ segmentation, and the formulation of the Logistic Risk Index, while the simulation subsection describes the Monte Carlo design used to assess alternative inventory policies under stochastic demand and lead-time conditions.

Section 3 reports the Results, structured analogously into empirical findings (Section 3.1) and simulation outcomes (Section 3.2). The empirical results characterise portfolio asymmetries, procurement risk, and inventory parameter misalignment, whereas the simulation results quantify the effects of risk-informed policies on stockout exposure, service continuity, logistical costs, and environmental indicators.

Section 4 discusses the findings in relation to the existing literature, emphasising governance implications, economic trade-offs, and sustainability considerations. Finally, Section 5 summarises the main contributions of the study and outlines directions for future research.

2. Materials and Methods

2.1. Context of the Empirical Study and General Design

This study is conducted in the pharmacy services of a high-complexity public oncology hospital in Chile (INCANCER), focusing on two operational sub-units: Oncology Pharmacy (FO) and Central Pharmacy (FC). We analyse operational data from 2023–2024 (plus reference snapshots in 2025), design a governance-oriented, risk-informed inventory framework, and evaluate an integrated approach combining ABC–XYZ segmentation, a continuous review policy (s, Q), a Logistic Risk Index (LRI), and a data-informed dashboard. In addition to operational efficiency and service continuity, the study incorporates an environmental perspective by estimating potential reductions in carbon emissions and pharmaceutical waste resulting from fewer emergency orders and improved inventory planning. This aligns the framework with sustainability goals and green supply chain principles [2,3,4]. The framework is implemented and assessed on a prioritised set of oncology medicines with high clinical and green logistical impact.

Data Sources and Scope. We use institutional operational records from (i) BODEFAR (inventory and dispensing), (ii) CODEBAR (purchase orders and receptions), and (iii) CENABAST reports (centralized intermediary compliance). Additional inputs include the validated therapeutic formulary, purchase ledgers, violation/complaint logs, wastage/expiry registers, and indirect cost ledgers. We restrict the analysis to medicines in the current formulary (2025) that have valid consumption and lead-time histories during 2023–2024; centralised items with no local management and occasional/non-formulary items are excluded. Environmental estimation relies on operational logs of urgent purchases and wastage registers. Urgent orders are used as a proxy for high-emission transport events, while wastage records inform potential reductions in pharmaceutical waste under risk-informed policies. These variables complement the core dataset to enable a combined socio-economic and environmental assessment.

2.1.1. Variables and Derived Fields

From these sources we construct a harmonized analysis table per medicine: storage location (FO/FC), price (PPP), monthly consumption (2023–2024), lead-time L by purchase modality (CENABAST, public tender, direct/urgent purchase), institutional stock parameters (min, max, reorder point), events (expiry, shortages, complaints), and indirect storage costs. We compute daily demand D, demand variability (σ_d, CV), adjusted safety stock SS, adjusted reorder point s, and economic order quantity Q (where applicable).

Data Quality, ETL, and Governance. A reproducible ETL (extract-transform-load) pipeline consolidates BODEFAR, CODEBAR, and CENABAST data, resolves item codes, removes duplicates/returns, and standardises units across FO and FC. We version the dataset (by date and source) and apply validation rules: minimum 6 valid months, CV cutoffs, and consistency checks against formulary and location. For governance, the pipeline is aligned with best-practice guidance on storage/distribution quality (WHO TRS 1025, Annex 7) and digital supply visibility (LMIS) to support evidence-based decisions and auditability. The ETL pipeline not only harmonises inventory and procurement data but also tags transactions by urgency level and packaging type, enabling traceability for environmental metrics. This design supports the computation of CO₂-equivalent emissions and waste-reduction indicators for the governance dashboard.

Segmentation: ABC–XYZ. We perform combined ABC–XYZ classification per sub-unit and over the aggregated portfolio. ABC classes are derived from cumulative annual expenditure shares (A: ∼70–80%, B: 15–25%, C: 5–10%); XYZ classes from monthly consumption CV thresholds (X: CV < 25 %, Y: 25–50%, Z: >50%). Crossing ABC with XYZ yields nine segments that guide differentiated service levels and replenishment focus (e.g., AX, AY, BX as priority; AZ/BZ/CZ as risk). The use of ABC–XYZ with forecast integration and decision support is well documented and provides a practical bridge from descriptive analytics to policy rules.

Logistic Risk Index (LRI). To translate descriptive analytics into actionable governance, we compute a ogistic Risk Index (LRI) per medicine, synthesising demand variability, supply performance, parameter misalignment, clinical importance, and critical events. The LRI is designed as a normalised weighted sum consistent with the criticality matrix used in:

$${\mathrm{LRI}}_i=w_1·f(∆{\mathrm{PR}}_i)+w_2·g({\mathrm{CV}}_i)+w_3·h({\mathrm{LTVar}}_i)+w_4·e({\mathrm{Events}}_i)+w_5·c({\mathrm{ABC}–\mathrm{XYZ}}_i),$$

where f, g, h, e, c map each criterion into [0, 1] (min-max scaling by portfolio percentiles). Recommended weights (aligned with the TFG’s matrix): w₁ = 0.25 (parameter misalignment), w₂ = 0.20 (demand variability), w₃ = 0.05 (lead-time variability), w₄ = 0.25 (critical events), w₅ = 0.25 (clinical/economic importance from ABC–XYZ). We classify LRI into three risk tiers—High (≥0.70), Medium (0.40–0.69), and Low (<0.40)—and use the tiers to drive service-level, alerting, and replenishment rules.

It is important to note that the Logistic Risk Index (LRI) is not intended as a universally optimal or theoretically exhaustive risk metric, but rather as a governance-oriented composite indicator designed for interpretability, transparency, and operational use in public hospital settings. The selected dimensions and weights reflect institutional priorities identified through the empirical context of the study, including parameter misalignment, operational disruptions, demand uncertainty, and clinical-economic criticality. Rather than optimising weights through purely statistical procedures, the LRI is constructed to support actionable decision-making, cross-functional communication, and auditability within constrained public-sector environments. The robustness of this design choice is subsequently assessed through simulation-based evaluation, where alternative inventory policies derived from the LRI are compared under stochastic demand and lead-time conditions.

2.1.2. Handling of Intermittent (Z-Class) Demand

Items classified as Z in the XYZ segmentation display intermittent or lumpy demand that does not satisfy continuous or approximately normal assumptions. To avoid distortions, Z-items were handled using conservative percentile-based consumption proxies (median–P80 range) rather than parametric variability estimates. In addition, the contribution of demand variability to the LRI was bounded for Z-items to prevent noise-driven inflation. This ensures that prioritisation and subsequent (s, SS, Q) adjustments are not driven by sparse observations and remain anchored to stable operational signals.

Continuous Review Policy (s, Q). We adopt a continuous-review (s, Q) policy. When inventory position falls to or below s, a replenishment order of fixed size Q is placed. Under stochastic demand and lead-times, we set service-level targets and compute safety stock and reorder points as follows:

$$\begin{array}{cc}\hfill D& =\mathrm{mean}\mathrm{daily}\mathrm{demand},\hfill \\ \hfill L& =\mathrm{mean}\mathrm{lead}\mathrm{time}(\mathrm{days}),\mathrm{by}\mathrm{purchase}\mathrm{channel},\hfill \\ \hfill SS& =Z·{\sigma }_d·\sqrt{L}(\mathrm{for}\mathrm{normal}\mathrm{approximation}),\hfill \\ \hfill s& =D·L+SS,\hfill \\ \hfill Q& =\sqrt{{\displaystyle \frac{2K{D}_a}{h}}},\hfill \end{array}$$

where Z is the standard normal quantile for the target service level (we use Z = 1.65 for 95%), σ_d is the daily demand standard deviation, D_a is annual demand, K is the fixed cost per order (administrative), and h is the annual holding cost per unit (derived from indirect storage costs). This (Q, R)/(s, Q) modelling approach is canonical in inventory theory and is widely applied in healthcare supply chains. In hospital pharmacy settings, (s, Q) decisions under non-normal demand with skewness/kurtosis and pandemic-related disruptions have been validated in practice [30].

Environmental impact estimation. Environmental impact estimation follows a simplified approach based on urgent order reduction:

$${\mathrm{CO}}_2\mathrm{avoided}(\mathrm{kg})=∆U\times E{F}_{transport}$$

$$\mathrm{Waste}\mathrm{avoided}(\mathrm{kg})=∆U\times W_{packaging}$$

where ∆U is the difference in annual urgent orders between scenarios, EF_transport is the emission factor per urgent shipment (assumed 50 kg CO₂/order for expedited courier), and W_packaging is the average packaging waste per order (assumed 2 kg/order) [2,3]. Sensitivity analyses are performed on these factors to account for variability in transport modes and packaging standards. The emission factor (EFtransport) and packaging coefficient (Wpackaging) are defined as representative operational approximations rather than precise life-cycle parameters. The value of 50 kg CO₂ per urgent order reflects typical emissions associated with expedited courier or small-batch pharmaceutical transport, including last-mile delivery and low load consolidation efficiency, as commonly observed in healthcare logistics.

Similarly, the packaging coefficient of 2 kg per order represents an average estimate of combined primary and secondary packaging materials (e.g., insulated containers, protective materials, and single-use transport packaging) associated with urgent procurement processes.

These parameters may vary depending on supplier characteristics, transport mode (e.g., air vs. ground), delivery distance, and packaging standards. Therefore, they should be interpreted as context-dependent proxies intended to capture relative differences between inventory policies rather than absolute environmental footprints.

2.1.3. Policy Mapping by Segment and LRI

We map ABC–XYZ segments and LRI tiers to differentiated parameters: (i) AX/AY/BX (High/Medium LRI): higher Z (e.g., 95–97.5%), earlier s, and continuous alerting; (ii) AZ/BZ/CZ (High LRI): conservative buffers, shorter review cycles, scenario stress-tests; (iii) CX/CY (Low/Medium LRI): routine control with bounded maximums to avoid overstock. This aligns with risk-aware decision-making principles in supply-chain risk management.

Selection of medicines for policy evaluation. Using FO/FC portfolios and the TFG’s criticality filters, we prioritise FO medicines with LRI High (or LRI Medium plus parameter misalignment ∆PR ≥ 40%). The evaluation set comprises 28 FO medicines with significant clinical and financial impact and representative variability/lead-time profiles. The (s, Q) parameters for these medicines are computed using 2023–2024 data, Z = 1.65, channel-specific L, administrative cost per order, and a per-unit annual holding cost derived from indirect storage expenditures.

Computational implementation and replicability of the empirical analysis. To ensure full replicability of the empirical results, the analytical workflow was formalised as a computational pipeline integrating data extraction, transformation, risk classification, inventory parameter estimation, and sustainability metrics. The complete sequence of operations—from raw institutional data to risk-informed inventory parameters and environmental impact estimation—is summarised in Algorithm 1.

Algorithm 1 Replicable empirical analytics pipeline for risk-informed inventory governance with sustainability metrics

Require:  Raw institutional sources: BODEFAR (inventory/dispensing), CODEBAR (POs/receptions), CENABAST reports, validated formulary; auxiliary logs (expiry/wastage, complaints, indirect cost ledgers). Ensure:  Harmonized item-level dataset; ABC–XYZ segment; LRI tier; risk-informed (s, Q) parameters; prioritized evaluation set; environmental indicators. 1: Extract. Import all raw tables for period 2023–2024 (and reference snapshots if needed). 2: Transform (ETL). Resolve item codes across systems; remove duplicates/returns; standardize units across FO/FC; enforce formulary filter; exclude non-managed centralized or occasional items. 3: Validate. Keep items with ≥ 6 valid months of observations; check consistency of location (FO/FC) and unit prices; apply CV plausibility cutoffs. 4: Construct derived fields (per item i).    Compute monthly demand series {di,m} and annual demand Da,i.    Compute daily demand mean Di and standard deviation σd,i.    Compute demand variability CVi = σ(di,m)/μ(di,m).    Compute lead-time statistics by channel Li,c and lead-time variability proxy LTVari.    Retrieve institutional parameters (min, max, reorder point) and event counts Eventsi (expiry, shortages, complaints). 5: ABC–XYZ segmentation.    ABC: rank by annual expenditure; assign A/B/C by cumulative shares (A ≈ 70–80%, B 15–25%, C 5–10%).    XYZ: assign by CV thresholds (X: CV < 0.25, Y: 0.25 ≤ CV ≤ 0.50, Z: CV > 0.50).    Segmenti ← cross of ABC and XYZ. 6: Compute parameter misalignment.    ∆PRi ← normalized gap between institutional reorder point and analytically implied reorder point. 7: Logistic Risk Index (LRI).    Map each criterion into [0, 1] using percentile-based min–max scaling.    LRIi ← 0.25f(∆PRi) + 0.20g(CVi) + 0.05h(LTVari) + 0.25e(Eventsi) + 0.25c(ABC–XYZi).    Assign tier: High (≥0.70), Medium (0.40–0.69), Low (<0.40). 8: Risk-informed inventory parameters (continuous review).    Select service level via Z by segment/tier.    $S{S}_i\leftarrow Z·{\sigma }_{d,i}\sqrt{L_i}$,    si ← DiLi + SSi.    $Q_i\leftarrow \sqrt{{\displaystyle \frac{2K{D}_{a,i}}{h_i}}}$. 9: Prioritize for evaluation.    Select items with High LRI or (Medium LRI and ∆PRi ≥ 40%). 10: Estimate environmental impact.    Compute ∆U = reduction in urgent orders vs baseline.    CO2 avoided = ∆U × EFtransport (assume 50 kg/order).    Waste avoided = ∆U × Wpackaging (assume 2 kg/order). 11: return Harmonized dataset + Segmenti + LRIi + tier + (si, Qi, SSi) + evaluation set + environmental indicators.

The algorithm begins with the extraction and harmonisation of heterogeneous administrative sources, including inventory records, procurement transactions, consumption logs, and auxiliary operational datasets. After standardisation and validation, item-level demand, variability, lead-time statistics, and institutional inventory parameters are derived in a consistent manner. This process enables the systematic application of ABC–XYZ segmentation and the computation of the Logistic Risk Index (LRI), which consolidates multiple dimensions of logistical and clinical risk into a single actionable metric.

Finally, Algorithm 1 formalises the derivation of continuous-review inventory parameters (s, Q) and safety stock levels based on risk tier and segment-specific service levels, and appends an environmental estimation step based on urgent order reduction. By explicitly encoding each transformation and decision rule, the algorithm provides a transparent and reproducible blueprint for implementing the proposed framework in other hospital settings or software environments.

• Reproducibility materials.

A minimal, executable pipeline capable of regenerating all preprocessing steps is provided in the Zenodo repository (DOI: https://doi.org/10.5281/zenodo.18851842). The deposit includes raw datasets, the Python script, a dependencies file, and usage instructions for end-to-end replication. All data preprocessing and table generation were performed in Python 3.11 (Python Software Foundation, Wilmington, DE, USA), using the open-source libraries pandas (≥1.5), numpy (≥1.23), and openpyxl (≥3.1). Analysis was executed in a Linux environment. See [31].

Ethics and Data Protection. Only operational, non-patient-sensitive data are used; records are institutional, governed by public-sector regulations, and were approved internally as an operational research project. No clinical interventions are performed; all analyses focus on the efficiency and resilience of the supply system.

2.2. Logistic Risk Index: Weighting, Validation, and Robustness Assessment

2.2.1. Weighting Rationale

The Logistic Risk Index (LRI) synthesizes five dimensions central to operational risk in oncology pharmaceutical supply: (i) parameter misalignment (∆PR) between institutional and analytically implied reorder points; (ii) demand variability (CV); (iii) lead-time variability by purchasing channel; (iv) critical operational events (e.g., expiries, shortages, formal complaints/incidents); and (v) clinical–economic importance derived from ABC–XYZ. We adopted governance-oriented weights to keep the composite interpretable and actionable in a public-hospital context. Specifically, w = {0.25, 0.20, 0.05, 0.25, 0.25} for ∆PR, CV, LTVar, Events, ABC–XYZ}, respectively. Each component is mapped to [0, 1] using portfolio-level percentile min–max scaling to preserve comparability and resist extreme outliers.

From a methodological perspective, the construction of composite risk indicators such as the LRI is connected to the broader family of multi-criteria decision-making (MCDM) approaches commonly applied in supply chain risk assessment. Methods such as the Analytic Hierarchy Process (AHP) [32], entropy-based weighting, or hybrid objective weighting techniques [33] have been widely employed to derive weights from structured expert judgment or data-driven criteria prioritisation. However, these approaches typically require extensive pairwise comparisons, consistency validation, or iterative expert elicitation processes, which may be difficult to implement in resource-constrained public hospital environments. In contrast, the LRI adopts a governance-oriented weighting scheme that emphasises interpretability, operational transparency, and ease of implementation. Rather than aiming to identify an optimal or universally valid set of weights, the proposed structure reflects empirically grounded institutional priorities designed to support actionable decision-making, cross-functional communication, and auditability. In this sense, the LRI can be interpreted as a pragmatic adaptation of MCDM principles into a data-driven governance tool tailored to the realities of public healthcare supply systems.

2.2.2. Internal Validation

We conducted three internal checks of construct validity and operational coherence: (i) Concordance with descriptive classes: we examined whether higher LRI tiers co-occur with risk-prone XYZ classes (Y/Z) and high expenditure tiers (A/B); (ii) Predictive face validity: for a prioritised subset, we assessed the relationship between LRI at t and baseline exposure to stockouts and urgent orders at t + 1 using nonparametric rank correlations and median contrasts by LRI terciles; (iii) Policy coherence: we verified that items flagged as High LRI (or Medium LRI with elevated ∆PR) are precisely those for which recalculated (s, Q) entails the largest adjustments in s and SS.

2.2.3. Sensitivity Analysis (Weights)

To address potential subjectivity in the weighting scheme, we conduct a comprehensive sensitivity and robustness analysis of the Logistic Risk Index (LRI) to evaluate the stability of risk classification and inventory decisions across alternative weighting configurations. To assess robustness to subjective weighting, we implemented both one-at-a-time and global sensitivity: (i) OAT: vary each weight by ±20% while keeping ∑w = 1 (remaining weights rescaled proportionally), then recompute LRI, tiering, and the % of items changing tier; (ii) Global: sample 10,000 weight vectors from a Dirichlet distribution centered on w (moderate concentration), and for each draw record (a) tier change rates per item, (b) stability of the prioritized set, and (c) Jaccard similarity between the base top-k and the top-k under alternative weights (with k aligned to operational bandwidth).

2.2.4. Sensitivity Analysis (Scaling and Thresholds)

We evaluated dependence on normalization and tier cutoffs by: (i) replacing min–max with robust scaling (median and IQR) and recomputing LRI and tiers; and (ii) shifting tier thresholds by ±0.05 (e.g., High ≥ 0.65/0.70/0.75; Medium [0.40, 0.69]), then measuring changes in prioritization and in the share of items requiring (s, SS, Q) reparameterization.

2.2.5. Operational Impact Linkage

Finally, we linked LRI robustness to operational impact: for each weight/threshold scenario, we measured (i) stability of the prioritised set and (ii) the induced changes in s/SS/Q and their implications for stockout exposure and urgent orders within the simulation (Section 3.2), reporting aggregates and confidence bands in Results.

2.3. Simulation Study

To validate and quantify the operational benefits of the risk-informed (s, Q) policy versus the institutional baseline, we design a discrete-event/Monte Carlo simulation with the following elements:

2.3.1. Input Models

Empirical demand (daily) per medicine with bootstrapped variability (σ_d and CV), empirical lead-time distributions per channel (CENABAST, tender, direct), and initial inventory levels from FO. Wastage and complaint rates are modelled as functions of overstock and stockout exposure, respectively. To enhance reproducibility and methodological transparency, several key elements of the simulation design are further clarified:

First, cost structures are modelled using standard inventory cost components. Holding cost is computed as a linear function of on-hand inventory, based on annualised indirect storage costs per unit, while ordering cost is represented as a fixed administrative cost per replenishment event. These values are derived from institutional cost records and applied consistently across simulation scenarios.

Second, stochastic demand is generated using an empirical bootstrapping approach. Daily demand observations are resampled with replacement from the historical demand series for each medicine, preserving the original distributional properties, including variability, skewness, and intermittency patterns. This avoids imposing parametric assumptions and ensures consistency with observed consumption behaviour.

Third, the order pipeline is modelled explicitly as a dynamic system of outstanding orders, each associated with a stochastic lead time sampled from empirical channel-specific distributions. Inventory position is updated according to standard practice as the sum of on-hand and on-order inventory minus backorders, and multiple overlapping orders are allowed to reflect real operational conditions.

Together, these design choices ensure that the simulation remains closely aligned with empirical data while maintaining a transparent and reproducible structure, consistent with the algorithmic representation provided in Algorithm 2.

2.3.2. Lead-Time Models

Lead times were modelled empirically for each purchasing channel using the hospital’s historical records. Instead of assuming parametric forms, we used the empirical lead-time distribution of each channel: (i) CENABAST (public centralised purchasing), characterised by long but relatively concentrated deliveries; (ii) public tender suppliers, which exhibited moderate dispersion; and (iii) urgent/direct purchases, which showed short but highly variable delays. For simulation purposes, lead times were sampled with replacement from the empirical distribution of each channel, preserving the observed asymmetry and episodic long tails known to affect replenishment reliability.

2.3.3. Order Pipeline Handling

The simulation incorporates an explicit order pipeline: whenever an order is placed, it enters an in-transit state with an associated lead time drawn from the corresponding channel. Multiple outstanding orders are allowed, consistent with real operations, and the inventory position is updated as $IP=\text{on-hand}+\text{on-order}-\mathrm{backorders}$. When the lead time elapses, the quantity Q is added to on-hand stock regardless of whether stockouts occurred during the transit period. This structure ensures that overlapping orders, channel variability, and late deliveries are captured realistically and that stockout episodes occurring during in-transit periods contribute to service penalties and urgent purchase triggers.

2.3.4. Channel Summary

Table 1. Lead-time modelling by channel.

Channel	Lead-Time Model	Operational Characteristics
CENABAST	Empirical distribution (historical)	Long, low variance; centralized approval
Tender suppliers	Empirical distribution	Medium lead time; moderate dispersion
Urgent/direct	Empirical distribution	Shortest but highest variability

summarises the lead-time treatment for each channel.

2.3.5. Scenarios

(i) Baseline: institutional parameters and current purchase cadence; (ii) Adjusted: updated s and SS (risk-informed service levels); (iii) Optimised: full (s, Q) with ABC–XYZ/LRI rules, alerts, and staggered reordering by channel.

Algorithm 2 MonteCarlo simulation of inventory policies under stochastic demand and lead time with sustainability metrics

Require:  Evaluation set of medicines $i=1,\dots ,n$ with: empirical daily demand model (bootstrapped), channel-specific lead-time distributions, initial on-hand inventory; policy parameters for three scenarios: Baseline, Adjusted (s, SS), Risk-informed (s, Q) with ABC–XYZ/LRI rules. Ensure:  KPI estimates per scenario with 95% confidence intervals (CIs), including environmental indicators. 1: Define scenarios $\mathcal{S}=\{\mathrm{B}\mathrm{A}\mathrm{S}\mathrm{E}\mathrm{L}\mathrm{I}\mathrm{N}\mathrm{E},\mathrm{A}\mathrm{D}\mathrm{J}\mathrm{U}\mathrm{S}\mathrm{T}\mathrm{E}\mathrm{D},\mathrm{R}\mathrm{I}\mathrm{S}\mathrm{K}\mathrm{I}\mathrm{N}\mathrm{F}\mathrm{O}\mathrm{R}\mathrm{M}\mathrm{E}\mathrm{D}\}$. 2: Choose horizon T (days) and replications R ≥ 1000. 3: for all $s\in \mathcal{S}$ do 4:       for r = 1 to R do 5:             for all medicine i do 6:                   Initialize inventory state: on-hand Ii,0, on-order pipeline Πi,0 ← ∅. 7:                   Initialize counters: demand served, demand lost/backordered, urgent orders, stockout-days, overstock metrics. 8:             end for 9:             for t = 1 to T do 10:                 for all medicine i do 11:                    Receive. If any order in Πi,t−1 arrives at day t, add quantity to on-hand. 12:                    Demand. Sample daily demand di,t from the empirical/bootstrapped model. 13:                    Serve. Serve min(Ii,t−1, di,t); update fill rate components. 14:                    if Ii,t−1 < di,t then 15:                     Record stockout exposure; record unmet demand. 16:                     Optionally trigger urgent order per scenario rules; increment urgent order counter. 17:                    end if 18:                    Update on-hand Ii,t. 19:                    Reorder logic (scenario-dependent). 20:                    Compute inventory position $I{P}_{i,t}=I_{i,t}+{\sum }_{\pi \in {\mathrm{\Pi }}_{i,t}}{q}_{\pi }$. 21:                    if IPi,t ≤ si then 22:                     Determine order quantity: 23:                     if s = $\mathrm{B}\mathrm{A}\mathrm{S}\mathrm{E}\mathrm{L}\mathrm{I}\mathrm{N}\mathrm{E}$ then 24:                    q ← institutional ordering rule (current cadence/institutional parameters). 25:                     else if s = $\mathrm{A}\mathrm{D}\mathrm{J}\mathrm{U}\mathrm{S}\mathrm{T}\mathrm{E}\mathrm{D}$ then 26:                    q ← institutional q (or fixed lot) but with updated s and SS. 27:                     else 28:                    q ← Qi (risk-informed EOQ/lot size), with LRI/segment-based overrides if applicable. 29:                     end if 30:                     Sample procurement channel and lead time $L\sim {\mathcal{L}}_{i,\mathrm{channel}}$. 31:                     Append order (q, t + L) to pipeline Πi,t. 32:                    end if 33:                    Cost accounting. 34:                    Holding cost ← hi · Ii,t; order cost $\leftarrow K·⊮[\mathrm{order}\mathrm{placed}]$. 35:                    Optionally model wastage/complaints as functions of overstock and stockout exposure. 36:                 end for 37:             end for 38:             Compute KPIs for replication r:     Stockout exposure (% days), fill rate (%), mean replenishment delay, urgent orders/year,     annual holding cost, total logistic cost.     Environmental metrics: Let ∆U be the reduction in urgent orders vs baseline for the scenario; then     CO2 avoided = ∆U × EFtransport (assume 50 kg/order),     Waste avoided = ∆U × Wpackaging (assume 2 kg/order). 39:       end for 40:       Aggregate KPI means and environmental metrics over R replications; compute 95% CIs (percentile or normal-based). 41: end for 42: return KPI table + CI bounds + scenario comparisons + sustainability indicators.

2.3.6. KPIs

Stockout exposure (% days with stockout risk), replenishment timeliness (mean effective days to receipt), service continuity (fill rate), storage efficiency (overstock units and holding cost), administrative burden (urgent orders), and total logistic cost. KPIs include traditional operational metrics (stockout exposure, fill rate, holding cost) and two environmental indicators: (i) estimated CO₂ emissions avoided by reducing urgent orders, and (ii) reduction in packaging and disposal waste. These indicators are computed for each scenario to quantify sustainability gains alongside service improvements.

2.3.7. Environmental Estimation and Sensitivity

Environmental impact was estimated using two components: (i) packaging waste per replenishment cycle, derived from supplier-specific packaging standards; and (ii) CO₂-equivalent emissions associated with transport, using a per-order emission factor applied uniformly across channels. Because these coefficients may vary by supplier or transport mode, we conducted a simple sensitivity analysis in which both factors were varied by ±50%. All sustainability metrics (packaging reduction and avoided CO₂) were recomputed under these scenarios to assess whether conclusions depend critically on environmental assumptions.

2.3.8. Replication/Design

At least N = 1000 simulation runs per scenario; 95% CIs for KPIs; sensitivity analyses on Z, L, CV, and h. This approach is standard for assessing continuous-review policies under stochastic demand/lead-time in healthcare contexts.

Demand uncertainty is modelled using an empirical bootstrapping approach based on historical daily consumption data, preserving the observed distributional characteristics without imposing parametric assumptions. Lead time variability is incorporated using empirical distributions derived from procurement records, reflecting the observed heterogeneity across supply channels.

The simulation model is calibrated using real operational data, including demand history, lead times, and inventory parameters. Inventory dynamics are modelled under a continuous-review framework, explicitly accounting for order pipeline delays and unmet demand (backorders).

Each simulation scenario is evaluated over N = 1000 Monte Carlo replications to ensure statistical stability of the estimated performance indicators. Performance metrics are computed as averages across replications, and variability is assessed to evaluate the robustness of the results.

The simulation model was further validated by verifying that the empirical bootstrapped demand and lead-time processes reproduce the main statistical properties observed in the original data, including central tendency, variability, and distributional shape. In addition, convergence diagnostics based on increasing numbers of replications confirmed that KPI estimates stabilise for N ≥ 1000, supporting the robustness of the simulation outputs.

Flowchart of the Governance and Analytics Pipeline. We provide a TikZ flowchart in Figure 1 to document the end-to-end process (data ingestion → segmentation → LRI → policy computation → simulation → environmental impact estimation → dashboard and governance).

Dashboard and Decision Support. We operationalise a logistics control dashboard that aggregates: stock coverage, adjusted reorder points (s), safety stock (SS), LRI tiers, lead-time compliance by channel, stockout alerts, overstock heatmaps, administrative effort (urgent orders), and sustainability indicators (estimated CO₂ emissions avoided and packaging waste reduction). Data sources update on a scheduled cadence, with role-based responsibilities for FO/FC and UA. This design follows WHO storage/distribution norms, LMIS visibility principles, and green supply chain guidelines for public-sector governance.

Statistical and Computational Methods. We compute CV and distributional summaries per item/month; service-level targets via normal approximation; bootstrapped CIs for KPIs; and sensitivity analyses for Z, L, CV, and h. For items with highly intermittent demand (XYZ class Z), we apply conservative buffers and stress tests instead of relying purely on normal approximations, consistent with risk-aware practice. Additionally, environmental metrics are estimated using simplified formulas:

$${\mathrm{CO}}_2\mathrm{avoided}(\mathrm{kg})=∆U\times E{F}_{transport},\mathrm{Waste}\mathrm{avoided}(\mathrm{kg})=∆U\times W_{packaging}$$

where ∆U is the reduction in urgent orders, EF_transport is the emission factor per urgent shipment (assumed 50 kg CO₂/order), and W_packaging is the average packaging waste per order (assumed 2 kg/order) [2,3].

Computational structure of the simulation study.

The simulation study was implemented as a discrete-time Monte Carlo experiment designed to evaluate the performance of alternative inventory policies under stochastic demand and lead-time conditions. To support reproducibility and facilitate independent verification, the simulation logic was formalised as a computational algorithm, summarised in Algorithm 2.

For each simulated scenario, the algorithm initialises the inventory state of the selected medicines using empirically observed demand distributions and procurement channel–specific lead-time models. Daily demand is generated using an empirical or bootstrapped process, while replenishment decisions follow scenario-dependent reorder and lot-sizing rules. Inventory position, order pipelines, and cost components are updated iteratively over the simulation horizon.

Algorithm 2 explicitly defines the handling of stockouts, emergency orders, holding costs, service-level indicators, and sustainability metrics (CO₂ emissions avoided and packaging waste reduction). Repeating this process over a large number of replications allows the estimation of mean performance measures and confidence intervals, providing a statistically robust basis for comparing baseline, adjusted, and risk-informed inventory policies.

3. Results

3.1. Empirical Study

Study Scope and Portfolio Characterisation. The empirical analysis distinguishes between the Oncology Pharmacy (FO) and the Central Pharmacy (FC) to provide institutional context and comparative insight into portfolio structure and procurement dynamics between the years 2023 and 2024. While both units are analysed descriptively, the subsequent policy evaluation and simulation focus primarily on FO, given its disproportionate concentration of pharmaceutical expenditure, clinical criticality, and logistical risk. This targeted focus enables the proposed risk-informed framework to be evaluated in areas where inventory decisions have the greatest potential impact on therapeutic continuity and sustainability outcomes. As shown in

Table 2. Portfolio scope and expenditure by subunit (2023–2024). This table compares demand volumes and cost distribution across operational units, highlighting portfolio asymmetries that inform subsequent segmentation and risk-informed inventory prioritisation.

Subunit	Medicines	Demand 2023	Demand 2024	Value 2023 (CLP MM)	Value 2024 (CLP MM)
FO	97	772,321	783,493	5062	5756
FC	273	3,572,135	3,474,182	822	818

, FO manages a substantially smaller number of medicines than FC, yet concentrates the majority of total pharmaceutical expenditure.

In 2024, FO accounted for approximately CLP 5.76 billion, compared to CLP 0.82 billion in FC. This asymmetric distribution confirms the strategic relevance of FO as the focal unit for risk-based inventory analysis, since marginal deviations in inventory parameters may translate into disproportionately large financial and clinical impacts.

Integrated Data Structure. A unified analytical dataset was constructed at the individual medicine level by integrating consumption records, procurement transactions, inventory parameters, administrative cost structures, and operational event logs. For each medicine, the dataset includes monthly and annual demand, unit acquisition cost, procurement channel, lead time statistics, institutional reorder points, and recorded operational disruptions.

This integrated structure ensures full traceability between empirical data and the decision rules defined in the methodological framework.

Procurement Lead Time Structure. Lead time behaviour differs substantially across procurement modalities. After excluding extreme outliers, descriptive statistics were computed for valid observations (

Table 3. Lead time and delivery mismatch by procurement modality (days). This table characterises variability and central tendency in delivery performance across procurement channels, supporting the modelling of lead-time uncertainty and its incorporation into risk-informed inventory parameters.

Procurement Channel	Orders	Mean	Median	SD
CENABAST	2677	28.8	29	9.0
Public tender	416	36.4	39	10.2

). Purchases through CENABAST exhibited a median lead time of 29 days, whereas public tendering showed a longer median of 39 days and higher dispersion.

Additionally, the mismatch between planned consumption and actual delivery dates was significantly larger for tender-based procurement, highlighting structurally heterogeneous supply risks across channels.

ABC–XYZ Segmentation Results. The ABC–XYZ classification reveals a highly concentrated expenditure structure in the FO subunit. As reported in

Table 4. ABC–XYZ segmentation for FO (2024 expenditure). This table summarises demand variability and expenditure concentration across inventory segments, highlighting high-impact and high-risk medicines that drive prioritisation within the risk-informed inventory framework.

Segment	Medicines	Value 2024 (CLP MM)	Share (%)
AX	23	2714	47.2
AY	20	1958	34.0
AZ	35	379	6.6
BX	10	296	5.1
BY	6	260	4.5
Others	3	149	2.6

, segments AX and AY jointly account for more than 80% of total pharmaceutical expenditure in 2024, despite representing a minority of items.

Figure 2 provides a compact visualisation of the ABC–XYZ segmentation for FO, reporting each segment’s share of the total 2024 expenditure. The heatmap highlights expenditure concentration in the most economically critical classes and reveals the presence of variable-demand medicines in segments with lower monetary weight.

Segments AZ and BZ, although less significant in monetary terms, exhibit high demand variability, indicating potential operational instability. Comparable patterns, with lower absolute values, are observed in the FC subunit (

Table 5. ABC–XYZ segmentation for FC (2024 expenditure). This table presents expenditure concentration and demand variability patterns across inventory segments, identifies cost drivers, and supports the prioritisation of medicines for risk-informed inventory management.

Segment	Medicines	Value 2024 (CLP MM)	Share (%)
AZ	25	376	46.0
AX	17	223	27.2
AY	7	55	6.7
BZ	23	45	5.5
Others	201	119	14.6

).

Logistic Risk Index Distribution. The Logistic Risk Index (LRI) was computed for all FO medicines using the weighted structure defined in the methodology.

Table 6. Distribution of Logistic Risk Index (FO). This table summarises the classification of medicines across risk tiers, illustrating the concentration of inventory risk and supporting the prioritisation of monitoring and control efforts within the framework.

Risk Tier	Medicines
Low	80
Medium	10
High	1

summarizes the resulting risk distribution, while

Table 7. Top medicines by Logistic Risk Index (FO). This table identifies the highest-risk medicines based on demand variability and event occurrence, highlighting critical items that drive risk-informed parameter adjustments and targeted inventory interventions.

Medicine	Segment	CV	Events	LRI
Alectinib 150 mg	AZ	0.51	2	0.709
Lenalidomide 25 mg	AY	0.27	0	0.540
Dexamethasone phosphate 4 mg	BX	0.11	0	0.477
Temozolomide 140 mg	AZ	0.59	0	0.473

reports the medicines with the highest LRI values.

High-risk medicines systematically combine large deviations in reorder parameters, elevated demand variability, structurally variable lead times, and recurrent operational events.

Figure 3 summarises the empirical distribution of the Logistic Risk Index (LRI) for FO medicines. The vertical thresholds at 0.40 and 0.70 correspond to the Low/Medium and Medium/High risk tiers, respectively, and visually support the risk-based screening and selection step described above.

Selection of Medicines for Policy Evaluation. Applying the selection criteria defined in Section 2, a reduced subset of FO medicines was identified for detailed policy evaluation (

Table 8. Medicines selected for policy evaluation.

Medicine	Segment	LRI	Risk Tier
Alectinib 150 mg	AZ	0.709	High
Lenalidomide 25 mg	AY	0.540	Medium
Temozolomide 140 mg	AZ	0.473	Medium

). Despite its limited size, this subset concentrates the highest levels of logistical vulnerability according to the composite risk metric.

Risk-Based Inventory Parameter Estimation. For the selected medicines, continuous review inventory parameters were recalculated using the proposed risk-adjusted framework.

Table 9. Risk-based inventory parameters for selected medicines. This table compares institutional and analytically derived reorder points, highlighting parameter misalignment (∆s) and the impact of demand variability and risk (LRI) on safety stock and order quantity decisions within the proposed framework.

Medicine	${\mathit{s}}_{\mathit{base}}$	${\mathit{s}}_{\mathit{calc}}$	$\mathbf{\Delta }\mathit{s}$	$\mathit{SS}$	Q	LRI
Alectinib 150 mg	224	394	170	53	12,993	0.709
Lenalidomide 25 mg	400	666	266	51	37,075	0.540
Dexamethasone phosphate 4 mg	800	2923	2123	92	201,807	0.477

reports estimated safety stock levels, reorder points, and economic order quantities, together with their institutional counterparts.

The results reveal substantial misalignment between existing institutional parameters and analytically derived values, confirming the limitations of static inventory rules in heterogeneous, risk-prone hospital pharmaceutical environments. The magnitude of the differences between institutional and analytically derived reorder points (∆s) is primarily driven by three interacting factors. First, demand variability directly influences safety stock requirements, leading to higher reorder points for medicines with volatile consumption patterns. Second, parameter misalignment between institutional settings and analytically implied values (∆PR) contributes significantly to the observed gaps, particularly where existing reorder points do not reflect updated demand or lead-time conditions. Third, the incorporation of risk-based adjustments through the Logistic Risk Index (LRI) further amplifies these differences for medicines classified in higher-risk tiers.

In particular, for medicines such as Dexamethasone phosphate 4 mg, the large adjustment reflects a combination of substantial parameter misalignment and the integration of variability and risk dimensions that are not fully captured under static institutional policies. This highlights the limitations of uniform parameterization and reinforces the value of risk-informed inventory design.

Environmental Baseline and Potential Gains. Analysis of urgent order logs shows that the institutional baseline generated an average of 27.4 urgent orders per year for the FO portfolio. Under the risk-informed configuration, this figure would decrease to approximately 14.8 orders, representing a reduction of 12.6 urgent shipments annually. Applying the emission factor (50 kg CO₂/order) and packaging waste proxy (2 kg/order), this translates into an estimated avoidance of 630 kg CO₂ and 25 kg of packaging waste per year. These results confirm that operational improvements are accompanied by measurable sustainability gains, reinforcing the relevance of integrated socio-economic-environmental governance.

Having established the empirical behaviour of the portfolio and the LRI distribution, we now examine the robustness of LRI-driven prioritisation before propagating variants into the simulation.

3.1.1. Internal Validation

LRI tiers aligned coherently with descriptive risk markers. Items in Y/Z classes concentrated in the upper LRI terciles, and A/B expenditure segments accounted for the majority of High LRI cases, indicating that the index simultaneously captures operational variability and clinical–economic salience. At baseline, LRI was positively associated with stockout exposure and urgent-order frequency (positive rank correlations and significant median contrasts), supporting its operational face validity.

3.1.2. Weight Sensitivity (OAT and Global)

Under the OAT sensitivity analysis (±20% variation per weight), 6.6% of items changed risk tier, while the prioritised set remained highly stable (Jaccard similarity = 0.88). In the global sensitivity analysis (Dirichlet sampling, N = 10,000), median top-k stability reached 0.91, with a relatively narrow 5th–95th percentile range of 0.84–0.96. In global sensitivity (Dirichlet, N = 10,000), median top-k stability was high and the 5th–95th percentile band was narrow, indicating that prioritisation is robust to reasonable variations in judgment. Sensitivity was higher when amplifying “Events” or “ ∆PR,” consistent with their role as triggers for reparameterization of s/SS. Overall, the results indicate that the LRI is robust to reasonable variations in weight selection and that the resulting prioritisation and policy adjustments are not driven by a specific parameter configuration.

Table 10. Robustness of the Logistic Risk Index (LRI) under alternative weighting schemes. This table reports key stability measures from the sensitivity analyses, showing that risk classification and prioritisation remain stable under plausible variations in the weighting structure.

Metric	OAT (±20%)	Global (Dirichlet)
Items changing risk tier (%)	6.6	9.1
Jaccard similarity (prioritized set)	0.88	0.90
Median top-k stability	–	0.91
5th–95th percentile band (top-k stability)	–	0.84–0.96

summarises the main quantitative results of the sensitivity analysis, providing explicit evidence that LRI-based prioritisation remains stable across a wide range of plausible weighting configurations.

3.1.3. Scaling and Threshold Sensitivity

Replacing min–max with robust scaling (median + IQR) and shifting thresholds by ±0.05 yielded high prioritised-set stability; tier changes were concentrated near cut points. Across scenarios, items motivating the largest (s, SS, Q) adjustments under the continuous-review policy remained within the prioritised set in the large majority of cases, suggesting that intervention targeting is stable.

3.1.4. Operational Implications

Propagating LRI variants into the simulation (Section 2.3) maintained reductions in stockout exposure and urgent orders within the previously reported ranges, with narrow 5th–95th percentile bands. Overall, the LRI is sufficiently robust to guide prioritisation and (s, Q) reparameterization in a public oncology setting without hinging on a unique set of weights or thresholds.

3.1.5. Intermittent Demand (Z-Class)

Applying the conservative treatment described in Methods did not materially affect prioritisation: Z-class items retained their original tiering, and (s, SS, Q) adjustments remained consistent with the main configuration.

3.2. Simulation Study Results

To assess the operational impact of the proposed risk-informed inventory framework, a simulation study was conducted comparing the institutional baseline policy with two alternative configurations: (i) an adjusted policy with updated reorder points and safety stock, and (ii) a fully risk-informed policy integrating ABC–XYZ segmentation and Logistic Risk Index (LRI) rules.

Table 11. Simulation results: comparison of baseline and risk-informed inventory policies (mean and 95% CI).

KPI	Baseline	Adjusted (s, SS)	Risk-Informed (s, Q + LRI)
Stockout exposure (% days)	6.8 [6.4–7.2]	4.9 [4.6–5.3]	3.7 [3.4–4.0]
Fill rate (%)	93.1 [92.4–93.8]	95.2 [94.7–95.8]	96.4 [95.9–96.9]
Mean replenishment delay (days)	41.3 [40.1–42.5]	36.8 [35.7–37.9]	33.5 [32.4–34.6]
Urgent orders (per year)	27.4 [25.9–28.9]	19.6 [18.3–20.9]	14.8 [13.7–15.9]
Annual holding cost (CLP MM)	412 [398–426]	438 [423–453]	456 [440–472]
Total logistic cost (CLP MM)	1284 [1248–1320]	1271 [1235–1307]	1269 [1233–1305]

summarises the main performance indicators obtained from 1000 Monte Carlo replications per scenario. Results are reported as mean values with 95% confidence intervals.

Relative to the baseline configuration, the adjusted policy reduces stockout exposure by approximately 28%, primarily through earlier reorder triggering for high-risk medicines. The fully risk-informed policy achieves a larger reduction of 46%, reflecting the combined effects of differentiated service levels, risk-based safety stock, and staggered replenishment by procurement channel.

Service continuity, measured through fill rate, improves from 93.1% in the baseline scenario to 96.4% under the risk-informed policy. At the same time, the simulation shows a reduction in urgent and emergency orders, indicating lower administrative burden and improved procurement predictability.

While holding costs increase moderately under the risk-informed policy due to higher buffers for high-risk medicines, total logistics costs remain stable. The increase in holding cost is offset by reductions in emergency purchasing, wastage associated with reactive ordering, and service disruptions. Overall, the simulation confirms that risk-informed parameterisation can improve resilience and service continuity without compromising cost efficiency.

Figure 4 shows that the risk-informed policy consistently reduces stockout exposure across Monte Carlo replications, shifting the distribution toward lower values and mitigating tail risk.

Figure 5 summarises the cost–service relationship under each scenario. The risk-informed configuration achieves higher fill rates while maintaining total logistic costs within the confidence bounds of the baseline, supporting the claim of improved resilience without compromising cost efficiency.

Taken together, the simulation results provide quantitative evidence that the proposed risk-informed inventory framework could be useful for enhancing service continuity and operational resilience in a high-complexity public oncology setting. By explicitly linking demand variability, procurement risk, and clinical criticality to inventory parameters, the framework outperforms static institutional rules under realistic stochastic conditions.

Environmental Impact under Simulated Scenarios. The Monte Carlo simulation corroborates the environmental benefits of risk-informed policies. Compared to the baseline, the adjusted scenario reduces urgent orders by approximately 28%, while the fully risk-informed scenario achieves a 46% reduction. Using the same conversion factors, the optimised policy avoids nearly 630 kg CO₂ emissions and 25 kg of packaging waste annually for the FO portfolio. These indicators were consistent across 1000 replications, with narrow confidence intervals, confirming that sustainability improvements are statistically robust and directly linked to inventory governance decisions. See

Table 12. Estimated environmental impact by scenario (annual values). This table quantifies the reduction in urgent orders and the associated decrease in CO₂ emissions and packaging waste under different inventory policies, illustrating the sustainability benefits of the proposed framework.

Scenario	Urgent Orders	${\mathrm{CO}}_2$ Avoided (kg)	Waste Avoided (kg)
Baseline	27.4	–	–
Adjusted	19.6	390	16
Risk-informed	14.8	630	25

.

Environmental Sensitivity

Varying the packaging and CO₂ factors by ±50% preserved the qualitative conclusions: reductions in packaging units and avoided CO₂ remained within the same order of magnitude, indicating that environmental results are robust to plausible variations in emission and waste coefficients.

4. Discussion

This study set out to bridge a persistent gap in public healthcare supply chain research: the lack of integrated, end-to-end analytical frameworks that connect empirical inventory behaviour, risk-aware optimisation, and institutional governance to the continuity of clinical care. Using real operational data from a high-complexity public oncology hospital, the results provide convergent empirical and simulation-based evidence that static, uniform inventory rules are structurally misaligned with the heterogeneous risk landscape of oncology pharmaceuticals [1,5]. Sensitivity analyses conducted on key parameters—including service-level targets (Z), lead-time distributions, demand variability, and holding cost assumptions—confirmed that the relative performance ranking of the evaluated inventory policies remains stable across plausible ranges. While absolute KPI values vary with parameter calibration, the risk-informed policy consistently outperforms the institutional baseline in terms of stockout exposure, service continuity, and reduction of urgent orders. This reinforces the robustness of the proposed framework under realistic operational uncertainty. Regarding external validity, although the empirical analysis is based on a single high-complexity public oncology hospital in Chile, the proposed framework is conceived as a modular and transferable governance structure rather than a context-specific solution. Its core components—ABC–XYZ segmentation, the Logistic Risk Index (LRI), and continuous-review (s, Q) policies—rely on standard operational inputs such as demand history, lead-time distributions, and procurement records, which are commonly available across healthcare systems.

Nevertheless, adaptation to local conditions remains essential. Differences in procurement structures (e.g., centralised vs. decentralised purchasing), regulatory environments, supplier reliability, and service-level priorities may influence parameter calibration, weight selection in the LRI, and policy thresholds. For example, systems characterised by shorter and more reliable lead times may require lower safety stock buffers, whereas highly regulated or fragmented procurement contexts may benefit from stronger weighting of supply-side risk dimensions.

Therefore, while numerical results and parameter values are inherently context-dependent, the underlying governance logic—linking descriptive analytics, risk assessment, and inventory policy design—remains broadly applicable across diverse healthcare supply chain configurations. This positions the framework as a scalable, adaptable decision-support tool for public health systems that could help enhance resilience, efficiency, and sustainability.

In addition, although the environmental parameters used in this study are simplified, they are consistent with typical ranges reported in healthcare logistics and are intended to provide decision-relevant signals rather than precise carbon accounting. The sensitivity analysis (±50%) confirms that the relative environmental benefits of the risk-informed policy remain stable across a wide range of plausible emission and packaging values, reinforcing the robustness of the conclusions under parameter uncertainty.

From descriptive analytics to actionable risk governance. The empirical findings confirm that pharmaceutical portfolios in oncology services are characterised by extreme asymmetry. Although the Oncology Pharmacy (FO) manages fewer medicines than the Central Pharmacy (FC), it concentrates the vast majority of pharmaceutical expenditure and clinical criticality. The ABC–XYZ segmentation reveals that a small subset of medicines (AX and AY) accounts for over 80% of total expenditure, while segments with high demand variability (AZ, BZ) persist even among lower-value items. These patterns reinforce prior evidence that expenditure-based prioritisation alone is insufficient for managing operational and clinical risk in hospital pharmacies [18,19].

The Logistic Risk Index (LRI) operationalises this insight by synthesising demand variability, supply performance, parameter misalignment, and proxies of clinical and economic importance into a single actionable metric. The observed concentration of high LRI values among medicines with both parameter misalignment and recurrent operational events demonstrates that risk emerges systemically rather than from isolated demand fluctuations. This supports the argument that descriptive tools such as ABC–XYZ become decision-relevant only when embedded within a broader risk-governance structure that translates classification into differentiated control rules [5,11].

Simulation evidence, therapeutic continuity, and sustainability. The simulation study provides quantitative validation of the proposed risk-informed framework under stochastic demand and lead-time conditions. Relative to the institutional baseline, both alternative scenarios reduce stockout exposure, but the fully risk-informed policy delivers the largest and most consistent improvements (up to a 46% reduction), with higher fill rates (93.1% → 96.4%) and shorter effective replenishment delays [5,11]. From a clinical perspective, these results are particularly relevant in oncology settings, where treatment interruptions compromise therapeutic efficacy and outcomes. Although patient-level outcomes are not explicitly modelled, lower stockout frequency and fewer urgent purchases constitute meaningful proxies of improved therapeutic continuity and reduced operational stress on clinical teams [1].

Importantly, these operational gains are accompanied by measurable environmental benefits. The optimised scenario reduces urgent orders from 27.4 to 14.8 per year (FO), which—under the stated assumptions—translates into an estimated avoidance of approximately 630 kg of CO₂ emissions and 25 kg of packaging waste per year. The environmental indicators reported in this study should be interpreted as operational proxies rather than as a full life-cycle assessment of pharmaceutical supply chains. Estimates of avoided CO₂ emissions and packaging waste are derived from observed reductions in urgent orders, which are strongly associated with expedited transport modes and additional packaging requirements in public healthcare procurement. Although simplified, these proxies are appropriate for managerial decision support and governance purposes, as they translate inventory policy choices into tangible sustainability signals. Future research could extend this approach by incorporating more granular transport data, packaging life-cycle assessments, and multimodal logistics modelling. This finding aligns with the literature on green logistics and sustainability in healthcare supply chains, particularly regarding reduced emissions from expedited transportation and lower waste generation [2,3]. As a result, the proposed framework advances a triple-impact perspective (clinical, economic, and environmental) consistent with the Sustainable Development Goals (notably SDG 3 and SDG 12) [6].

It is important to emphasise that the environmental indicators used in this study are not intended to represent a full life-cycle assessment (LCA), but rather simplified, decision-oriented proxies linking urgent procurement events to environmental impact. As such, the estimated reductions in CO2 emissions and packaging waste should be interpreted as indicative orders of magnitude rather than precise measurements.

In real healthcare supply chains, environmental impact is influenced by multiple interacting factors, including transport modes (e.g., air versus ground), delivery distances, supplier-specific logistics practices, and packaging configurations [34,35,36]. These elements are not explicitly modelled in the present framework and therefore introduce variability that is not fully captured by the simplified coefficients.

Future research could extend this work by integrating more detailed logistics data and life-cycle assessment methodologies to refine environmental estimates and better capture the complexity of healthcare supply chain emissions and waste generation.

Economic trade-offs and governance implications. From an economic standpoint, the simulation reveals a critical trade-off: moderate increases in holding costs due to differentiated safety buffers are offset by reductions in urgent orders, reactive purchases, and operational disruptions, keeping total logistics costs broadly stable [5]. Related analyses have shown that inventory cost savings correlate with supply chain success factors when governance mechanisms align analytics with managerial routines [37]. Beyond technical optimisation, the primary contribution of this study lies in its governance framing. By integrating ABC–XYZ segmentation, LRI thresholds, and (s, Q) policies within a transparent analytical pipeline and an operational dashboard, the framework facilitates coordination among clinical, logistical, and administrative units. In doing so, it addresses common failures in public-sector supply chains, such as limited visibility, fragmented information, and rigid procurement rules [1,22]. The explicit definition of thresholds, alerts, and scenario-based evaluation aligns inventory management with institutional traceability and auditability requirements and can be readily extended to green supply chain practices in public hospitals [3].

While the proposed framework is designed to support improved coordination between clinical services, pharmacy operations, and procurement management, these governance benefits should be interpreted as potential outcomes enabled by the analytical structure rather than directly observed effects within the scope of this study. The results of the simulation demonstrate improvements in operational indicators—such as reduced stockout exposure, improved service levels, and lower reliance on urgent orders—which create favourable conditions for enhanced coordination and decision-making. However, the actual realisation of these governance improvements depends on institutional adoption, integration into decision-support systems, and alignment with organisational processes. In practice, the framework can be implemented through dashboards, monitoring tools, and standardised decision rules that facilitate communication across functional units and support proactive inventory management. Future research could evaluate the real-world impact of such implementations on coordination, governance efficiency, and organisational performance.

Limitations and future research.

Several limitations should be acknowledged:

• First, the study focuses on a single public oncology hospital, which may limit external generalizability. While the empirical analysis is based on a single high-complexity public oncology hospital in Chile, the contribution of this study lies primarily in the analytical structure and governance logic of the proposed framework rather than in the specific parameter values obtained. The end-to-end pipeline—combining data integration, ABC–XYZ segmentation, risk synthesis through the LRI, continuous-review inventory policies, and simulation-based validation—is transferable to other public hospital systems facing similar constraints. Context-specific calibration is required for demand patterns, procurement channels, and institutional priorities; however, the underlying decision-support architecture and risk-informed governance approach remain broadly applicable across public healthcare supply chains.
• Second, while the simulation incorporates realistic stochastic structures, it relies on historical demand and lead-time patterns and does not explicitly model extreme systemic shocks.
• Third, clinical outcomes are inferred indirectly through service-continuity proxies rather than patient-level data.

Future research could (i) extend the framework to multi-hospital networks with centralised coordination (e.g., channel-specific SLA calibration and LRI thresholds at the ministerial level), (ii) integrate real-time forecasting and adaptive learning mechanisms into the LRI, and (iii) link logistical indicators with clinical outcomes and more comprehensive environmental metrics, including packaging life-cycle assessment, multimodal transport, and safe waste disposal [2,11,22]. Overall, the findings demonstrate that risk-informed inventory governance offers a viable and scalable pathway for strengthening therapeutic continuity, operational resilience, and sustainability in public healthcare systems [1,5]. Compared to existing stochastic inventory and risk-based prioritisation approaches, the proposed framework emphasises operational integration and governance applicability, bridging analytical modelling with decision-making processes in public healthcare environments.

5. Conclusions

This study proposes and empirically validates a data-driven, risk-informed framework for pharmaceutical inventory management in a public oncology hospital. By integrating descriptive analytics, ABC–XYZ segmentation, a Logistic Risk Index (LRI), and a continuous-review (s, Q) policy within a governance-oriented decision-support structure, the framework moves beyond static inventory rules toward adaptive, evidence-based management [5,11].

Empirical results reveal substantial misalignment between institutional inventory parameters and analytically derived values, particularly for high-risk oncology medicines. Simulation-based evaluation demonstrates that risk-informed policies significantly reduce stockout exposure and emergency procurement while improving service continuity, without increasing total logistics costs [1,5].

Crucially, the framework also delivers estimated environmental benefits through the reduction of urgent orders, avoiding approximately 630 kg of CO₂ emissions and 25 kg of packaging waste per year in the Oncology Pharmacy (FO). This outcome advances a holistic socio-economic-environmental perspective aligned with green logistics principles and the Sustainable Development Goals [2,3,6].

From a governance perspective, the framework provides actionable indicators, explicit thresholds, and monitoring tools that could be useful for enhance coordination among clinical, logistical, and administrative stakeholders. This supports a shift from reactive inventory management toward anticipatory, transparent, and accountable decision-making in public healthcare settings [1,22].

The proposed approach is scalable and transferable to other public hospitals and health systems facing demand uncertainty, procurement constraints, and high clinical stakes, contributing both methodologically and practically to the literature on healthcare supply chains and sustainability-oriented decision-making [11,23].