The price of resilience and the cost of equity in a budget-centric framework for humanitarian logistics

Humanitarian supply networks must simultaneously achieve operational efficiency, ensure equitable distribution across vulnerable populations, and maintain service continuity under disruptions; yet few frameworks jointly quantify these trade-offs in actionable budget terms. We address this gap by developing a hierarchical optimization pipeline that integrates three objectives in a principled sequence: (i) budget-constrained service maximization via a multi-commodity network flow model, (ii) distributional equity analysis using a proportional service floor with a closed-form threshold, and (iii) adversarial resilience assessment through validated k-interdiction. The term “adversarial” refers not solely to malicious actors but to worst-case disruption scenarios—including natural hazards, infrastructure failures, and conflict-induced damage—that humanitarian planners must anticipate as a matter of prudent risk management. We benchmark our greedy interdiction heuristic against candidate-set exact enumeration over a restricted arc set, achieving 0% optimality gap (within the candidate set) for k ≤ 2 and only 0.87% gap at k=3 while running 620 × faster. Applied to a national-scale Colombian network (55 nodes, 124 arcs, six commodity groups), the model identifies a knee budget of $491 M delivering 9,911 service units. We derive a critical equity threshold τ*=0.63 that delineates a costless equity region—where fairness improvements impose no efficiency loss—from the true trade-off region. Under worst-case three-arc interdiction, greedy attack degrades service by 44% versus 29% under flow-ordered removal, revealing 52% higher relative damage that conventional heuristics miss. The Price of Resilience metric translates continuity targets into budget terms: recovering baseline service after a single adversarial failure requires an additional $1.06 B in budget (a 217% increase), while recovery from three coordinated failures demands an additional $1.66 B (a 337% increase). A parametric sensitivity analysis across 28 scenarios confirms that while the numerical value of τ* is instance-dependent—varying from 0.03 to 0.99 with demand heterogeneity as the dominant driver—the structural two-regime property persists across all tested scenarios. A seven-scenario uncertainty analysis under ± 20% perturbations to demand, supply, and cost shows that the Price of Resilience ranges from 2.87 × to 4.62 × baseline budget at k=3, while the cost of equity remains below 0.6% across all scenarios, confirming that both metrics are robust to plausible parameter uncertainty. Benchmarking against weighted-sum scalarization demonstrates that the hierarchical pipeline achieves Pareto-competitive outcomes while producing actionable decision rules—the equity threshold, the Price of Resilience, and protect-versus-pay guidance—that simultaneous scalarization cannot generate. These policy-facing quantities translate abstract trade-offs into implementable rules for budgeting, infrastructure hardening, and contingency planning.