# Option-Based Framing and Valuation of Supply Chain Resilience Investments

Kai Trepte, Walid Klibi, James Blayney Rice, Yves Ducq

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Kai Trepte, Walid Klibi, James Blayney Rice, Yves Ducq. Option-Based Framing and Valuation of Supply Chain Resilience Investments. 2026. hal-05498741

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Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
Option-Based Framing and Valuation of Supply Chain
Resilience Investments

Kai Trepte¹,², Walid Klibi¹,³, James Blaney Rice¹, and Yves Ducq²

¹Center for Transportation and Logistics, Massachusetts Institute of Technology, USA,

²University of Bordeaux, CNRS UMR 5218, IMS, Talence, France,

³The Centre of Excellence for Supply Chain Innovation and Transportation (CESIT), Kedge Business School, Talence, France,

Abstract

Organizations face growing pressure to invest in supply chain resilience, yet boom-
bust capital budgeting remains episodic because conventional metrics frame resilience
as a static, risk-centric expense rather than a strategic financial investment. We ad-
dress this gap with a simulation-based, option-framed valuation that models resilience
building as a dynamic, multi-stage decision process across interconnected supply chain
network nodes. Our approach links action costs to plausibility-weighted performance
outcomes (rather than worst cases), integrates time to recover and time to survive met-
rics with network-level profit propagation, and ranks actions using financially legible
KPIs. Applying the framework to a large pharmaceutical supply chain network, we
show that sustained, option-framed programs outperform reactive, event-driven spend-
ing, delivering higher expected gross profit with lower variability. Treating resilience
actions as sequential real options enables managers to evaluate investments based on
probability-weighted performance outcomes rather than worst-case scenarios, decou-
pling budget allocation from crisis-driven timing. The results demonstrate that option-
based sequencing creates probability-weighted resilience outcomes 3.6 times lower in expected loss than worst-case. This gap between worst-case and plausible outcomes explains why traditional approaches drive boom-bust cycles where organizations over-invest based on improbable tail events, then retrench when projected benefits fail to materialize. By bridging operational planning and financial justification, we re-frame resilience as a dynamic, financially grounded capability and offer a foundation for theory and practice in resilient supply chain design.

**Keywords:** Supply chain resilience, real options, capital budgeting, operations-finance interface, sequential decision-making, network simulation

# 1 Introduction

## 1.1 Motivation

When COVID-19 struck, shipping container costs spiked more than fourfold (Figure 1), warehouse construction materials surged by multiples, and lead times increased sharply across industries. Yet these dramatic cost increases eventually stabilized—revealing a pattern that has recurred for decades: resilience spending surges after crises, then declines sharply once conditions normalize. This 'boom-bust' cycle (Trepte and Rice (2018); Cohen et al. (2022)) persists because most firms rely on risk-based evaluations that emphasize immediate hazard mitigation rather than resilience as a long-term, evolving capability. Similar shocks from natural disasters, geopolitical tensions, energy crises, and inflationary pressures have reinforced the urgency of resilience (Klibi et al., 2024; Alicke et al., 2024; Görner et al., 2022). Yet organizational responses have often been reactive: firms expand capacity or stockpile inventory immediately after a crisis, only to scale back once conditions stabilize. The result is costly over-correction, followed by retrenchment, which leaves companies exposed to the next disruption. Recent survey evidence confirms the persistence of this pattern: nine in
ten executives reported significant supply chain challenges in 2024, yet many organizations
are slowing their resilience initiatives, with fewer new projects and declining board-level
engagement in risk management (Alicke et al., 2024). Taken together, these observations
raise a central question for operations strategy: *how can firms design and justify resilience
investments that are financially sustainable over time, rather than episodic responses to
individual crises?*

<figure><img src="image_2.png" /><figcaption>Figure 1: Examples of cost surges, peaks and returns after COVID</figcaption></figure>

Figure 1 illustrates this volatility. Warehouse construction material costs are used as a proxy for capital expenditures (CapEx), average lumber costs as a proxy for working capital, and container costs as a proxy for operating expenditures (OpEx). All three surged by multiples after COVID-19, then partially stabilized. Prior research has advanced our understanding of resilience drivers and metrics (Blackhurst et al., 2011; Gao et al., 2019), but most approaches remain static. They assess resilience at a single point in time and lack a financial lens, leaving managers to justify initiatives reactively, based on memories of past disruptions (Rice et al., 2022; Nikookar et al., 2024). Without explicit financial validation, resilience projects rarely secure consistent funding. Evidence from prior downturns also shows that firms that invest programmatically in resilience—by strengthening balance sheets, managing costs, and pursuing selective growth—outperform peers in total shareholder returns during and after crises (Görner et al., 2022). However, the resilience literature offers limited guidance on how firms should structure and value such programmatic investments
over multiple decision periods.

Existing assessment methods typically evaluate isolated projects or mitigation strategies (Mathews et al., 2007; Carbonara and Pellegrino, 2018). They struggle to account for the interdependencies of multiple actions over time, and many resilience expenditures are irreversible or yield negative returns (Pindyck, 1993). The result is underinvestment in proactive measures and an overreliance on disruptive triggers to justify spending (Bedsworth and Soos, 2018). From a theoretical perspective, this suggests a missing link between operational resilience decisions, which are inherently dynamic and path-dependent, and the investment evaluation tools that guide capital allocation under uncertainty.

Our research responds by shifting from episodic assessments to an enterprise-wide, programmatic perspective. We develop a methodology that (i) determines appropriate budgets for resilience investments over long horizons and (ii) supports the selection and sequencing of actions over time. In doing so, it directly addresses two unresolved managerial questions: How much should be budgeted for resilience? And what financial returns can such investments generate? We address these questions by conceptualizing resilience investments as a portfolio of real options embedded in a supply chain (SC) network and by operationalizing this perspective through a multi-period, scenario-based simulation applied to a large pharmaceutical SC network.

## 1.2 Contributions

This is the first study to integrate option-based financial valuation with resilience modeling, thereby bridging a long-standing gap between operational research and managerial decision-making in supply chain design. While prior work has identified resilience drivers and quantified operational effects, it has provided little guidance on how firms should allocate and justify investments financially. We position our contribution at the intersection of the supply chain resilience literature and the literature on investment under uncertainty. We advance the literature and practice in three ways:
* We re-frame resilience as a strategic financial problem. Traditional worst-case reasoning overstates expected losses by focusing on tail events with low probability of occurrence (in our pharmaceutical case, there is a 3.6x plausibility gap). This gap explains why boom-bust cycles persist: organizations over-invest when extreme scenarios seem salient and under-invest when such scenarios fail to materialize. By modeling resilience investments as options valued on probability-weighted gross profit outcomes, we show how to anchor decisions in demonstrable value rather than speculative worst-case avoidance.

* We develop a simulation-based valuation approach that applies real options logic to link resilience actions with financial outcomes. This method enables organizations to assess and sequence investments under uncertainty, rather than relying on static, one-off evaluations. It introduces a set of novel KPIs that translate resilience outcomes into financial terms. The framework explicitly captures intertemporal interdependencies between decisions, accommodates multiple failure modes and network configurations, and yields implementable decision rules for ranking actions under budget constraints.

* Grounded in empirical data from a major pharmaceutical SC network, we provide the evidence that option-based valuation shifts investment priorities relative to traditional risk-based assessments. A key insight is that sequencing investments by option value systematically narrows the gap between time to recover and time to survive, offering a novel mechanism to stabilize costs and sustain resilience over time. The empirical analysis demonstrates that option-based sequencing generates higher expected gross profit with lower variability over a 20-year horizon than alternative metrics, thereby illustrating how the proposed framework can be applied in practice.

The remainder of the paper is structured as follows: Section 2 reviews the literature, Section 3 outlines the methodology, Section 4 presents the empirical investigation, and Section 5 discusses implications and conclusions.
# 2 Literature Review

Our work builds on and contributes to three complementary streams of research in supply chain resilience. The first stream focuses on the measurement and assessment of resilience, including frameworks and metrics that capture system vulnerability and recovery capacity. The second examines actions that enhance resilience, such as inventory buffering, supplier diversification, and network reconfiguration, while also highlighting the difficulty of securing organizational funding for these initiatives. The third addresses the relationship between resilience and financial performance, with growing attention to valuation approaches but limited progress on translating resilience into the financial metrics used in managerial decision-making. Together, these streams establish a strong foundation but leave unresolved the question of how resilience investments can be systematically evaluated and prioritized in financial terms—a gap this study aims to address.

## 2.1 Quantification of Supply Chain Resilience

The measurement of supply chain resilience has evolved significantly over time. Early assessments sought to determine how well an organization's capabilities aligned with the risks it faced, recognizing that resilience investments incur costs (Pettit, Timothy J., 2008). A key contribution of Pettit's SCRAM framework was its emphasis on balancing resilience costs with expected risk reduction. Building on this foundation, Blackhurst et al. (2011) further decomposed supply chain mitigation strategies, providing a structured approach to assess whether specific interventions enhance or hinder resilience. Despite these advances, resilience assessments remain risk-centric, with a focus on specific threats rather than engineered resilience outcomes (Bedsworth and Soos, 2018). For instance, Bedsworth and Soos examined climate change adaptation, but their methodology can be generalized to other disruptive events.

In practice, many organizations discount rare but high-impact events, perceiving them as
unlikely, which results in underinvestment in resilience (Kunreuther and Pauly, 2004). This
behavioral bias—widely documented in decision sciences (Camerer and Kunreuther, 1989)—
leads managers to ignore low-probability but high-consequence disruptions. To counteract
this tendency, organizations are increasingly quantifying resilience to improve awareness and
decision-making (Yadav et al., 2022; Mehryar et al., 2022). However, as Mehryar et al.
(2022) highlight, resilience initiatives often get overridden by recent high-profile risks, even
when long-term assessment frameworks suggest different priorities. Practitioner evidence
echoes this difficulty: complex dashboards or indices are often abandoned in favor of simpler
heuristics or technology-based visibility tools (Colehower, 2023).

A growing consensus in the literature favors time-to-recover (TTR) versus time-to-survive (TTS) metrics over multi-dimensional resilience indices (Hosseini et al., 2019; Simchi-Levi et al., 2014). This shift is driven by computational and data collection constraints—multi-factor resilience indices are resource-intensive to compute (McDermott and Surminski, 2018)—and by specialized expertise requirements, since interpreting complex risk-exposure models requires advanced analytical skills (Mehryar and Surminski, 2021). When too many factors are involved, resilience assessment tools become inefficient and difficult to act upon (Roostaie et al., 2019; Zavala-Alcívar et al., 2020); conversely, overly simplistic models fail to capture key risk dependencies (Likierman, 2009; Muller, 2019). Current research, therefore, relies predominantly on single-metric resilience models combined with simulation-based evaluations (Kiers et al., 2022; Yadav et al., 2022; Aldrighetti et al., 2021). Our approach expands on this by modeling resilience as a probability distribution of outcomes, allowing for better risk-adjusted decision-making (Klibi and Martel, 2012). We propose a multi-metric approach by segmenting the metrics to address specific aspects of system vulnerability (Klibi and Martel, 2012), thereby capturing system complexity through a series of sequential models.

These approaches improved measurement but remain risk-centric and static, leaving little
guidance on how resilience can be valued financially over time.
## 2.2 Selecting Resilience Actions

A substantial body of literature explores the value of resilience investments (Linkov et al., 2020). However, most research remains loss-prevention-focused rather than treating resilience as a strategic investment (Gao et al., 2019). Various mitigation strategies have been studied, including inventory buffering to absorb supply shocks (Song and Zipkin, 1996), supplier diversification such as dual sourcing and contractual agreements for safety stock (Nguyen et al., 2021), and simulation-based network assessments to quantify recovery potential under disruption (Munoz and Dunbar, 2015). In response to the limitations of these approaches, Simchi-Levi et al. (2014) developed the TTR versus TTS framework, which provides a useful benchmark for evaluating the performance of mitigation strategies.

While each of these approaches enhances resilience, they do not provide a comprehensive financial justification for investment decisions (Saisridhar et al., 2023). As Saisridhar et al. (2023) emphasize, resilience investments require clear financial metrics to secure organizational funding and move through the budgeting process (Inc., 2018). Organizations increasingly recognize that supply chain resilience is closely linked to financial performance and competitive advantage (Li et al., 2017). However, reactive investments—those funded after a disruption—are easier to justify than proactive ones, since recent financial losses create clear motivation for funding risk mitigation (Li et al., 2017). Further research highlights that financing constraints also shape resilience decisions (Li et al., 2022). To reduce uncertainty, organizations attempt to leverage data analytics (Pramanik et al., 2020), yet available data sources rarely provide the granularity needed for financial justification, forcing reliance on expert judgment (Rajesh, 2019). Practitioner evidence suggests firms often adopt piecemeal strategies such as visibility platforms or predictive sensing, rather than embedding resilience as a programmatic investment logic (Colehower, 2023).

Although there is strong evidence for mechanisms that enhance resilience (Rajesh, 2022; Mubarik et al., 2022) and for methods that quantify resilience improvements (Gao et al., 2019; Simchi-Levi et al., 2014), most research stops short of linking these improvements to
a structured financial model for resilience budgeting. This missing link between operational measures and financial valuation forms a key gap that our study addresses.

## 2.3 Financial Justification of Resilience Investments

A key challenge for practitioners is not demonstrating that resilience adds value, but justifying specific investments financially under uncertainty (Li et al., 2017). While the broad financial benefits of resilience are widely acknowledged, traditional valuation methods such as Net Present Value (NPV) and Expected Value frequently fail to capture its dynamic and path-dependent impacts (Mansouri et al., 2010). As a result, many resilience initiatives remain vulnerable to scrutiny in the budgeting process, particularly when no recent disruption provides a clear justification for funding. Practitioner research echoes this issue, emphasizing that one of the primary barriers is the difficulty of making the financial case for resilience to top management and boards (Rice et al., 2022).

Real options analysis has been proposed as a promising alternative, since it views resilience investments as flexible, sequential decision pathways rather than static expenditures (de Neufville et al., 2006). This perspective enables valuation based on the optionality created by resilience investments, rather than relying solely on immediate payoffs. Recent practitioner-oriented work also highlights the relevance of real options logic in structuring resilience investments under uncertainty (Klibi et al., 2024). However, despite this promise, the core issue remains unresolved: translating resilience benefits into the financial metrics that decision-makers use to allocate resources (Cooper, 2013).

In short, while existing research has acknowledged the financial relevance of resilience, it has not yet provided a structured framework for evaluating and prioritizing resilience investments in financial terms. Addressing this gap is the central aim of our study.
# 3 Methodology

We develop a six-layer methodology that enables organizations to evaluate and sequence resilience investments as a portfolio of real options under uncertainty, addressing the gap between operational resilience measures and the financial decision criteria that drive capital allocation. The six layers are: (1) Network, (2) Vulnerability, (3) Resilience Action, (4) Evaluation, (5) Decision & Selection, and (6) Sequential Investment & Learning. Layers (1)–(2) expand Klibi and Martel (2012), while layers (3)–(6) build on Klibi et al. (2024). Beyond their individual expansion, the innovation lies in their integration: by coupling scenario-based vulnerability assessment with option-framed financial valuation, budget-constrained decision logic, and dynamic state updating, the methodology supports adaptive sequencing of actions over multi-year horizons while remaining accessible and interpretable for practitioners.

Figure 2 illustrates this structure and the flow of information through each layer. Sequential decision cycles incorporate feedback loops that enable organizational learning through state updates and re-evaluation.

<figure><img src="image_3.png" /><figcaption>Figure 2: Methodology framework for assessing resilience investments</figcaption></figure>
## 3.1 Network Layer

We model the supply network as a directed graph with nodes $n \in N$ (located at $l(n) \in L$) and arcs $e = (n, n') \in E$. The network converts inputs to outputs and ultimately serves demand zones Consistent with practice and prior work, we distinguish suppliers, manufacturing sites, and distribution facilities (RDC/CDC/FC), which allows vulnerability and resilience levers to be specified and costed at the right granularity (Blackhurst et al., 2011; Pettit, Timothy J., 2008; Klibi and Martel, 2012). Figure 3 depicts an illustrative topology with suppliers (S), component Mfg (CM), finished-goods Mfg (M), RDC/CDC, and demand zones (DZ). Node labels indicate an example of their contribution to nominal gross profit at a given time period.

<figure><img src="image_4.png" /><figcaption>Figure 3: Representative supply chain (from the pharmaceutical case in Section 4)</figcaption></figure>

Nominal gross profit at time $t$ is

$$GP_{t}^{\text{nom}} = GR_{t} - TC_{t}. \qquad (1)$$

where $GR_t$ and $TC_t$ respectively denote the gross revenue and total cost of the SC network in period $t$. This total gross profit is allocated to nodes through shares $\theta_{n,t} \in [0, 1]$ with $\sum_{n \in N} \theta_{n,t} = 1$, so that node-level gross profit is $GP_{n,t}^{\text{nom}} = \theta_{n,t} GP_{t}^{\text{nom}}$. This allocation
enables us to value node-level disruptions and actions directly in monetary terms and to later aggregate results to any scope (site, region, enterprise) (Klibi et al., 2024; Rice et al., 2022). Under uncertainty, gross revenue and cost are scenario-specific; we introduce this notation below and account for it in the simulation. For a complete reference of all notation employed throughout this paper, see Appendix A.

## 3.2 Vulnerability Layer

Vulnerabilities are the susceptibility of network elements to external risks; realized risks trigger failure modes that propagate through the network (Ponomarov and Holcomb, 2009; Hosseini et al., 2016; Sheffi and Rice, 2005; Berle et al., 2011). We structure this layer with arrivals, exposure, and severity.

*Arrivals.*

$$K_{m,t} \sim \text{Poisson}(\lambda_m \Delta t). \qquad (2)$$

$$I_{m,t} \sim \text{Bernoulli}(1 - e^{-\lambda_m \Delta t}), \quad \text{Pr}(K_{m,t} \ge 1) = 1 - e^{-\lambda_m \Delta t}. \qquad (3)$$

When return-period estimates ($RP_m$) are available, set $\lambda_m = 1/RP_m$; details in Appendix B.

*Exposure.*

$$ATT_{n,m,t} \sim \text{Bernoulli}(p_{n,m,t}), \quad A_{n,m,t} := I_{m,t} \cdot ATT_{n,m,t} \in \{0, 1\}. \qquad (4)$$

*Severity/recovery.*

$$\beta_{n,m,t} \sim \text{Triangular}(a, b, c), \quad 0 < a \le b \le c, \qquad (5)$$

$$TTR_{n,t}^{\text{eff}} = \max_{m} \left\{ A_{n,m,t} (\overline{TTR}_{n} \cdot \beta_{n,m,t}) \right\}. \qquad (6)$$

Eq.(6) defines the effective recovery time at node $n$ in period $t$ as the maximum recovery time weighted by exposure across failure modes. Parameterization and instantiation of arrival rates ($\lambda_m$), exposure probabilities ($p_{n,m,t}$), and severity distributions ($\beta_{n,m,t}$) for
our pharmaceutical case study are provided in Appendix B.2. Distributional and functional choices are guided by available data and common practice and can be readily adapted to alternative moments or specifications without altering the framework. Following Klibi and Martel (2012), an *environment* is the internal/external operating condition in a period; a *scenario* is a sequence of environments over the horizon. We work with plausible scenarios $\omega \in \Omega$ with probabilities $p(\omega)$, $\sum_{\omega} p(\omega) = 1$. We assume period-to-period independence of arrivals (e.g., annual periods) as detailed later in the scenario generation process.

## 3.3 Resilience Action Layer

Figure 4 contrasts option-based (early, proactive) with boom-bust (reactive) investment strategies across three archetypal resilience actions: capital expenditure (CapEx), working capital (WC), and operating expense (OpEx). Each category carries distinct cost, timing, and benefit profiles. The figure illustrates why option-based investments outperform reactive ones across all three types.

<figure><img src="image_5.png" /><figcaption>Figure 4: Option-based versus boom-bust resilience investment strategies</figcaption></figure>

*Panel (a): CapEx-based resilience.* Early infrastructure investment at time $t$ enables rapid capacity expansion when needed, versus delayed investment at $t+2$ under boom-bust logic. The time gap $\Delta t$ represents how many periods sooner the option-based firm gains access to additional capacity, enabling faster disruption response and reduced downtime.
Panel (b): Working capital-based resilience. Proactive inventory buildup delivers two advantages: earlier access ($\Delta t$) and higher available capacity ($\Delta c$) relative to reactive procurement. Reactive sourcing during disruptions faces supplier constraints and market shortages (e.g., semiconductor crises), preventing firms from acquiring full desired inventory. Proactive buffers circumvent these constraints.

Panel (c): OpEx-based resilience. Early supplier qualification ensures availability during disruptions, avoiding both qualification lead times ($\Delta t$) and capacity gaps ($\Delta c$). Suppliers onboarded during or immediately after a disruption typically cannot provide full committed capacity within the recovery window due to competing orders and limited operational slack.

We now formalize this strategic logic into a quantitative framework. Resilience actions are modeled as stochastic interventions that reduce the TTR/TTS gap with uncertain efficacy. We quantify their value by translating promised resilience gains into probabilistically weighted gross profit outcomes across scenarios. Resilience actions $r \in RA$ increase survival time (TTS) for a cost $C^{(r)}$ (e.g., inventory buffers, backup suppliers, capacity add-ons) (Rice et al., 2022; Klibi et al., 2024). The Vulnerability Layer provides $TTR_{n,t}^{\text{eff}}(\omega)$; here we map actions to realized survival time and ultimately to value.

Promised increment and efficacy. We model the efficacy of action $r$ as uncertain: the promised increment $\Delta TTS_{n,t}^{(r)}$ is characterized by an uncertain realization controlled by stochastic efficacy parameter $\rho$ that is uniformly distributed per node $n$ and period $t$ as given in eq. (7) under scenario $\omega$, where $0 < \kappa_r < 1$ bounds minimum efficacy below the promised level.

$$ \rho_{n,r,t}(\omega) \sim \mathcal{U}(\kappa_r, 1), \quad 0 < \kappa_r < 1. \qquad (7) $$

$$ TTS_{n,t}^{(r)}(\omega) = TTS_{n,t}^{\text{base}} + \rho_{n,r,t}(\omega) TTS_{n,r,t}^{\text{nom}}. \qquad (8) $$

Eq.(8) defines realized time-to-survive as the baseline TTS plus a scenario-dependent adjustment, where $\rho$ scales the nominal TTS benefit of action $r$ by its efficacy.
Downtime under action r is the excess of recovery time over realized survival time:

$$DT_{n,t}^{(r)}(\omega) = \max\{0, TTR_{n,t}^{\text{eff}}(\omega) - TTS_{n,t}^{(r)}(\omega)\}. \quad (9)$$

*From days to dollars.* Working days per year are $WD_t = (\text{Days in Year})_t - (\text{Days Not Open})_t$, and daily margin is $DD_{n,t} = GP_{n,t}^{\text{nom}}/WD_t$. Node-level gross profit under action r is:

$$GP_{n,t}^{(r)}(\omega) = GP_{n,t}^{\text{nom}} - DD_{n,t} DT_{n,t}^{(r)}(\omega). \quad (10)$$

Aggregating across scenarios with probabilities $p(\omega)$:

$$\widehat{GP}_{n,t}^{(r)} = GP_{n,t}^{\text{nom}} - DD_{n,t} \sum_{\omega} p(\omega) DT_{n,t}^{(r)}(\omega). \quad (11)$$

Total expected gross profit across all nodes and periods is:

$$\widehat{GP}^{(r)} = \sum_{t \in T} \sum_{n \in N} \widehat{GP}_{n,t}^{(r)}, \quad \Delta \widehat{GP}^{(r)} = \widehat{GP}^{(r)} - \widehat{GP}^{(0)}. \quad (12)$$

Computing $GP^{(r)}$ requires accounting for time-invariant action costs ($C^{(r)}t = C^{(r)}0$), which decompose into capital ($C^{(r)}\text{capex}$), working capital ($C^{(r)}\text{wc}$), and operating expenses ($C_{\text{opex}}^{(r)}$).

Figure 5 illustrates how we measure the value that resilience investments generate. The left plot contrasts gross profit distributions under "No Action" (gray) versus an illustrative action "Add Backup 3PL" (black), generated under multiple scenarios. The right panel shows the differential value $\Delta \widehat{GP}$, i.e., the incremental gross profit from the action. This distribution enables the evaluation layer to perform cost-benefit assessment.

## 3.4 Evaluation Layer

For each resilience action r, the performance assessment begins by computing the scenario-specific gross profit $GP_{n,t}^{(r)}(\omega)$ (Eq. (10)) for each node n and period t under scenario ω. To ob-
<figure><img src="image_6.png" /><figcaption>Figure 5: Illustration of $\widehat{GP}$ comparing No Action vs. Adding a Backup 3PL</figcaption></figure>

tain gross profit over the entire network for a given period under scenario $\omega$, these quantities are aggregated over all nodes: $GP_t^{(r)}(\omega) = \sum_{n \in N} GP_{n,t}^{(r)}(\omega)$. The total gross profit over the entire 20-year horizon and all nodes under scenario $\omega$ is given by $GP^{(r)}(\omega) = \sum_{t \in T} GP_t^{(r)}(\omega)$.

We then compute expected gross profit by aggregating scenario-specific outcomes weighted by probabilities $p(\omega)$. Expected gross profit at each node and period is $\widehat{GP}_{n,t}^{(r)}$, given by Eq. (11); total expected gross profit over the entire 20-year horizon and all nodes is $\widehat{GP}^{(r)}$ given by Eq. (12).

To characterize the distribution of outcomes under uncertainty, we compute the mean $\mu^{(r)} = \widehat{GP}^{(r)}$ and standard deviation $\sigma^{(r)}$ of gross profit across all scenarios. These statistics characterize, respectively, the central tendency and dispersion of performance under action $r$, and serve as inputs to the KPI formulas (Eqs. (13)–(17)).

*Plausible value improvement.*

$$ \widehat{VAR}^{(r)} = \mu^{(r)} - \mu^{(0)}. \qquad (13) $$

This indicator captures the expected incremental monetary value derived from implementing action $r$ relative to maintaining the status quo (denoted by $r = 0$). A positive $\widehat{VAR}^{(r)}$ thus reflects a direct gain in expected profitability attributable to the intervention.
Stability gain (coefficient-of-variation reduction).

$$ \Delta CoV^{(r)} = \frac{\sigma^{(0)}}{\mu^{(0)}} - \frac{\sigma^{(r)}}{\mu^{(r)}}. \qquad (14) $$

While the previous metric focuses on expected value, $\Delta CoV^{(r)}$ quantifies the change in stability. It reflects whether the action reduces relative volatility in gross profit outcomes, offering a view on risk mitigation or consistency improvement. A higher value signals enhanced performance reliability across possible futures.

Marginal benefit (per dollar of cost).

$$ MB^{(r)} = \frac{\Delta \widehat{GP}^{(r)}}{C^{(r)}}. \qquad (15) $$

The marginal benefit measure expresses how efficiently each dollar invested in action $r$ translates into incremental expected profit. This provides a cost-effectiveness perspective, emphasizing proportional returns rather than absolute value creation.

Option value (net of cost).

$$ OV^{(r)} = \widehat{VAR}^{(r)} - C^{(r)}. \qquad (16) $$

The option value incorporates both the expected value improvement and its associated cost, serving as an integrated measure of action desirability. It mirrors the logic of real options, where the decision-maker evaluates whether the expected benefits sufficiently offset the required investment.

Multi-criteria score.

$$ MCS^{(r)} = w_1 \widehat{VAR}^{(r)} + w_2 \Delta CoV^{(r)} + w_3 MB^{(r)} + w_4 OV^{(r)}, \quad \sum_{i=1}^{4} w_i = 1, w_i \ge 0. \qquad (17) $$

Finally, the multi-criteria score provides a composite indicator that balances multiple dimensions.
sions of value, stability, efficiency, and net gain. The weights ($w_1, \dots, w_4$) can be calibrated
through governance or stakeholder workshops to reflect organizational priorities, risk toler-
ance, and strategic emphasis. This aggregation facilitates transparent, quantitative compar-
isons among competing actions while retaining interpretive flexibility across contexts.

We remark that expected gross profit (Eqs. (11)–(12)) is computed without temporal dis-
counting because actions are compared *simultaneously* within each period, not across sep-
arated investment timings. The real option value derives from within-period uncertainty
resolved through scenario analysis, not temporal waiting (McDonald and Siegel, 1986).

**3.5 Decision & Selection Layer**

The selection rule accommodates any budget level $B_t$ and can identify multiple actions per
period by iterating through the ranked list until budget exhaustion. For clarity, we illustrate
the methodology under the assumption that $B_t$ is calibrated to fund exactly one action
per period. This stylized case highlights the sequential logic and state-updating mechanism
without loss of generality: extending to multiple actions per period is straightforward (actions
are selected in rank order until the cumulative cost exceeds $B_t$). For a given decision period
t, the process is summarized in Figure 6.

Managers often seek actions that rank highly not only at a single time but repeatedly
over the horizon. To identify such candidates, define $RA_{r,t}$ as the rank (1 = best) of resilience
action $r \in RA$ at time $t$ under the chosen KPI (e.g., $OV_t^{(r)}$, $MB_t^{(r)}$, or $MCS_t^{(r)}$). An action's
robustness across time is measured by its best rank over the entire horizon. Then, the best
candidate is the action with the lowest $VRA_r$ value—that is, the action that achieves the best
rank (closest to 1) most consistently. The vulnerability resilience action (VRA) is computed
as $VRA_r = \min_t RA_{r,t}$, and the optimal action is selected as $\text{BestRA} = \arg \min_{r \in RA} VRA_r$.
<figure><img src="image_7.png" /><figcaption>Figure 6: Computation flow chart from scenarios generation to the decision step.</figcaption></figure>

## 3.6 Sequential Investment & Learning Layer

To dampen boom-bust patterns, we evaluate and select actions at each decision point, then update the network state to reflect implemented actions. At each period $t$, we observe the current network state (topology, survival times $TTS^{base}$, cost structure, and prior actions). Using the selection rule from Section 3.5, we identify and implement the highest-ranked action $r_t^*$. This action increases the base survival time at affected nodes: for node $n$ targeted by $r_t^*$, we update $TTS_{n,t+1}^{base} = TTS_{n,t}^{base} + \Delta TTS_{n,r_t^*}$. Similarly, sustained costs (working capital, opex) are carried forward. We then re-run the vulnerability and resilience action layers on the updated network state to generate KPIs for period $t+1$.

Figure 7 illustrates this cycle. At each period ($t_0, t_1, \dots, t_n$), the network state includes all prior actions. At $t_0$, we evaluate all candidate resilience actions on the base network $N_0$ and select $r_0^*$ (e.g., “Invest in Supply Base”). This action increases survival times, shifting the network to $N_0 + r_1$ and improving expected gross profit from $\widehat{GP}^{(0)}$ to $\widehat{GP}^{(1)}$. At period $t_1$, we re-evaluate remaining actions on the updated network $N_0 + r_1$; a different action $r_1^*$ (e.g., “Invest in Mfg. Base”) now ranks highest, reflecting the changing landscape. After
implementing $r_1^*$, the network evolves to $N_0+r_1+r_2$, and gross profit grows to $\widehat{GP}^{(t)}$. This sequential, state-dependent process continues over the horizon, naturally producing sustained, adaptive investment trajectories. In each subsequent period, the budget is revealed, the scenario set is updated, and the network nodes TTRs are recomputed.

<figure><img src="image_8.png" /><figcaption>Figure 7: Illustration of the cascading effects of investments in resilience over time</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Figure 8: Four-quadrant analysis: expected gross profit vs. coefficient of variation at time t</figcaption></figure>

From an organizational perspective, a traditional four-quadrant (4-Box) analysis facilitates decision-maker communication. The two dimensions—probability-weighted gross profit ($\widehat{GP}$) and coefficient of variation (CoV)—directly convey that high gross profit with low variability dominates alternatives. Actions in the high-$\widehat{GP}$, low-CoV quadrant (e.g., “Invest in
Supply Base”) emerge as most attractive, combining strong expected performance with out-
come stability. The value of option-framing is that it goes further: by explicitly comparing
investment cost $C^{(r)}$ with generated value $\Delta \widehat{GP}^{(r)}$, we can identify actions that are both
high-value and cost-efficient, enabling rigorous prioritization. Figure 8 maps each candidate
action into this two-dimensional space, allowing decision-makers to visually identify actions
in the high-value, low-variability quadrant. This figure depicts expected gross profit vs. co-
efficient of variation at a point in time to facilitate decision making and investment selection
(the decision point $t_0$ shown in this example).

# 4 Empirical Investigation

This section empirically instantiates the proposed framework using data from a large phar-
maceutical supply network, developed through a multi-year collaboration with an industry
partner, to illustrate how sequential, budget-constrained resilience decisions unfold over time.
We evaluate resilience actions under probability-weighted plausible scenarios and compare
alternatives using the KPIs defined in Section 3. The empirical setting is particularly well-
suited to this analysis because it combines long lead times, heterogeneous resilience options,
and high consequences of supply disruption.

## 4.1 Case Study Setting & Data Calibration

The empirical analysis is based on a multi-year, intensive collaboration with a major phar-
maceutical company. This partnership involved regular workshops, structured interviews,
and iterative validation sessions with supply chain, operations, procurement, analytics, and
risk/resilience management teams. All data presented in this case study—network topology,
financial exposures, operational parameters, failure modes, and action costs—were sourced
directly from company records, validated against historical incident logs, and refined through
multiple rounds of stakeholder feedback and expert elicitation. For confidentiality reasons,
the network is anonymized and simplified for presentation, while meticulously preserving the
structural and operational characteristics relevant to resilience decision-making.

The evaluation horizon spans 20 years with yearly decision periods, reflecting both prod-
uct life expectancy and the long-term nature of resilience investments. The pharmaceutical
supply network provided a uniquely demanding and informative empirical setting for our
resilience framework. First, resilience actions exhibit highly heterogeneous cost structures
and implementation timelines—ranging from relatively fast inventory adjustments (weeks)
to capital-intensive capacity expansions or supplier development efforts (6–18 months)—
requiring careful sequencing and timing decisions. Second, many critical raw materials
(such as active ingredients) have long lead times, implying that disruptions can result in
prolonged recovery periods (60–180 days). Third, product cost structures are frequently
dominated by high-value inputs with limited shelf life, constraining the feasibility of con-
ventional inventory-based mitigation strategies. Finally, many products serve life-saving or
essential medical functions, generating substantial economic and societal costs when supply
is interrupted—motivating the company’s historical reliance on worst-case reasoning.

Critically, the company had been justifying resilience investments using worst-case sce-
narios, leading to perceived underperformance of many initiatives ex post (realized disrup-
tions rarely aligned with assumed extremes). This real-world tension motivated our collab-
oration to apply the option-based framework.

Network, Data, and Calibration

The initial network analyzed comprises 1,200 nodes across suppliers, component manufac-
turing, finished-goods manufacturing, and distribution (Figure 3), spanning five business
segments and two distinct value streams. The geographic footprint initially focused on US
facilities to simplify data gathering and iterative model validation with company stakehold-
ers. Figure 9 shows the illustrative risk exposure overlaid on a US base map, aligning external
hazard layers with network topology. Data gathering combined three sources, each validated
through structured stakeholder review:
1. *Company-provided extracts:* Node identifiers, locations, type (supplier/ manufacturing/ distribution), throughput, and financial allocations ($\theta_{n,t}$). Baseline operational parameters ($\overline{\text{TTR}}_n$ worst-case recovery and $\text{TTS}_{n,t}^{\text{base}}$ survival times without resilience action) were extracted from company recovery procedures and validated against 10-year incident history. Candidate resilience actions and costs ($C^{(r)}$, promised increments $\Delta\text{TTS}_r$) were identified through interviews with supply chain and procurement teams.

2. *External public references:* FEMA National Risk Index database for county-level return periods of natural hazards; published industry benchmarks (Klibi et al., 2012; Berle et al., 2011) for supply-chain recovery distributions and failure-mode taxonomy.

3. *Expert elicitation and validation:* In three structured workshops (each 6–8 hours) with company operations, procurement, and risk teams, we collectively reviewed baseline parameters, calibrated failure-mode intensities for operational disruptions, and refined severity distributions. Participants confirmed that triangular distributions with published percentile bounds appropriately captured their uncertainty about recovery times. Historical incidents were reviewed case-by-case to validate exposure probabilities and action efficacy assumptions.

Node financial mapping ($GP_{n,t}$) is based on 250 working days/year. Baseline recovery and survival parameters are documented in Appendix B and Table 6, showing observed TTR values ranging from 9 days (fast-moving distribution centers) to 180 days (manufacturing bottlenecks with long active ingredients lead times).

Failure modes $m$ were parameterized through a hybrid approach: (i) for natural hazards, intensities $\lambda_m$ were derived from FEMA return periods via $\lambda_m = 1/\text{RP}_m$; (ii) for operational modes (labor, supply, financial, distribution, transportation, operations disruptions), return periods were calibrated from company incident logs and validated in expert workshops. Node-specific exposure probabilities $p_{n,m,t}$ account for geography and operational capability. These probabilities were jointly estimated by company risk managers and veri-
fied against historical incident frequency data (Appendix B.2, Table 7). Recovery severity ($\beta_{n,m,t}$) is modeled using triangular distributions, calibrated via: (i) company worst-case recovery times (mode $b_{n,m} = \overline{TTR}_n$), (ii) industry percentile benchmarks (bounds $a_{n,m}, c_{n,m}$), and (iii) mode-specific expert adjustments (e.g., labor disruptions resolve faster than supply disruptions). Appendix B.2 details the calibration approach.

We consider five resilience archetypes: Supply Base, Manufacturing Base, Contract Base, Distribution Base, and Regional Base; corresponding to common actions such as inventory buffers, backup contracts, dual sourcing, and capacity expansions, each with costs $C^{(r)}$ (CapEx/working capital/OpEx) and efficacy $\rho_r(\omega)$. Efficacy lower bounds $k_r$ were set based on company experience: e.g., inventory buffers rarely achieve full promised survival benefit due to shelf-life constraints ($k_r = 0.7$); dual-sourcing efficacy is 60–100% due to second-supplier capacity limitations ($k_r = 0.6$). Annual budgets $B_t$ were specified ex ante by company financial planning with periodic updates at decision cycles $t$ reflecting revised business conditions. All cost and efficacy assumptions were cross-checked against company’s historical data on implemented resilience projects.

## Instantiation of Methodology Layers

Following Section 3, we instantiated the scenario-based framework through the following procedure, conducted in close collaboration with company analytics and risk teams:

We generated 1,000 scenarios per decision cycle using Monte Carlo simulation across four uncertainty dimensions: arrivals ($I_{m,t}$, Eq. (3)), node-level exposure ($ATT_{n,m,t}$, Eq. (4)), severity factors ($\beta_{n,m,t}$, Eq. (5)), and action efficacy ($\rho_{n,r,t}(\omega)$, Eq. (7)). All scenarios are equiprobable with probability $p(\omega) = 1/|\Omega|$. Scenarios are propagated through Eqs. (8)–(11) to compute downtime, gross profit impact, and KPIs for each action. The full computational pipeline—scenario generation, network state propagation, downtime and gross-profit calculation, KPI computation, action ranking, and state updates—was implemented in R (version 4.4.2) using standard packages for simulation and data analysis. The pipeline evaluates 20
rolling 1-year decision steps over the full 20-year horizon, generating approximately 5 million scenario-action-outcome records across all periods. Results are presented for the first five years ($t = 1$ to $t = 5$), with the full horizon analysis confirming sustained performance. On a standard workstation (Intel i7, 16 GB RAM), the full pipeline completes in approximately 45 minutes.

The implementation was validated through sensitivity analyses across key parameter ranges (return periods, action efficacy, financial exposures), with results reviewed and approved by the company. Complete parameterization procedures, data sources, scenario generation details, and validation results are documented in Appendix B.

<figure><img src="image_10.png" /><figcaption>Figure 9: Anonymized US network with illustrative risk exposure (colors) and sample flows.</figcaption></figure>

## 4.2 Anchoring Resilience in Plausibility

In examining sequential decision processes for resilience investment, it is critical to establish a baseline that reflects plausible outcomes rather than extreme scenarios. Consistent with behavioral research, organizations often discount worst-case scenarios because they are perceived as improbable and weakly connected to realized performance. By applying Monte Carlo simulation and incorporating scenario probabilities (Section 3), we derive a plausible
outcome distribution that more accurately reflects realized organizational performance. The discrepancy between worst-case and plausible outcomes—the plausibility gap—is central to understanding boom-bust investment cycles: decision-makers over-invest when extreme scenarios seem salient and under-invest when such scenarios fail to materialize.

Rather than model each risky event in isolation, disruptions are grouped into failure modes representing generalized patterns of system breakdowns. Each failure mode is modeled as a stochastic process with arrivals, exposure, and severity probabilities derived from empirical data and expert elicitation (Eqs. (2)–(6)). Monte Carlo simulation then generates probability-weighted outcome distributions over 1,000 replications across a 20-year horizon for each decision cycle.

<figure><img src="image_11.png" /><figcaption>Figure 10: Option-based vs. worst-case resilience valuation</figcaption></figure>

Figure 10 illustrates three gross-profit trajectories at time $t$ for the base network $N_t$, derived from the underlying triangular distributions: a worst-case trajectory (maximum severity), a baseline trajectory evaluated at the mode $\widehat{GP}_t^{(0)}$, and a resilient trajectory after implementing action $r$ evaluated at the mode $\widehat{GP}_t^{(r)}$. In other words, for the sake of clear illustration, the figure shows *modal estimates* obtained by taking, for each trajectory, the most probable realization implied by the theoretical distributions.

The *most probable* resilience benefit in the figure is the difference between these two modal trajectories, $\widehat{GP}_t^{(r)} - \widehat{GP}_t^{(0)}$. This “mode gap” captures how much gross profit improvement
can be expected under the most likely operating conditions, as opposed to extreme realizations. The same figure also makes visible the gap between the worst-case trajectory and the modal baseline, which highlights how far worst-case reasoning can deviate from more plausible outcomes.

By contrast, the table that follows reports the *probability-weighted* (plausible) equivalents computed via Eq. (12), where gross profit is averaged over the entire GP distribution produced by all simulated scenarios using their probabilities $p(\omega)$. These tabulated values are not mode-based point estimates but expectations: they aggregate the full distribution of outcomes rather than focusing on a single most probable point.

<table><caption>Table 1: Sequential resilience investments: cumulative value and tail-risk reduction over time</caption><thead><tr><th>Stage</th><th>Action</th><th>Worst Case GP Loss ($M)</th><th>Plausible Case GP Loss ($M)</th><th>TTR-TTS Gap (In Days)</th><th>Step Improvement ($M)</th></tr></thead><tbody><tr><td>0</td><td>Base</td><td>11,543</td><td>3,212</td><td>64</td><td>—</td></tr><tr><td>1</td><td>+Invest in Supply Base</td><td>11,046</td><td>3,174</td><td>62</td><td>497</td></tr><tr><td>2</td><td>+Invest in Mfg Base</td><td>11,011</td><td>3,174</td><td>62</td><td>35</td></tr><tr><td>3</td><td>+Invest in Contract Base</td><td>10,874</td><td>3,174</td><td>61</td><td>136</td></tr><tr><td>4</td><td>+Invest in Regional Base</td><td>10,823</td><td>3,174</td><td>61</td><td>51</td></tr></tbody></table>

Table 1 quantifies the plausibility gap using the pharmaceutical case data. In the base network $N_t$, the worst-case scenario (99.5th percentile) projects $11,5M in GP loss with a 64-day TTR-TTS gap, while the probability-weighted plausible case yields $3,2M a 3.6x difference that represents the plausibility gap. This gap reveals a critical insight: worst-case analysis dramatically overstates expected losses by focusing on tail events with only 0.5% probability of occurrence. The sequential investment progression further illuminates this dynamic. Across four resilience actions, worst-case GP loss decreases by $720M (from $11,5M to $10,8M), representing a 6.2% improvement. However, the plausible case GP loss decreases by only $38M (from $3,212M to $3,174M) a mere 1.2% improvement. This asymmetry demonstrates that the investments primarily address tail risk rather than expected-value outcomes. The TTR-TTS gap narrows from 64 to 59 days, confirming operational improvements, yet the disproportionate impact on worst-case versus plausible outcomes reveals that resilience investments address tail risk. Worst-case reasoning promises $720M in "value creation" that
rarely materializes—tail events occur with negligible probability, driving boom-bust cycles of over-investment followed by disillusionment. Option-based valuation reveals this misallocation, systematically targeting probable disruptions invisible to traditional methods. Probability-weighted improvements (Table 1) deliver robust $38M gains versus unreliable worst-case projections, making sustained resilience investment credible.

Together, the figure and the table show that (i) worst-case projections substantially underestimate both modal and expected performance, and (ii) the investment case for resilience is more robust when evaluated on probability-weighted improvements in gross profit than when justified solely by worst-case avoidance. By anchoring investment decisions in recurring, demonstrable value relative to plausible scenarios—rather than in speculative worst-case avoidance—organizations are more likely to sustain commitment to resilience-building. This shift provides a more defensible business case for sustained resilience spending and motivates the KPI- and option-based evaluation used in the following subsections.

## 4.3 Option-Value & Selection of Resilience Actions

By integrating failure-mode modeling with probabilistic scenario analysis, the approach moves beyond static, worst-case thinking to offer a dynamic, risk-adjusted view of resilience. This enables decision-makers to prioritize resilience investments not on hypothetical extremes, but on the expected impact across a spectrum of plausible disruptions. In doing so, we provide a more actionable and financially defensible basis for strategic resilience planning, aligning managerial intuition with rigorous analytical support.

In our work with research partners, we observed that resilience investment decisions are rarely selected based on expected performance at a single time point. This is consistent with evidence that resilience investments are more valuable when they are robust across time. We account for this by selecting the highest-ranked resilience action in each period and tracking how frequently it appears over the decision horizon; the list of resilience actions and parameters are detailed in Table 2 below. As mentioned earlier, resilience actions impact
TTS in our model, reflecting their ability to increase the survivability of the supply chain.

<table><caption>Table 2: Resilience action parameters by node</caption><thead><tr><th>Node</th><th>Resilience Action</th><th>TTS</th><th>Cost in $m</th></tr></thead><tbody><tr><td>S1</td><td>Invest in Supply Base</td><td>5</td><td>0.060</td></tr><tr><td>S2</td><td>Invest in Supply Base</td><td>5</td><td>0.060</td></tr><tr><td>S3</td><td>Invest in Supply Base</td><td>5</td><td>0.060</td></tr><tr><td>S4</td><td>Invest in Supply Base</td><td>5</td><td>0.060</td></tr><tr><td>M1</td><td>Invest in Manufacturing Base</td><td>2</td><td>0.008</td></tr><tr><td>M2</td><td>Invest in Manufacturing Base</td><td>2</td><td>0.008</td></tr><tr><td>CM1</td><td>Invest in Contract Base</td><td>5</td><td>0.040</td></tr><tr><td>CM2</td><td>Invest in Contract Base</td><td>5</td><td>0.040</td></tr><tr><td>CDC1</td><td>Invest in Distribution Base</td><td>7</td><td>0.025</td></tr><tr><td>CDC2</td><td>Invest in Distribution Base</td><td>7</td><td>0.025</td></tr><tr><td>CDC3</td><td>Invest in Distribution Base</td><td>7</td><td>0.025</td></tr><tr><td>CDC4</td><td>Invest in Distribution Base</td><td>7</td><td>0.025</td></tr><tr><td>RDC1</td><td>Invest in Regional Base</td><td>5</td><td>0.060</td></tr></tbody></table>

<figure><img src="image_12.png" /><figcaption>Figure 11: Evolution of cost versus value as resilience investments are evaluated</figcaption></figure>

Figure 11 summarizes how alternative resilience actions compare along the cost-value
dimension at $t_0$, combining expected gross profit improvements with implementation costs. Actions that appear attractive on a single metric (e.g., marginal benefit) may deliver lower option value once cost and uncertainty are accounted for. The KPIs defined in Section 3.4 (expected value improvement, stability gain, marginal benefit, and option value), together with the multi-criteria score, are used to rank actions under a budget constraint. Table 3 provides these metrics at $t_0$ metrics relative to Base network, and $t_1$ metrics relative to state after $t_0$ action. It underscores differences in resilience investment selection $t_0$ versus $t_1$ using Value at Risk, Marginal Benefit and Option-Value as the decision criteria for selecting the resilience investment to implement.

<table><caption>Table 3: Resilience investment using Value at Risk, Marginal Benefit and Option-Value</caption><thead><tr><th rowspan="2">Criterion</th><th colspan="4">t<sub>0</sub> Decision</th><th colspan="4">t<sub>1</sub> Decision</th></tr><tr><th>Action</th><th>VAR ($M)</th><th>MB ($M)</th><th>OV ($M)</th><th>Action</th><th>VAR ($M)</th><th>MB ($M)</th><th>OV ($M)</th></tr></thead><tbody><tr><td>Option Value</td><td>Invest in Supply Base</td><td>497</td><td>208</td><td>289</td><td>Invest in Manufacturing Base</td><td>35</td><td>14</td><td>20</td></tr><tr><td>Marginal Benefit</td><td>Invest in Distribution Base</td><td>464</td><td>194</td><td>269</td><td>Invest in Distribution Base</td><td>464</td><td>194</td><td>269</td></tr><tr><td>Value At Risk</td><td>Invest in Manufacturing Base</td><td>35</td><td>14</td><td>20</td><td>Invest in Manufacturing Base</td><td>35</td><td>14</td><td>20</td></tr></tbody></table>

The robust choice rule then identifies actions that repeatedly achieve high ranks across decision periods. In this case we see the recommended action based on the selection methodology and the value that each performance metric assigned to that selection, e.g., Option Value recommended “Invest in Supply Base” as its first action and then the values assigned by the other methods; at $t_1$ the methods recommend the next action given that the $t_0$ action was implemented. For each action $r \in RA$, its rank $RA_{r,t}$ at time $t$ under the chosen KPI is recorded, and its robustness index $VRA_r = \min_t RA_{r,t}$ is computed. The robust choice set comprises actions with low $VRA_r$ values that remain attractive over the horizon; we see this in Figure 8 where the resilience options are ranked in a typical 4-Box value grid that highlights the tradeoffs at each decision point. In the case study, the action selected at $t_0$ under the multi-criteria score also appears frequently among the top-ranked actions in later cycles, supporting its robustness.
## 4.4 Sequential Valuation of Resilience Actions

A central strength of the approach lies in its ability to evaluate resilience investments dynamically and iteratively across multiple decision points and performance metrics. Unlike static, one-time assessments, the simulation-based model updates the expected cost-benefit profile of each resilience action as operational and environmental conditions evolve.

At each decision point, the distribution of outcomes associated with each performance metric is evaluated. When outcome distributions are probability weighted, it becomes possible to identify which action offers the highest expected value for the current decision cycle. As the decision window advances, this updating ensures that selected actions reflect the most favorable trade-off between implementation cost and improvement in outcome stability.

<figure><img src="image_13.png" /><figcaption>Figure 12: Evolution of cost vs value as resilience investments are implemented sequentially</figcaption></figure>

Figure 12 shows how the cost-value relationship evolves as resilience investments are implemented sequentially across the supply base and the contract base (snapshot taken after the first resilience action is implemented at ($t_1$)). The first dimension for assessment is the outcome distribution: outcomes for the supply base are relatively dispersed, whereas outcomes for the contract base are more tightly clustered. The second dimension is implementation cost, illustrated by the vertical line, which differs between actions. Following the logic of option-based evaluation, probability-weighted outcomes are compared against implementation cost. When the probability-weighted outcome lies to the left of the cost, the action is unlikely to generate value in that cycle, even if it may have been attractive in earlier conditions. The lower plot of Figure 12 illustrates how this dynamic updating mechanism acts as a counterweight to boom-bust investment patterns. As successive ac-
tions are implemented, both the cost and the value generated by each action evolve. If internal or external conditions change, both the expected value and cost of resilience actions are updated, enabling consistent re-alignment of investment decisions with evolving outcome distributions.

Figure 13 shows the sensitivity of cumulative value creation to the performance measure used for action selection. The option-value approach yields higher total value over the decision horizon than alternative metrics. In the reported case, option-value selection generates approximately $0.043M of incremental value at a cost of $0.037M, while a multi-criteria approach incurs lower cost (about $0.018M) but delivers lower incremental value (about $0.023M). This illustrates how traditional methods may either over- or under-allocate resources by failing to balance uncertainty, cost, and expected value.

<figure><img src="image_14.png" /><figcaption>Figure 13: Comparison of option value and multi-criteria performance measures over time.</figcaption></figure>

## 4.5 Robustness and Statistical Validation

To establish the statistical significance of the KPI-based approaches, three complementary statistical tests are conducted: paired t-tests, Kolmogorov-Smirnov (KS) tests, and bootstrap confidence intervals on the 1,000 Monte Carlo replications.

All four KPI-based approaches generate gross profit distributions significantly different from no-action ($p < 0.001$). T-statistics range from roughly 599 to 600, and bootstrap 95%
<table><caption>Table 4: Statistical tests of KPI-based evaluation approaches.</caption><thead><tr><th>Comparison</th><th>T-Test</th><th>P-Value</th><th>KS-Statistic</th><th>KS P-Value</th><th>Bootstrap 95% CI</th></tr></thead><tbody><tr><td>Base to Option-Value</td><td>600.43</td><td>p &lt; 0.001</td><td>1.000</td><td>p &lt; 0.001</td><td>[0.0027, 17.1568]</td></tr><tr><td>Base to Multi-Criteria</td><td>600.22</td><td>p &lt; 0.001</td><td>1.000</td><td>p &lt; 0.001</td><td>[0.0027, 17.1583]</td></tr><tr><td>Base to Coeff. of Variation</td><td>600.22</td><td>p &lt; 0.001</td><td>1.000</td><td>p &lt; 0.001</td><td>[0.0027, 17.1562]</td></tr><tr><td>Base to Marginal Benefit</td><td>599.29</td><td>p &lt; 0.001</td><td>1.000</td><td>p &lt; 0.001</td><td>[0.0027, 17.1436]</td></tr><tr><td>Option-Value to Multi-Crit.</td><td>39.21</td><td>p &lt; 0.001</td><td>0.048</td><td>p &lt; 0.001</td><td>[0.0027, 0.0030]</td></tr><tr><td>Option-Value to CoV</td><td>39.21</td><td>p &lt; 0.001</td><td>0.048</td><td>p &lt; 0.001</td><td>[0.0027, 0.0030]</td></tr><tr><td>Option-Value to MB</td><td>-83.99</td><td>p &lt; 0.001</td><td>0.217</td><td>p &lt; 0.001</td><td>[-0.0124, 0.0029]</td></tr></tbody></table>

confidence intervals for incremental value demonstrate substantial and consistent improvements over the 20-year horizon. These results confirm that resilience investments, when evaluated by any of the KPI frameworks, deliver measurable and statistically significant value relative to no-action.

When comparing approaches directly, marginal benefit yields slightly higher point outcomes but does so by maximizing efficiency per dollar without accounting explicitly for absolute investment cost. Option value incorporates cost directly, balancing value magnitude, affordability, and risk. The outcome distributions reveal option value's stability advantage: although point outcomes differ only modestly, the Kolmogorov-Smirnov test indicates meaningfully different distributional shapes.

<figure><img src="image_15.png" /><figcaption>Figure 14: Distribution of gross profit under option-value and marginal-benefit evaluation.</figcaption></figure>

Figure 14 shows the density plots of gross profit outcomes when resilience actions are selected using marginal benefit versus option value. Marginal benefit concentrates a larger
fraction of outcomes at or below the base case (essentially no improvement), while option
value spreads outcomes more evenly across the range and reduces downside concentration.
This figure provides further evidence to support the argument that marginal benefit does
not fully account for investment cost and uncertainty trade-offs, whereas option-value-based
selection yields more robust performance over the 20-year horizon.

# 5 Discussion

This study addresses a fundamental gap in supply chain resilience research: how to evalu-
ate and sequence resilience investments financially over time, rather than treating them as
episodic responses to crises. We develop a simulation-based, option-framed valuation frame-
work that models resilience investments as a portfolio of flexible, staged commitments. By
integrating operational resilience metrics (TTR/TTS) with real options logic and scenario-
based analysis, we bridge the operations-finance divide and provide decision-makers with
financially credible tools for sustained resilience planning.

The core contribution is methodological: we show that treating resilience as sequential
real options fundamentally changes investment prioritization and timing. Rather than single-
point evaluations (*Does this action reduce worst-case loss?*), the framework asks: *What is the
probability-weighted value of this action, given current network state and future flexibility?*
This shift—from crisis-driven justification to probability-anchored strategy—addresses why
boom-bust cycles persist and how organizations can escape them.

## 5.1 The Pitfalls of Boom-Bust Investing

The boom-bust phenomenon is well-documented but poorly understood through a financial
lens. Organizations spike resilience spending after major disruptions (COVID-19, natural
disasters, geopolitical shocks), then retrench sharply as conditions normalize. Survey evi-
dence confirms this pattern: nine in ten executives reported supply chain challenges in 2024,
yet many are slowing resilience initiatives (Alicke et al., 2024).

The root cause is not neglect but flawed financial reasoning. Traditional metrics—ROI, NPV, payback period—struggle with resilience investments because future cash flows under uncertainty are heavily discounted or excluded, yielding negative ROI. Worst-case reasoning inflates perceived threats by focusing on tail events with 0.5% probability, justifying massive spending that seems irrational in hindsight. Subjective likelihood estimates decay as disruption memories fade, triggering rapid retrenchment once external pressure eases.

Our pharmaceutical case quantifies this gap: worst-case analysis projects $11.5M in gross profit loss, while probability-weighted analysis shows $3.2M, a 3.6× difference. This gap explains the boom-bust cycle perfectly. Executives see $720M in "value creation" from tail-risk mitigation, justify large programs, then become disillusioned when extreme events don't materialize. Without distinguishing probable from improbable outcomes, organizations cannot make rational, sustained commitments. Alternative metrics (marginal benefit, coefficient of variation) inadvertently worsen this by favoring low-cost, high-variance interventions such as reactive inventory stockpiling that provide short-term relief but create excess capacity and write-offs when conditions stabilize. The result is cyclical over-then under-investment, leaving companies perpetually underprepared.

Our framework escapes this trap by anchoring all decisions in probability-weighted gross profit distributions. This probability-anchored approach bridges operations and finance, transforming resilience from speculative worst-case avoidance into demonstrable, defensible strategic investment.

## 5.2 The Strategic Potential of Option Value

Real options analysis has long been proposed for strategic problems (de Neufville et al., 2006) and more recently for resilience (Klibi et al., 2024), yet its practical application remains limited because operationalization has been missing. Our contribution is methodological: we show *how* to apply real options logic to a realistic, large-scale network with multiple
failure modes, actions, and constraints.

The key insight is that resilience investments create embedded flexibility. An action implemented today (e.g., supplier qualification) preserves future choices and reduces recovery times for subsequent disruptions. Traditional evaluation ignores this optionality; option-value approaches capture it explicitly. By modeling resilience as sequential decisions over 20 years, we demonstrate that sequencing matters critically. Actions that rank best at $t = 0$ may rank differently at $t = 5$ after prior investments have shifted network vulnerabilities. Option-value logic dynamically adapts recommendations, whereas static methods become locked into suboptimal paths.

The TTR-TTS gap narrowing emerges as the key operational mechanism linking to financial value. Sequential option-based investments reduce the gap from 64 to 59 days (Table 1), systematically targeting the highest-leverage bottlenecks. This operational metric directly translates to financial resilience via daily margin calculations, bridging operations and finance in a way that traditional metrics cannot.

Probability-weighted value proves robust across uncertainty. Sensitivity analysis confirms that option-value sequencing remains optimal across ±25% perturbations in return periods, efficacy bounds, costs, and KPI weights, justifying commitment even under calibration uncertainty. Over a 20-year horizon, option-based sequencing generates sustainable expected gross profit improvements with lower variability than reactive or alternative-metric-based approaches, providing the financial performance case that boards require.

Critically, our framework is not *another* resilience metric—it is a *decision logic* that ranks actions and sequences investments operationally while maintaining financial rigor. This dual grounding (operations + finance) is why it gains traction with practitioners: supply chain leaders understand TTR/TTS; CFOs understand option value and expected returns.
## 5.3 Transferability and Operational Implications

The pharmaceutical network exhibits characteristics common to capital-intensive, long-lead-time industries: 9-180 day recovery times, high-value shelf-life-constrained inputs, 6-18 month implementation timelines for resilience actions, and severe consequences of supply disruption. This profile applies directly to aerospace (9-24 month lead times, $10M+ components), semiconductors (6-12 month lead times, single-source risks), and specialty chemicals (similar recovery profiles and regulatory complexity).

Three boundary conditions determine where the framework adds value. First, recovery times must exceed one week; intertemporal interdependencies and gap-narrowing mechanisms matter only if disruptions last weeks or months. Short-recovery industries (food distribution, retail) see less benefit from sequencing. Second, investments must involve irreversibility or sunk costs; actions with high implementation costs or long lead times (capacity, supplier qualification) involve commitment, whereas flexible, low-cost interventions (demand pooling, information sharing) have minimal option value. Third, disruption timing and magnitude must be uncertain enough that scenario-based valuation diverges meaningfully from point estimates; predictable, seasonal disruptions (monsoon patterns) benefit less from probabilistic analysis.

The framework yields four actionable principles transferable across contexts. First, decoupling investment timing from crisis salience enables real options logic to defer irreversible commitment until uncertainty clarifies. For example, supplier qualification initiated in year 1 yields payoff in year 3-5 when disruptions materialize; decisions are made calmly, not reactively. Second, anchoring in plausible outcomes rather than extremes reduces overcommitment while remaining credible. Probability-weighted analysis (3.6× more conservative than worst-case) allows organizations to justify sustained annual spending to boards as defensible, not speculative. Third, systematically prioritizing gap-narrowing actions directs capital efficiently to bottlenecks by identifying which nodes and failure modes warrant investment. Fourth, institutionalizing rolling re-evaluation reduces inertia by allowing action
reranking as conditions evolve. Managers see that prior investments shift future recommen-
dations, legitimizing adaptation rather than treating it as backtracking.

These principles are operationalized via the six-layer methodology (Sections 3.1–3.6),
which any organization can instantiate using public FEMA data, industry benchmarks,
and expert elicitation. Reproducibility is central: the framework is transparent, parameter
choices are documented, and sensitivity analysis validates robustness.

**5.4 Limitations and Future Research**

Two substantive limitations merit explicit discussion. First, parameterization depends criti-
cally on data quality and expert judgment. Failure-mode intensities, exposure probabilities,
and action efficacies derive from company incident logs (10 years) plus expert workshops.
In data-sparse industries or for novel disruption types (e.g., cyber attacks with limited his-
tory), elicitation quality becomes the limiting factor. Sensitivity analysis helps—we show
robustness to ±25% perturbations—but severe data gaps may limit applicability.

Second, we assume resilience actions improve TTR and TTS without creating new vul-
nerabilities. This holds for structural interventions (backup suppliers, inventory buffers, ca-
pacity add-ons) but may break for complex trade-offs. Centralizing inventory for efficiency,
for example, may increase TTR if a single node fails; distributed redundancy improves re-
silience but raises costs. Our framework assumes actions are additive; richer interaction
modeling would require enhanced formulation.

Future research directions include portfolio optimization across multiple business units to
study shared resilience responsibilities and trade-offs such as inventory pooling and supplier
sharing. Integration of qualitative dimensions—sustainability, regulatory exposure, labor
resilience, community impact—via multi-criteria decision-making would enhance applicabil-
ity to regulated industries. Adaptive control frameworks that update scenarios and re-rank
actions in real-time as disruptions occur and beliefs evolve would move planning from of-
fline to online adaptation. Network effects modeling, where resilience investments at one
node propagate through supply chain topology amplifying or dampening benefits, would capture system-level dynamics. Finally, behavioral validation with practicing supply chain executives would test whether option-value framing actually shifts investment commitment compared to traditional approaches, grounding theory in practice.

Ultimately, this research establishes a methodological foundation for financially rigorous, operationally grounded, and strategically adaptive resilience planning. By bridging operations and finance, we provide managers with tools to justify sustained resilience investment and boards with confidence that commitments are probability-weighted and defensible.
# Appendix A Table of notation and definitions

<table><caption>Table 5: Unified notation used in the paper (sets, processes, financial mapping and KPIs).</caption><thead><tr><th>Symbol</th><th>Name</th><th>Description</th></tr></thead><tbody><tr><td colspan="3"><em>Sets, indices, and horizon</em></td></tr><tr><td>Ω</td><td>Set of scenarios</td><td>All simulated equiprobable scenarios with ω ∈ Ω</td></tr><tr><td>ω</td><td>Scenario index</td><td>A realization of all the random variables over the horizon.</td></tr><tr><td>p(ω)</td><td>Scenario probability</td><td>Probability of scenario ω; from the simulation procedure.</td></tr><tr><td>T</td><td>Time periods</td><td>Discrete decision points indexed t ∈ T.</td></tr><tr><td colspan="3"><em>Network and financial allocation</em></td></tr><tr><td>N</td><td>Nodes</td><td>Suppliers, manufacturing and distribution nodes.</td></tr><tr><td>E</td><td>Directed edges</td><td>Material flow links between nodes.</td></tr><tr><td>L</td><td>Locations</td><td>Geographic locations; l(n) denotes location of node n.</td></tr><tr><td>GP<sub>t</sub></td><td>Aggregate gross profit</td><td>Total supply chain gross profit in period t.</td></tr><tr><td>θ<sub>n,t</sub></td><td>Node profit share</td><td>Fraction of GP<sub>t</sub> attributed to node n; ∑<sub>n</sub> θ<sub>n,t</sub> = 1.</td></tr><tr><td>GP<sub>n,t</sub></td><td>Node gross profit</td><td>GP<sub>n,t</sub> = θ<sub>n,t</sub> GP<sub>t</sub>.</td></tr><tr><td>WD<sub>t</sub></td><td>Working days</td><td>Number of operating days in period t (typically 250).</td></tr><tr><td>DD<sub>n,t</sub></td><td>Daily margin</td><td>Daily impact of downtime: DD<sub>n,t</sub> = GP<sub>n,t</sub>/WD<sub>t</sub>.</td></tr><tr><td colspan="3"><em>Hazards, arrivals, and exposure</em></td></tr><tr><td>M</td><td>Failure modes</td><td>Disruptive modes m ∈ M (hazards, labor, supply, etc.).</td></tr><tr><td>λ<sub>m</sub></td><td>Hazard intensity</td><td>Per-period Poisson arrival rate of mode m.</td></tr><tr><td>Δt</td><td>Period length</td><td>One period (e.g., 1 year).</td></tr><tr><td>K<sub>m,t</sub></td><td>Event count</td><td>Number of mode m events in period t ~ Poisson(λ<sub>m</sub>Δt).</td></tr><tr><td>I<sub>m,t</sub></td><td>Arrival indicator</td><td>1 if mode m occurs in t; ~ Bernoulli(1 - e<sup>-λ<sub>m</sub>Δt</sup>).</td></tr><tr><td>p<sub>n,m,t</sub></td><td>Exposure probability</td><td>Probability node n is impacted by mode m in t.</td></tr><tr><td>ATT<sub>n,m,t</sub></td><td>Exposure draw</td><td>1 if node n exposed to m in t ~ Bernoulli(p<sub>n,m,t</sub>).</td></tr><tr><td>A<sub>n,m,t</sub></td><td>Active impact</td><td>A<sub>n,m,t</sub> = I<sub>m,t</sub> · ATT<sub>n,m,t</sub>; mode occurs and reaches node.</td></tr><tr><td>β<sub>n,m,t</sub></td><td>Severity factor</td><td>Severity multiplier ~ Triangular(a, b, c).</td></tr></tbody></table>
<table><thead><tr><th>Symbol</th><th>Name</th><th>Description</th></tr></thead><tbody><tr><td colspan="3"><em>Recovery and survival times</em></td></tr><tr><td>TTR<sub>n</sub></td><td>Nominal recovery time</td><td>Conservative recovery time for node n (days).</td></tr><tr><td>TTR<sub>n,t</sub><sup>eff</sup>(ω)</td><td>Effective recovery time</td><td>Realized recovery at node n in t under scenario ω.</td></tr><tr><td>TTS<sub>n</sub><sup>base</sup></td><td>Base survival time</td><td>Survival without resilience action (days).</td></tr><tr><td>RA</td><td>Resilience actions</td><td>actions r ∈ RA (inventory, logistics, sourcing, capacity).</td></tr><tr><td>C<sup>(r)</sup></td><td>Action cost</td><td>Investment cost of action r (CapEx, working capital, OpEx).</td></tr><tr><td>ΔTTS<sub>n</sub><sup>(r)</sup></td><td>Promised increment</td><td>Nominal survival-time increase from action r (days).</td></tr><tr><td>ρ<sub>n,r,t</sub>(ω)</td><td>Efficacy factor</td><td>Realized effectiveness of r; ~ Uniform(k<sub>r</sub>, 1), k<sub>r</sub> ∈ (0, 1).</td></tr><tr><td>TTS<sub>n,t</sub><sup>(r)</sup>(ω)</td><td>Realized survival time</td><td>Actual survival with action r at node n in t under ω.</td></tr><tr><td colspan="3"><em>Downtime and gross-profit impact</em></td></tr><tr><td>DT<sub>n,t</sub><sup>(r)</sup>(ω)</td><td>Downtime (days)</td><td>Days node n non-functional: max{0, TTR<sup>eff</sup> - TTS<sup>(r)</sup>}</td></tr><tr><td>GP<sub>t</sub><sup>(r)</sup>(ω)</td><td>Scenario GP at t</td><td>Gross profit in t under ω and action r, accounting for downtime losses.</td></tr><tr><td>GP<sup>(r)</sup></td><td>Total expected GP</td><td>Expected gross profit over horizon under action r.</td></tr><tr><td colspan="3"><em>Key performance indicators</em></td></tr><tr><td>VAR<sup>(r)</sup></td><td>Value improvement</td><td>Expected incremental gross profit from action r vs. baseline.</td></tr><tr><td>ΔCoV<sup>(r)</sup></td><td>Stability gain</td><td>Reduction in coefficient of variation from action r.</td></tr><tr><td>MB<sup>(r)</sup></td><td>Marginal benefit</td><td>Expected incremental profit per dollar invested.</td></tr><tr><td>OV<sup>(r)</sup></td><td>Option value</td><td>Net benefit: expected value improvement minus cost.</td></tr><tr><td>MCS<sup>(r)</sup></td><td>Multi-criteria score</td><td>Weighted aggregate of four KPIs.</td></tr><tr><td colspan="3"><em>Action selection and ranking</em></td></tr><tr><td>RA<sub>i,t</sub></td><td>Rank of action i</td><td>Ranking (1=best) at time t under chosen KPI.</td></tr><tr><td>VRA<sub>i</sub></td><td>Best observed rank</td><td>Minimum rank of action i across periods.</td></tr><tr><td>BestRA</td><td>Robust choice</td><td>Action with lowest VRA value.</td></tr><tr><td>B<sub>t</sub></td><td>Budget at time t</td><td>Available budget for action selection in period t.</td></tr></tbody></table>
# Appendix B Supplementary Data and Calibration Details

This appendix documents how we instantiated the general methodology from Section 3 in collaboration with the pharmaceutical company partner. The material is organized consistently with Section 4.1: (i) company-provided data validated against a 10-year incident history, (ii) external public references (FEMA, industry benchmarks), and (iii) expert elicitation through structured workshops. We then summarize the parameterization of arrivals, exposure, and severity, scenario generation and implementation, back-testing, and validation procedures, providing additional detail beyond the main description in Section 4.1.

## Appendix B.1 Data collection: company, public sources, and expert elicitation

**Company-provided data and 10-year historical validation** The pharmaceutical company supplied a comprehensive dataset spanning 2013–2023, which underpins all baseline parameters used in the empirical study (See Section 4.1 for the main exposition of the case setting). The dataset included: (i) network topology for 1,200 physical nodes, aggregated for illustration purposes into the 13-node representation shown in Figure 3; (ii) node locations, functional classes (suppliers, component manufacturing, finished-goods manufacturing, regional and country distribution centers), and throughput; (iii) financial allocations mapping each modeled node to corporate gross profit via proportions $\theta_{n,t}$ (used in the main text to define $GP_{n,t}^{\text{nom}}$); (iv) baseline operational parameters extracted from company recovery procedures and 10-year incident logs, namely worst-case recovery times $\overline{TTR}_n$ and survival times $TTS_{n,t}^{\text{base}}$ (as reported in Table 6); and (v) candidate resilience actions identified with supply chain and procurement leadership, together with associated costs $C^{(r)}$ and promised survival-time increments $\Delta TTS_r$.

Recovery times were grounded in both documented procedures and observed disruptions. For each historical incident, the company recorded its duration, affected nodes, and financial impact. The maximum observed recovery duration by node type was used to set $\overline{TTR}_n$, which the company confirmed as appropriate for conservative planning. Survival times $TTS_{n,t}^{\text{base}}$ re-
flect product shelf-life constraints and demand urgency; for high-value, shelf-life-constrained pharmaceutical inputs, survival windows are typically 1–4 days, as summarized in Table 6.

We consider five resilience archetypes—Supply Base, Manufacturing Base, Contract Base, Distribution Base, and Regional Base—corresponding to four broad action classes: (1) inventory buffers, (2) backup contracts/logistics, (3) dual sourcing, and (4) capacity expansions. Each arch type has documented costs $C^{(r)}$ (CapEx/working capital/OpEx), implementation timelines, and promised survival-time increments $\Delta TTS_n^{(r)}$, consistent with the company's historical capital project data (see Section 4.1).

**External public references and hybrid calibration** For parameters not available in company records, we combined public data and published benchmarks. Natural-hazard return periods were obtained from the FEMA National Risk Index database (county-level estimates for earthquakes, floods, hurricanes, tornadoes, wildfires, and volcanic events). For each facility location, we extracted the relevant county return periods and converted them to arrival intensities and per-period occurrence probabilities following the Poisson-based logic described in the Vulnerability Layer (Section 3.2). These hazard-specific parameters feed directly into the arrival process modeled through Eqs. (2)-(3) in the main text.

For non-natural-hazard failure modes (labor, supply, financial, operations, distribution, transportation), no comparable public database exists. We therefore used company incident logs (2013–2023) to calibrate empirical estimates, which were subsequently reviewed and adjusted in expert workshops to reflect anticipated trends (e.g., increasing cyber risk). Industry recovery benchmarks from Klibi et al. (2012) and Berle et al. (2011) provided recovery-time percentiles by node type. These percentiles informed the bounds of the triangular severity distributions used in Eq. (5): minimum, mode, and maximum recovery-time multipliers relative to $TTR_n$. This hybrid approach combines company-specific knowledge with external validation, consistent with the calibration logic summarized in Section 4.1.
**Expert elicitation and structured workshop validation** Three structured workshops with company personnel were used to refine and validate all calibrated parameters.

Workshop 1 involved supply chain and operations managers, who reviewed baseline *TTR/TTS* parameters, discussed recovery procedures at each node, identified candidate resilience actions, and confirmed cost ranges. Workshop 2 brought together risk managers and operations personnel to calibrate failure-mode intensities, review the 10-year incident history, and estimate node-specific exposure probabilities *p*<sub>n,m,t</sub>, which are used in Eq. (4). Workshop 3 involved senior operations and finance personnel and focused on validating tri- angular severity distributions (Eq. (5)), confirming action efficacy bounds (entering Eq. (7)), discussing realistic budget levels *B*<sub>t</sub>, and reviewing pilot scenario results.

Node-specific exposure probabilities $p_{n,m,t}$ were estimated using three information sources: (i) geography (e.g., whether nodes are located in hazard-prone regions for each mode), (ii) operational capability (e.g., presence of backup generators, inventory buffers, or redundant suppliers), and (iii) historical frequency by node type. Exposure probabilities range from low values for well-protected manufacturing sites in low-hazard regions to higher values for more exposed suppliers. Recovery severity distributions were calibrated by eliciting (minimum, mode, maximum) triplets for each $(n, m)$, with the mode anchored at $\overline{TTR}_n$ and the bounds checked against published percentile ranges. Action efficacy lower bounds $k_r$ were elicited to capture implementation risk differences among action classes (inventory, logistics, dual sourcing, capacity), in line with the efficacy modeling in Eq. (7).

All workshops were documented via decision logs that recorded parameter values, ra-
tionales, and agreed adjustments. These logs support the reproducibility of the calibration
process for other industries or networks.

**Appendix B.2 Scenario modeling, generation, and implementation**

Failure modes were parameterized using the hybrid approach described above: company
incident logs provided empirical frequencies; FEMA and published benchmarks informed
severity ranges; and expert workshops validated and refined all values.

The empirical study considers six representative failure modes (financial, HR/labor, operations, distribution, transportation, supply) across all time periods. Arrival characteristics follow the Poisson process in Eqs. (2)-(3), exposure is modeled via Eq. (4), and severity/effective recovery times are handled through Eqs. (5)-(6).

We generated 1,000 scenarios per decision cycle using a combination of Latin Hypercube Sampling and Monte Carlo simulation. Each scenario $\omega \in \Omega$ comprises consistent draws across four uncertainty dimensions: arrivals $I_{m,t}$ (Eqs. (2)-(3)), node-level exposure masks $ATT_{n,m,t}$ (Eq. (4)), severity factors $\beta_{n,m,t}$ (Eq. (5)), and action efficacy $\rho_{n,r,t}(\omega)$ (Eq. (7)). All scenarios are equiprobable with probability $p(\omega) = 1/|\Omega|$, as assumed in the Evaluation Layer (Section 3.4). Common random numbers were used when comparing alternative resilience actions to ensure that differences in key performance indicators arise from the actions themselves rather than sampling noise.

Back-testing and validation followed two complementary mechanisms. First, we performed out-of-sample back-testing against company's historical data by calibrating the framework on an initial subset of years and evaluating whether the resulting risk rankings anticipated vulnerable node-mode combinations observed in later years. The framework correctly placed the vast majority of disrupted node-mode pairs in higher-risk deciles, supporting the operational relevance of the calibrated arrivals, exposure, and severity parameters. Second, we conducted sensitivity analyses across key parameter ranges (return periods, action efficacy bounds, baseline TTS, action costs, and KPI weights). Across these perturbations, the option-value-based sequencing logic remained robust and consistently outperformed worst-case-based approaches, as reported in Section 4.

## Base-case network parameters

Table 6 documents baseline recovery times $\overline{TTR}_n$, survival times $TTS_{n,t}^{\text{base}}$, and TTR-TTS gaps for all 13 aggregated nodes at $t_0$. These values are derived from company operational
procedures, validated against the 10-year incident history, and cross-checked against industry benchmarks. They serve as inputs to the Vulnerability and Resilience Action layers (Sections 3.2 and 3.3) and define the initial state from which sequential investments proceed.

<table><caption>Table 6: Base-case network parameters at $t_0$. *TTR* (time to recover) derived from company recovery procedures and 10-year incident history; *TTS* (time to survive without action) reflects product shelf life and demand urgency. The *TTR-TTS* gap identifies critical vulnerabilities where resilience investment is most impactful.</caption><thead><tr><th>Node</th><th>Node Type</th><th>Baseline TTR (days)</th><th>Baseline TTS (days)</th><th>TTR-TTS Gap (days)</th></tr></thead><tbody><tr><td>S1</td><td>Supplier</td><td>9</td><td>1</td><td>8</td></tr><tr><td>S2</td><td>Supplier</td><td>67</td><td>1</td><td>66</td></tr><tr><td>S3</td><td>Supplier</td><td>28</td><td>1</td><td>27</td></tr><tr><td>S4</td><td>Supplier</td><td>43</td><td>1</td><td>42</td></tr><tr><td>CM1</td><td>Component Mfg</td><td>61</td><td>1</td><td>60</td></tr><tr><td>CM2</td><td>Component Mfg</td><td>86</td><td>2</td><td>84</td></tr><tr><td>M1</td><td>Final Mfg</td><td>65</td><td>1</td><td>64</td></tr><tr><td>M2</td><td>Final Mfg</td><td>180</td><td>4</td><td>176</td></tr><tr><td>RDC1</td><td>Regional DC</td><td>147</td><td>3</td><td>144</td></tr><tr><td>CDC1</td><td>Country DC</td><td>14</td><td>1</td><td>13</td></tr><tr><td>CDC2</td><td>Country DC</td><td>52</td><td>1</td><td>51</td></tr><tr><td>CDC3</td><td>Country DC</td><td>67</td><td>1</td><td>66</td></tr><tr><td>CDC4</td><td>Country DC</td><td>14</td><td>1</td><td>13</td></tr></tbody></table>

## Failure mode parameters

Table 7 summarizes the calibrated parameters for the six failure modes and four recurrence tiers used in the empirical study. For each mode-tier combination, the table reports the return period, implied annual occurrence probability (consistent with Eqs. (2)-(3)), and the ranges used to calibrate severity multipliers and action efficacy factors. These ranges are consistent with the triangular and uniform distributions appearing in the Vulnerability and Resilience Action layers; they are not additional equations but numerical instantiations of the general model in Section 3.

The table complements the qualitative description in Section 4.1 by making explicit how frequent operational disruptions and rare tail events are differentiated in terms of arrival likelihood, recovery-time amplification, and the scope for resilience actions to be effective.
<table><caption>Table 7: Failure mode parameters at $t_0$. Six modes (financial, HR/labor, operations, distribution, transportation, supply) at four recurrence tiers. Return periods and probabilities calibrated from company incident logs and FEMA data. Severity (triangular multiplier on TTR) and efficacy (uniform factor on promised action benefit) derived from expert elicitation and industry benchmarks. Annual modes capture frequent operational disruptions; 30-year modes capture rare tail events.</caption><thead><tr><th>Failure Mode</th><th>RP (yr)</th><th>Annual Prob.</th><th>Sev. Min</th><th>Sev. Max</th><th>Eff. Min</th><th>Eff. Max</th></tr></thead><tbody><tr><td colspan="7">Annual modes (RP = 1 year, q<sub>m,t</sub> ≈ 63%)</td></tr><tr><td>Financial</td><td>1.00</td><td>0.630</td><td>0.05</td><td>0.19</td><td>0.05</td><td>0.19</td></tr><tr><td>HR/Labor</td><td>1.00</td><td>0.630</td><td>0.05</td><td>0.19</td><td>0.05</td><td>0.19</td></tr><tr><td>Operations</td><td>1.00</td><td>0.630</td><td>0.05</td><td>0.19</td><td>0.05</td><td>0.19</td></tr><tr><td>Distribution</td><td>1.00</td><td>0.630</td><td>0.05</td><td>0.19</td><td>0.05</td><td>0.19</td></tr><tr><td>Transportation</td><td>1.00</td><td>0.630</td><td>0.05</td><td>0.19</td><td>0.05</td><td>0.19</td></tr><tr><td>Supply</td><td>1.00</td><td>0.630</td><td>0.05</td><td>0.19</td><td>0.05</td><td>0.19</td></tr><tr><td colspan="7">Decennial modes (RP = 10 years, q<sub>m,t</sub> ≈ 9.5%)</td></tr><tr><td>Financial</td><td>10.0</td><td>0.095</td><td>0.19</td><td>0.39</td><td>0.19</td><td>0.39</td></tr><tr><td>HR/Labor</td><td>10.0</td><td>0.095</td><td>0.19</td><td>0.39</td><td>0.19</td><td>0.39</td></tr><tr><td>Operations</td><td>10.0</td><td>0.095</td><td>0.19</td><td>0.39</td><td>0.19</td><td>0.39</td></tr><tr><td>Distribution</td><td>10.0</td><td>0.095</td><td>0.19</td><td>0.39</td><td>0.19</td><td>0.39</td></tr><tr><td>Transportation</td><td>10.0</td><td>0.095</td><td>0.19</td><td>0.39</td><td>0.19</td><td>0.39</td></tr><tr><td>Supply</td><td>10.0</td><td>0.095</td><td>0.19</td><td>0.39</td><td>0.19</td><td>0.39</td></tr><tr><td colspan="7">Vicennial modes (RP = 20 years, q<sub>m,t</sub> ≈ 4.9%)</td></tr><tr><td>Financial</td><td>20.0</td><td>0.049</td><td>0.39</td><td>0.79</td><td>0.39</td><td>0.79</td></tr><tr><td>HR/Labor</td><td>20.0</td><td>0.049</td><td>0.39</td><td>0.79</td><td>0.39</td><td>0.79</td></tr><tr><td>Operations</td><td>20.0</td><td>0.049</td><td>0.39</td><td>0.79</td><td>0.39</td><td>0.79</td></tr><tr><td>Distribution</td><td>20.0</td><td>0.049</td><td>0.39</td><td>0.79</td><td>0.39</td><td>0.79</td></tr><tr><td>Transportation</td><td>20.0</td><td>0.049</td><td>0.39</td><td>0.79</td><td>0.39</td><td>0.79</td></tr><tr><td>Supply</td><td>20.0</td><td>0.049</td><td>0.39</td><td>0.79</td><td>0.39</td><td>0.79</td></tr><tr><td colspan="7">30-year modes (RP = 30 years, q<sub>m,t</sub> ≈ 3.2%)</td></tr><tr><td>Financial</td><td>30.0</td><td>0.032</td><td>0.79</td><td>1.00</td><td>0.79</td><td>1.00</td></tr><tr><td>HR/Labor</td><td>30.0</td><td>0.032</td><td>0.79</td><td>1.00</td><td>0.79</td><td>1.00</td></tr><tr><td>Operations</td><td>30.0</td><td>0.032</td><td>0.79</td><td>1.00</td><td>0.79</td><td>1.00</td></tr><tr><td>Distribution</td><td>30.0</td><td>0.032</td><td>0.79</td><td>1.00</td><td>0.79</td><td>1.00</td></tr><tr><td>Transportation</td><td>30.0</td><td>0.032</td><td>0.79</td><td>1.00</td><td>0.79</td><td>1.00</td></tr><tr><td>Supply</td><td>30.0</td><td>0.032</td><td>0.79</td><td>1.00</td><td>0.79</td><td>1.00</td></tr></tbody></table>

## Reproducibility and code availability

All scenario generation, network propagation, and KPI computation code is maintained under version control and is available from the corresponding author on reasonable request. The pharmaceutical case-study dataset remains confidential per company policy. However, the empirical setup is fully reproducible using: (i) public FEMA data, (ii) published benchmarks for recovery-time percentiles, (iii) the anonymized parameters reported in Tables 6 and 7, and (iv) standard open-source *R* libraries for sampling and simulation.
# Appendix C Supplementary Results

This appendix presents complementary figures and analyses that extend the main empirical findings. The results illustrate the full action portfolio at key decision points and compare alternative KPI-based evaluation approaches.

## Full resilience action portfolio at decision point $t_0$

Figure 15 extends Figure 12 by presenting all candidate resilience actions evaluated at the first decision point, rather than the two actions highlighted in the main text. The expanded view allows practitioners to observe cost-value trade-offs across the complete action set and to identify which actions offer favorable risk-return profiles given the current network state. The selection status indicates whether each action was ranked as the top choice under the option-value criterion.

<figure><img src="image_16.png" /><figcaption>Figure 15: Complete resilience action portfolio at $t_0$: cost versus value trade-offs for all candidate actions. Actions in the high-value, low-cost region are preferred under the option-value criterion.</figcaption></figure>

## Comparison of evaluation approaches across decision periods

Figure 16 complements Figure 13 in the main text by displaying the temporal evolution of action rankings under all four KPI methods (value improvement, stability gain, marginal
benefit, and option value) across five sequential decision periods. A key observation is that the option-value approach systematically rotates recommendations across diverse resilience actions, whereas the alternative metrics tend to converge on a limited subset. In practitioner settings, this “diversity of investment” behavior mitigates lock-in effects and aligns with observed patterns in which managers face pressure to “double-down” on prior investments rather than rebalance.

<figure><img src="image_17.png" /><figcaption>Figure 16: Action ranking trajectories under alternative KPI-based selection criteria across five sequential decision cycles ($t \in \{0, 1, 2, 3, 4, 5\}$). Option-value ranking rotates through the action set, while other metrics exhibit stickiness to repeated selections.</figcaption></figure>

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