Securing the Flow: Maritime Energy Resilience under Correlated and Decision-Dependent Disruptions

TL;DR

This paper presents a novel stochastic multi-commodity flow model for resilient maritime energy networks, incorporating correlated disruptions, decision-dependent probabilities, and risk mitigation, with applications to Indian energy imports.

Contribution

It introduces a new MILP reformulation for decision-dependent probabilities and a Benders decomposition approach for large scenario sets, advancing maritime energy resilience modeling.

Findings

The model achieves exact solutions for scenario sets up to 729.

VSS is 14.8%, indicating significant value from stochastic modeling.

The network shows structural joint-failure resilience, absorbing correlated disruptions.

Abstract

We develop a two-stage stochastic multi-commodity flow model to design a resilient maritime energy supply network under correlated chokepoint disruptions. A planner selects strategic inventories and infrastructure activations prior to uncertainty resolution, then routes crude oil, LNG, LPG, and fertilizer through a capacitated network. Three features distinguish this model: disruption scenarios are \emph{correlated}, reflecting the reality that proximate chokepoints (e.g., Hormuz, Bab el-Mandeb) fail jointly; scenario probabilities depend endogenously on first-stage decisions via affine distortion, formalizing \emph{risk exposure through utilization}; and a mean-CVaR objective mitigates tail-risk shortages. Methodologically, the decision-dependent probability model admits an exact MILP reformulation via McCormick linearization. CVaR preserves scenario-wise decomposability, and our Benders decomposition with corridor-based group-failure cuts converges finitely. The model is calibrated to Indian maritime energy imports (16 nodes, 28 arcs) using EIA, UNCTAD, World Bank, and operational data from the 2026 Hormuz crisis. Benders recovers the extensive-form optimum for scenario sizes up to $|S|=729$ with a constant iteration count (10-11). Empirically, the value of the stochastic solution (VSS) is 14.8%; the value of decision-dependent probabilities (VEP) ranges from 0.93% to 8.18%. The mean-CVaR frontier exhibits a design phase transition at confidence level $\alpha\approx 0.75$. Notably, the value of modeling correlation is identically zero across stress tests: the network's diversified portfolio absorbs joint-corridor disruptions using the same hedging mechanisms as single-corridor disruptions (\emph{structural joint-failure resilience}). Finally, LPG emerges as the most exposed commodity, whereas crude oil is fully hedgeable via reserves and pipeline bypasses.