Estimating the cascading global impacts of gas disruptions in Qatar

Introduction and Background

Qatar is one of the world’s largest exporters of liquefied natural gas (LNG), with production centered at Ras Laffan Industrial City, the largest LNG complex in the world. Accounting for 20% of globally traded LNG, Qatar is a critical node in the energy security of major importing economies across Asia (China, India, Japan, South Korea) and Europe, making international markets highly sensitive to any disruption in its output.

Most Qatari exports transit through the Strait of Hormuz, a narrow and geopolitically exposed corridor that adds considerable systemic risk to global energy supply. In early March 2026, Iranian strikes on key LNG infrastructure at Ras Laffan and Mesaieed took approximately 17% of Qatar’s LNG export capacity offline, equivalent to roughly 13 million tons per year, with recovery timelines potentially extending over several years [13].

The disruption to Qatar’s gas sector is reverberating across the world, with Asia and Europe bearing the heaviest burden. In India and Pakistan, where LNG and liquefied petroleum gas (LPG) imports are heavily sourced from Qatar and routed through the Strait of Hormuz, supply tightening has already disrupted LPG distribution, leaving millions unable to cook and forcing the closure of small businesses and restaurants [2]. The Philippines has declared a national emergency in response to rapidly rising fuel prices and introduced shortened workweeks, while Pakistan has closed schools to conserve energy [20].

The reported effects extend to countries with no direct trade relationships with Qatar. For example, even though the US is a major producer and net exporter of gas, a disruption in Qatar’s gas sector results in higher prices for American households. When Qatari supply falls, global gas prices rise, causing US gas to be diverted to higher-paying export markets.

Despite the scale of these disruptions, the cascading second- and third-order effects on the global economy remain poorly understood. Beyond Qatar, major LNG producers include Australia, Norway, Russia, Canada, and Algeria, and a key open question is whether these countries can fill supply gaps through export reallocation or increased production. Addressing this requires modeling tools capable of capturing the complex interdependencies that allow shocks to propagate across sectors and countries.

Multiregional input-output (MRIO) models are widely used for this purpose, as they explicitly represent how production linkages transmit shocks through global supply networks [6]. Firm-level and network-based studies confirm that disruptions can generate substantial indirect effects, particularly in supply chains characterized by limited substitutability and dense interconnections [12, 23]. Extensions of MRIO frameworks to energy systems have further shown that interregional trade can partially offset demand deficits following production disruptions, though the degree of mitigation depends critically on network structure and capacity constraints [10].

These approaches have important limitations. Conventional MRIO models assume fixed production structures, precluding trade reallocation across alternative suppliers under binding constraints, and can yield economically infeasible outcomes when supply and demand shocks occur simultaneously [17]. Koks and Thissen [15] address some of these shortcomings by combining multiregional supply-use structures with cost-minimizing optimization, incorporating supply constraints, production inefficiencies, and substitution across suppliers. However, in their framework reallocation is driven by optimization objectives rather than grounded in existing trade relationships and capacity constraints. As a result, neither conventional MRIO models nor optimization-based extensions fully capture how production and trade adjust when reallocation is shaped by real-world structural constraints.

In this study, we develop a global MRIO optimization model that incorporates disruption, reallocation, and capacity expansion using the GTAP 12 database. We use it to examine how shocks to Qatar’s gas sector (QAT-GAS) propagate through international supply chains.

We construct three hypothetical disruption scenarios: varying levels of gas disruption, partial reallocation by six largest gas-producing countries (TOP-GAS) outside the Gulf region, and increased gas production by these same countries. Together, these scenarios allow us to unravel the relative importance of supply shocks, trade reallocation, and production responses. Our modeling framework captures both direct effects (reduced gas supply to importing countries) and indirect effects (downstream impacts on industries that rely on gas as an input). A reduction in gas supply not only affects the energy sector; it cascades through the economy, leading to broader output and final demand losses. We consider a global networked trade flow model where we model the industries and final demand region of each country as nodes and flow of goods between them as edges with capacities. Using this networked model of trade flow, the effects of a localized gas disruption can be traced across sectors and countries, showing how a single, highly connected node, in our case, Qatar’s gas sector, can generate ripple effects reaching nearly every region in the world. Furthermore, by comparing outcomes across scenarios, we can assess the extent to which global supply chains exhibit resilience or vulnerability, and identify key regions and sectors that are most exposed to such shocks. This approach provides a systematic basis for understanding the broader economic implications of energy supply disruptions and the potential effectiveness of alternative adjustment mechanisms.

Results

We consider three disruption scenarios as described in Table 1. (1) All trade linkages (edges) originating from Qatar’s gas sector have their capacities reduced uniformly by 30%, 50%, and 70%, representing varying levels of supply contraction. This scenario captures the shock to global gas supply and its cascading effects on dependent sectors and countries, with no mitigation; (2) The six largest gas-producing countries outside the Gulf region partially reallocate their exports to global markets, with adjustments of 10%, 20%, and 30% of the flow, reflecting trade diversion and substitution effects under constrained supply conditions; (3) These same producers increase their primary inputs by 5%, 10%, and 20% in the gas sector. To accommodate the additional production, enabled by the increase in primary resources, global trade edge capacities are increased proportionally, enabling the redistribution of supply across the network.

Component	Scenario 1	Scenario 2	Scenario 3
Disruption: Reduction in Flow Capacity (QAT-GAS)
Edges affected	QAT-GAS → ALL	QAT-GAS → ALL	QAT-GAS → ALL
Magnitude ($\delta$)	{0.3, 0.5, 0.7}	0.3	0.3
Adaptation: Increase in Flow Capacity
Edges affected	–	TOP-GAS → ALL	GLOBAL
Magnitude ($\alpha$)	–	{0.1, 0.2, 0.3}	{0.05, 0.1, 0.2}
Adaptation: Increase in Production Capacity through primary inputs
Firms affected	–	–	TOP-GAS
Magnitude ($\beta$)	–	–	{0.05, 0.1, 0.2}

We develop a linear programming (LP) approach to find solutions to MRIO models for these scenarios using the GTAP 12 database, which covers 163 countries and 65 sectors (see Section 4 for details). This is used for the industry-to-industry flow linkages within each country and between countries to build our networked trade model. The sectors of each country (e.g., US-Gas, China-electronics) form the nodes, and the flow linkages form the directed edges, whose capacities are originally set to the MRIO values in USD. Additionally, there is one ‘sink’ node per country to represent the final demand. We analyze properties of a solution to the LPs for these scenarios. While these are feasible solutions, we note that solutions need not be unique, and some country specific properties might vary for other solutions.

Throughout the text, we denote the six Gulf countries of Saudi Arabia, Qatar, UAE, Kuwait, Bahrain, and Oman together as GULF. Also, we denote the set of six top gas-producing sectors by gross output, excluding GULF, as TOP-GAS, namely, those of US, Russia, Norway, Canada, Australia and Algeria.

Scenario 1: Disruption without any mitigation

We model the disruption by proportionally reducing the flow capacities of edges from QAT-GAS to all other nodes, controlling the disruption percentage with a parameter $\delta$. In this baseline scenario, all other flow capacities remain unchanged, which implies that the flows cannot exceed their original values to mitigate the demand loss. In Figure 1 (a), we show the original gas flows from major gas producers to different regions of the world as a heatmap, illustrating the dependency structure on gas. These gas flows are used either as intermediate inputs (i.e., as input to other firms) or as final demand by the households. Figure 1 (b) reports the loss of gas flows due to the disruption (i.e., the original gas flows minus the flows under disruption). The impacted regions are largely those that were directly dependent on Qatar gas. While the impact is global, it is most concentrated in Asia, where several regions experience gas supply shortfalls of up to 10 billion USD¹. Western Europe also incurs losses on the order of billions. Beyond Qatar, gas flows from the rest of the world (ROW), which includes other Gulf producers, are affected to a lesser extent, indicating indirect dependence on Qatari gas as an input into their own production. This secondary disruption further amplifies losses, particularly across Asia and Europe.

Next, we examine the cascading effects of these gas-flow disruptions on the overall economies of countries around the world. Figure 2 shows the negative changes in final demand and gross output (compared to the original values, i.e., Scenario 1 - Original) aggregated at a country level and visualized as global heatmaps. Nearly all countries are affected to some degree, but regions in Asia and Europe are affected the most, aligning closely with the gas flow losses seen in Figure 1. In terms of loss in final demand, the large Asian economies of India, China, Korea are heavily affected, followed by Italy and the US. This is directly connected to the loss of gas supply from Qatar, as seen in Figure 1. However, the US is an exception here, as the direct flow of Qatar gas to the US is negligible. This demonstrates the impact of indirect channels of disruption, for example, the directly affected Asian sectors propagating production losses to US customers. Output losses are somewhat more contained but have overlapping geographic regions, with additional impacts observed in Taiwan. This suggests that gas from Qatar is a critical input to industry in these regions, and that a disruption in this input can cascade through their highly integrated internal economies. Figure 3 shows the aggregate losses for the top 5 countries as the disruption parameter $\delta$ varies. As $\delta$ increases from 0.3 to 0.5, the losses nearly double for India and China, whereas losses in other countries rise more gradually. This difference reflects the varying dependence on gas imports and downstream processing capacity across economies.

Scenario 2: Disruption combined with reallocation

In this scenario, we assume that the outgoing edges from TOP-GAS (a set of top six gas-producing firms by gross output excluding GULF) can change their flow capacity by $\alpha\%$. That is, the flow on these outgoing edges can increase by at most $\alpha\%$ from its original value (i.e., at $\delta= 0$), and decrease by at most $\alpha\%$ below its Scenario 1 value². Note that the disruption remains the same as in Scenario 1. Further, for all edges (other than the outgoing edges from TOP-GAS), the flow capacity remains the same as before.

Note that in this scenario, we assume that these sectors do not increase their production as they are still limited by their inputs, but can only reallocate out-flows to their recipient firms. Our linear programming approach (Section 4) finds the optimal re-allocation under these constraints. fig:1c shows the change in distribution of gas flows to different regions (compared to Scenario 1, i.e., Scenario 2 - Scenario 1) when reallocation is allowed by TOP-GAS. We find significant reallocation of gas to the affected regions, with Asia and Western Europe being the major beneficiaries. Regions in red see a decline in flow and regions in green are gaining flow. While Eastern Asia sees an increase in gas flows from all the major gas producers, especially Russia and the US (also stated in articles [19, 5]), Western Europe relies more on increased gas supplies from Algeria and Canada. The US redirects its gas flows mostly towards Asia instead of Europe. Notably, Western Asia benefits little from the reallocation, with Southern Asia also losing out to East Asia in attracting larger gas flows. Australia also redirects its flows to Eastern Asia and away from the rest of the regions. Notably, these additional flows are coming at the cost of domestic supply in TOP-GAS regions, which can been seen in the declines to Oceania, North America, North Africa, Eastern Europe etc. In this scenario, the optimal strategy tends to partly redirect domestic supply towards critically unmet demand abroad. This suggests that when given additional flow capacities, gas suppliers prioritize systemically important sectors in the world, which are often located in East Asia and Western Europe, if the goal is to maximize the overall output and final demand in the world.

When we assess the global economic losses in Figure 4, we see that the increase in flow capacity leads to wider

improvements in output and final demand in Asia and Southern Europe. Countries such as China, Korea, and Italy benefit from increased gas flows through higher economic output. In TOP-GAS countries (e.g., US, Canada, Australia), redirecting gas away from domestic consumption toward foreign unmet demand (shown in fig:1c) yields a net positive effect: the aggregate demand and output of their nation-wide economies increases above the baseline values in Scenario 1 (Figure 4). This demonstrates that prioritizing exports to “bottleneck” firms abroad over domestic supply can lead to aggregate gains in the domestic economies. This suggests that redirected flows propagate through global supply chains, ultimately generating increased economic demand and output in the exporting countries. Figure 5 shows the loss in aggregate final demand and outputs for the top 5 countries as the reallocation parameter $\alpha$ varies, while keeping the disruption parameter $\delta$ fixed. We observe that the recovery due to this adaptation is not uniform. Countries like the US, Korea, and China reduce their losses by up to two orders of magnitude as $\alpha$ is doubled from 0.1 to 0.2. This contrasts with India, which sees much more modest improvement, while Pakistan shows no improvement despite the possibility of reallocation.

Scenario 3: Disruption mitigated through increased gas production

In this scenario, we assume that TOP-GAS firms increase their primary input by $\beta\%$ to help fulfill the unmet demands due to the disruption. For any given firm, effective utilization of this additional capacity requires corresponding increases in both intermediate inputs and outbound flow capacities. In the absence of sufficient downstream flow capacity, firms may be unable to realize higher production levels without generating excess or unused output.

Accordingly, we first augment the primary inputs of the TOP-GAS firms by $\beta\%$. Even a localized increase in demand or production can propagate through the network, inducing higher input requirements across interconnected sectors and regions. This creates a non-trivial allocation problem: which specific edge capacities should be expanded to support the intended production increase? To address this, we adopt a simplified approach: we allow a uniform expansion of flow capacities across all edges, while restricting the increase in primary inputs to the selected TOP-GAS firms. This ensures that the augmented production can be effectively distributed throughout the network without binding capacity constraints. Just like in Scenario 2, we control the reallocation by setting $\alpha= \beta$. Each edge can increase its flow by $\alpha\%$ over its original value and can decrease by up to $\alpha\%$ below its Scenario 1 values.

fig:1d shows the change in distribution of gas flows from major producers to different regions as compared to the Scenario 1 values. With additional production capacity, all TOP-GAS countries improve their supply to affected regions as well as to their own economies. Invariably, domestic gas demand improves significantly in each producer country. The gains for Eastern Europe and Western Asia intensify as compared to Scenario 2 (in Figure 1(c)). Differing from Scenario 2, there is increased Australian gas flow to Southeastern Asia, Russian gas to Eastern and Western Europe, and American gas to South America and Western Europe. Western Asian gas supply is now much improved compared to Scenario 2, bolstered with additional flows from Algeria and the US. There is only a modest increase in flows to Southern Asia, even though the region faces large shortfalls in gas.

In Figure 6, we plot the global heatmap of changes in final demand flows and gross output per country. We measure these changes relative to Scenario 1 values. The combination of production expansion and an increase in global flow capacity substantially mitigates losses, particularly in large economies such as the US, China, and India. At the same time, reallocation redistributes impacts on final demand, with countries in the Americas experiencing relatively greater losses compared to Scenario 1. Gains in gross output are observed across much of the world, including heavily affected economies such as China, India, and Italy. This suggests that enabling reallocation over all edges can lead to higher intermediate demand relative to final demand, even though we give equal weights to both in our optimization objective. TOP-GAS group, the benefits accrue disproportionately to countries with strong integration into global gas-dependent supply chains. In particular, economies such as India, China, and South Korea capture a significant share of the gains, alongside the TOP-GAS countries themselves. Figure 7 shows the sensitivity of the losses of the 5 most affected countries to the parameter $\beta$. Similar to Scenario 2, the recovery is heterogeneous with countries like India and Pakistan improving only modestly with the increase in $\beta$, while others like China and Korea see substantial improvements. Notably, China’s output losses decline sharply, from approximately 630 billion USD to nearly zero as $\beta$ increases from 0.05 to 0.1, underscoring the uneven distribution of resilience across economies.

Disruption propagation networks

While MRIO models quantify overall impacts, the specific pathways through which disruptions propagate are not immediately captured in the aggregated results. To better understand how shocks propagate in a highly interconnected system, it is useful to study disruption propagation networks within the global input–output network. We define a disruption propagation network as a directed graph consisting of edges $(u,v)$ over which the flow after disruption reduces more than a defined loss threshold. These networks can help identify critical bottlenecks and amplification nodes where the shock either intensifies or can be effectively mitigated through policy interventions.

In Figure 14 (in the appendix), we show the distribution of the shortest path distances for all nodes (i.e., sectors and final demand regions) from the source node, QAT-GAS, in the disruption propagation network. We show that the structure of this network is very different depending on the loss threshold: a lower threshold generates a network which is not only larger and has more nodes, but also more interconnected as evidenced by the narrow shape of the distribution. A lower threshold creates shorter paths from the source to each node in comparison to a higher threshold. For the purpose of our following study, we use a higher loss threshold of 100 mUSD to filter out less important paths of disruption propagation. We study two such partial networks below: one focusing on US final demand and the other on Taiwan’s electronic sector.

Figure 9 shows the indirect effects of a 30% disruption in Qatar’s gas sector on chemicals, machinery, electronics, and final demand across economies. The immediate impact falls on China’s chemical sector (CHN-CHM) and Qatar’s petroleum and coal products sector (QAT-P-C). The initial disruption is amplified as it propagates through the network. Despite originating from a 30% disruption, this leads to a 100% disruption in the flow from China’s Rubber and Plastic Products manufacturing sector (CHN-RPP) to final demand of the US (Y-USA) in the first subgraph, and 91.75% from CHN-RPP to Taiwan’s electronics sector (TWN-ELE) in the second subgraph. Naptha, a co-product of LNG production, feeds into petrochemicals and helium into electronic equipment (CHN-EEQ), with losses rippling further to Taiwan’s electronics sector (TWN-ELE). Gas supply constraints also propagate through Taiwan’s electricity sector (TWN-ELY), disrupting electronics manufacturing and affecting Korea’s electronics sector (KOR-ELE). Korea’s electronics sector further suffers losses through China’s machinery sector (CHN-OME) at 93.03%, reflecting broader network dependence on gas-intensive intermediate production. These results illustrate that a single supply disruption propagates through multiple channels, including feedstocks, energy supply, and intermediate manufacturing sectors.

Finally, to get a bigger picture of the global trend in losses under scenario 1, we examine correlations of country’s population size and output loss; and correlation of loss per capita versus GDP per capita. The results are shown in Figure 8(a) and (b) respectively. The dashed lines in Figure 8(a) indicate the median population and median loss, dividing countries into four groups. Larger, more populous economies tend to experience higher aggregate losses, as seen in the upper-right quadrant where countries like China and India are located. However, the spread of points shows that population alone does not determine impact, some smaller countries also exhibit relatively high losses, reflecting differences in economic structure and dependence on gas-linked supply chains.

Figure 8(b) shows losses on a per capita basis. A positive relationship shows higher-income countries experience larger losses per person. Economies such as Singapore, Qatar, and Taiwan lie toward the upper end, indicating greater exposure per capita, likely due to their deeper integration into global, energy-intensive production networks. Lower-income countries are clustered at lower per capita losses, although some still face meaningful impacts.

These figures highlight the uneven nature of the effects of disruption. Aggregate losses are concentrated in large economies, while per capita impacts are more pronounced in wealthier, highly interconnected countries.

Discussion

Our analysis shows that a disruption to Qatar’s gas sector can generate widespread, and sometimes unexpected, cascading effects across sectors and regions through global supply chains. The largest impacts fall on the major Asian economies of India, Pakistan, China, and South Korea, followed by Italy and the United States. The severity of the US impact is notable given that the country has no direct gas-based trade with Qatar and is itself one of the world’s largest gas producers, underscoring the reach of indirect transmission channels. Output losses display a similar geographic pattern, with high impact on Taiwan. We observe that the reallocation of flows leads to significant benefits for final demand, with China, the US, and Korea seeing the largest improvements. Finally, production expansion by the top gas producers, and flow reallocation substantially mitigates losses in some large economies such as China and Korea but even after increasing $\beta$ to 0.2, India and Pakistan’s output only partially improve, as shown in Figure 7. This implies that there may be other structural bottlenecks that cannot be overcome by just expanding production by TOP-GAS. Our results show that the solution space under increased production and reallocation is very complex, and the final outcomes depend on how countries prioritize output losses versus final demands. For instance, Indian officials gave priority to households over businesses under pressure from gas shortages [18]. In our experiments, we give equal weight to both, i.e., $\lambda_1 = \lambda_2$. However, our linear programming and disruption propagation network analysis methods provide a framework to systematically explore potential solutions and tradeoffs, by assigning different weights to output and final demand.

Aside from LNG, Ras Laffan jointly produces condensate, helium, liquefied petroleum gas, naphtha, and sulphur, which will lead to export reductions of 24%, 14%, 13%, 6% and 6% respectively [4, 3]. These disruptions propagate downstream affecting household energy use and different sectors including transportation, petrochemicals, and semiconductors, among others. In Japan and South Korea, where naphtha imports are heavily sourced from the Middle East, production of ethylene, PVC, and polyethylene, which are inputs to plastics, packaging, and construction materials, have also been disrupted [21]. Taiwan and South Korea import approximately 69% and 64.7% of their helium, a critical input in semiconductor fabrication, from Qatar respectively, making both countries’ chip industries directly exposed. Disruptions in these materials need to be considered along with gas disruptions, in order to understand the full economic impact.

This work has several limitations. MRIO captures fixed production relationships and does not account for price adjustments which means substitution driven by price signals is not captured. Adaptation is modeled through exogenous increase in flow and production capacities, and hence does not capture real-world frictions like long-term contracts, strategic reserves, geopolitics etc., and assumes reallocation is feasible once capacity is increased. Finally, the linear program provides multiple feasible solutions and does not guarantee uniqueness.

There are several caveats in the counterfactual scenarios on reallocation and production increase we study here. Aside from Qatar, the US and Australia are also major LNG producers, but neither can immediately fill the supply gap. Both countries are operating close to capacity, with production already committed under long-term contracts [22]. Reallocation is further constrained by energy security priorities. LNG exports are not purely market-driven, as governments may intervene to prioritize domestic supply during periods of shortage, consistent with policies such as Australia’s Domestic Gas Security Mechanism [8].

We also note that there are challenges in studying disruptions in other materials associated with gas production. For instance, helium supply does not necessarily increase with natural gas production. Helium is only recoverable from gas streams with sufficiently high concentrations and requires dedicated processing infrastructure, which means that only a limited number of gas fields are commercially viable for extraction [11]. Despite being a major LNG exporter, Australia does not have the infrastructure to capture helium from its gas production [7]. These supply-side rigidities mean that disruption cannot be resolved through market reallocation alone, and its economic consequences will propagate across global production networks for an extended period. LNG liquefaction projects take an average of 4-5 years between the final investment decision and completion, with no new capacity expected to come online on a sufficient scale to address the disruption in the next 2-3 years [14]. While these constraints limit immediate supply-side responses, understanding the potential mitigating effects of partial trade reallocation and capacity expansion remains critical for policy. Thus, we consider scenarios to quantify the global economic impact of disruption and evaluate the extent to which these adaptive responses could reduce its consequences.

Methodology

Input-Output Network

We employ a multiregional input-output (MRIO) model [16]. The MRIO table is obtained from the newly released GTAP 12 database for the year 2023, which covers 163 countries and 65 sectors [1]. We consider an economy consisting of production sectors, denoted by $S$, and final demand regions or countries, denoted by $R$. Each sector $S \in\mathcal{S}$ produces a unique good, e.g., steel, gas, etc. A $firm$ is a sector in a country, identified by a tuple (country, sector), e.g. USA-GAS for US gas industry, CHN-CHM for China chemicals industry. The set of all firms is denoted by $\mathcal{F}$. Note that each firm belongs to a global sector along with other firms producing the same good, e.g., USA-GAS, RUS-GAS, CAN-GAS etc. all belong to the global GAS sector. A firm produces its goods using intermediate inputs from other firms and primary inputs such as labor, capital etc. The gross output $x_i$ of a firm $i$ is the sum of its intermediate inputs and value added.

We model the flow of goods between firms and end-users as a directed capacitated network. In this network, each firm is a node and each country has one representative node for its final demand. There are two types of edges: firm-to-firm edges forming the set $E_I$, and firm-to-final demand edges forming the set $E_H$. Each edge carries a flow of goods whose maximum value (in USD) cannot exceed the stated edge capacity (in USD). Each firm sends its goods along this network to other firms (intermediate flows) and final demand regions (final demand flows). The flow value from firm $i$ to $j$ is denoted by $z_{i,j}$, and the flow from firm $i$ to final demand region $r$ is denoted by $h_{i,r}$. In the Leontief framework, the core assumption is that each firm operates on fixed production recipes based on known input coefficients. In our model, products of the same sector sourced from different countries are substitutable. Thus, an input coefficient $A_{S,i}$ is computed as the total amount of input required from the firms in sector $S$ to produce one unit of output in firm $i$,

All of the output of a firm is distributed to other firms

subject to,

(1) Leontief constraints:

(2) Conservation of flow:

(3) Flow capacity bounds:

(4) Disruption & adaptation:

and final demand as,

LP formulation

We model a disruption or an adaptation as a change in flow-capacities for a given subset of edges. Given a disruption, our goal is to find an equilibrium, i.e., the allocation of flows $\{z_{i,j}:(i,j)\in E_I\}$, $\{h_{i,r}:(i,r)\in E_H\}$ and firm outputs $\{x_i:i\in\mathcal{F}\}$ on the IO network such that the solution is optimal according to a given objective. We adopt an optimization approach where we want to find the flow allocations and firm outputs which maximize the total output and total final demand flows in the network. We formulate this bi-objective problem as a weighted combination with parameters $\lambda_1$ and $\lambda_2$ controlling the importance given to intermediate demand flows versus final demand flows. In this study we maintain $\lambda_1 = \lambda_2$, i.e., give equal weight to both intermediate and final demand. Due to the linearity of the Leontief framework, this problem can be formulated as a linear program as shown in Table 3. (1) The Leontief constraints ensure that the solution flows adhere to the production function defined for every pair of sectoral input flow and firm production (as shown in Equation 1). (2) The conservation of flow constraints ensure that everything that is produced by any firm is distributed to other firms and final demand regions along its outgoing edges, i.e., there is no wasted production (as shown in Equation 2). (3) We have the flow capacity bound for each edge $(i,j)$ which is set to the original MRIO value, $Z^{*}_{i,j}$, by default. (4) However, if it is in the disrupted subset of edges, the capacity is reduced by $\delta$ fraction of the original value. And if it belongs to the adaptive edges (Scenario 2 & 3), then the flow is constrained to be in the interval $[(1-\alpha)Z^{*}_{i,j},(1+\alpha)Z^{*}_{i,j}]$. Finally, for scenario 3, we also allow increase in primary input for selected firms by $\beta$ fraction.

We find that the above LP is difficult to solve using the Gurobi solver. We introduce an approximation to speed up the computation by aiding the LP solver to reach convergence faster. We modify the standard Leontief equilibrium condition to allow slack in the production, i.e., sectoral input flows need not be fully utilized by the current production level. For each sector $S$ and firm $i$ pair, this is given by $\epsilon_{S,i} = \sum_j z_{j,i} - A_{S,i}x_i$. Each wasted input flow is limited to a maximum value, $W_{max}$, and is penalized in the objective to move the solution towards minimizing overall wasted flows. We observe a tradeoff in speed and accuracy when we increase $W_{max}$ from 0 to 100 mUSD, the computation time reduces by up to 20 times {sup}6`, while the total wasted input flow increases to 0.08% of the total flows $\sum_{(i,j)\in E_I} z_{i,j}$. For the penalty term in the objective, we control the scale of the penalty using a parameter $\lambda_3$, set to a small value $10^{-6}$, so that it doesn’t distort the solution space while discouraging wasted flows.

Experimental setup

Dataset The multiregional input-output (MRIO) table is obtained from the newly released GTAP 12 database, which covers 163 countries and 65 sectors with 2023 as the reference year [1]. We construct the table from the database using the same tools as used in prior works [9]. Each country has a representative firm for each sector, and a representative household for final demand. The number of firms in our model is 10,595. We treat the flows in this table (also referred to as the original values) as the edge capacities, except where it has been disrupted

or is adaptive in our scenarios.

Scaling to large networks Given that the MRIO table has flows ranging from $10^{-12}$ to $10^{6}$ mUSD, we construct the IO network using some thresholds. The total number of possible flows could be in the order of hundreds of millions, which leads to an explosion in the number of flow variables in the LP model. To improve the tractability of the optimization problem, we introduce a flow threshold: a flow between any two nodes with an MRIO value smaller than $\tau_{flow} = 0.01$ mUSD is ignored. This reduces the number of edges (and thus, flow variables) while preserving the significant links in the network. Finally, the input coefficients $\{A_{S,i}\}$ also have a wide range from $10^{-8}$ to $10^{5}$. We introduce a threshold that ignores any input coefficients smaller than $\tau_{ic} = 10^{-5}$, reducing the number of Leontief constraints. From a modeling perspective, very small value of a flow or input coefficient is treated as a signal that the input is easily substitutable or otherwise not critical to production in a strict Leontief production limiting sense, justifying the use of these thresholds.

Evaluation on scenarios We evaluate our methods on the three scenarios under the defined disruption and analyze the allocation of flows and outputs for the firms in the IO network. For this, we select a range of values for each parameter $\delta,\alpha,\beta$ to evaluate each scenario as given in Table 1. To model the disruption coming from QAT-GAS, we set the $\delta$ parameter in the LP in Table 3 to reduce the upper bound, i.e., capacity, for the subset of edges which originate at QAT-GAS and terminate at any other node, including final demand nodes. In Scenario 1, we set only $\delta$ to a non-zero value, while $\alpha= \beta= 0$, i.e., no edge is made adaptive. In Scenario 2, in addition to a non-zero $\delta$, we set $\alpha$ to allow reallocation of flows over the subset of edges which originate from any firm in TOP-GAS group and terminate at any other node, including final demand regions. We set $\beta= 0$. In Scenario 2, we set all three parameters to non-zero values where $\alpha$ is set for all edges in the network, and $\beta$ is set only for the TOP-GAS firms.

The linear program for the study of trade disruptions and adaptations. The symbols are described in Table 2.

Sets	$\mathcal{F}$	Set of all firms
	$S \subseteq\mathcal{F}$	Set of firms with same product called sector
	$\mathcal{F}_{GAS}$	Set of TOP-GAS firms
	$S$	Set of all sectors
	$\mathcal{R}$	Set of all final demand regions
	$E_I \subseteq\mathcal{F} \times\mathcal{F}$	Set of all firm-to-firm flow edges
	$E_H \subseteq\mathcal{F} \times\mathcal{R}$	Set of all firm-to-region flow edges
	$E_{\delta}$	Set of disrupted edges
	$E_{\alpha}$	Set of adaptive edges enabling reallocation
Variables	$x_i \ \forall i \in\mathcal{F}$	Output of each firm $i$
	$z_{i,j} \ \forall(i,j) \in E_I$	Flow from firm $i$ to firm $j$
	$h_{i,r} \ \forall(i,r) \in E_H$	Flow from firm $i$ to final demand region $r$
	$\epsilon_{S,i} \ \forall(S,i) \in S \times\mathcal{F}$	Wasted input from sector $S$ to firm $i$
Constants	$A_{S,i}, \ \forall S \in S, i \in\mathcal{F}$	Input coefficient of firm $i$ from sector $S$
	$B_i \ \forall i \in\mathcal{F}$	Primary input coefficient of firm $i$
	$P_i^*, Z_{i,j}^*, H_{i,r}^*, X_i^*$	MRIO baseline values for primary inputs, intermediate flows, final demand flows, firm outputs respectively
	$Z_{i,j}^{\delta}, H_{i,r}^{\delta}$	Scenario 1 values for intermediate flows and final demand flows respectively.
	$\delta$	Flow capacity disruption parameter
	$\alpha$	Flow capacity reallocation parameter
	$\beta$	Primary input capacity increase parameter
	$W_{\max}$	Max allowable wasted flow for a (sector, flow) pair

We analyze the LP solutions first by studying the gas flows. We collect all the flows emerging from firms in the GAS sector. For each country, we aggregate these gas flows from a GAS firm that is being consumed by that firm within the country or by its representative final demand node. This is called the total gas flow value from a GAS firm being consumed by that country. We further aggregate these country-wise gas inflows into broader regional gas inflows (e.g., US, CAN, MEX etc. become North America) and plot these gas flows as heatmaps in Figure 1. To analyze the broader impact of the gas flow distribution on countries, we aggregate the outputs $\{x_i\}$ of all firms in a given country to obtain the country gross output. Next, we aggregate all the flows into the final demand node for each country to obtain the aggregate final demand. Finally, to plot the changes between scenarios, we take the difference between these aggregate values for each country and plot them as heatmaps.

To construct the disruption propagation network, we first select a threshold for the flow loss above which we include an edge as part of the disruption network. Given this network, we extract partial subgraphs for a given target node for analysis using the following method: Find all the paths, i.e, sequence of edges, in the disruption network that begin at the source node, i.e, QAT-GAS, and terminate at the target node under analysis, e.g., US final demand node. We limit the length of such paths to 3 edges in our experiments both for computational reasons, and for analyzing the shorter more direct paths. We compute the weight of a path by summing the losses over each constituent edge. We sort these paths by weight in descending order, and report the top 10 paths in our results.

All hyperparameters settings used in our experiments are given in Table 4 (moved to the appendix).

Symbol	Description	Value
$\tau_{flow}$	Flow Threshold	0.01 mUSD
$\tau_{ic}$	Input Coefficient Threshold	$10^{-5}$
$\lambda_1$	Weight for total intermediate demand flows in LP objective	1
$\lambda_2$	Weight for total final demand flows in LP objective	1
$\lambda_3$	Weight for penalty term for wasted input flows in LP objective	$10^{-6}$
$W_{max}$	Upper bound for an individual input across sector-to-firm pair	100 mUSD
$\tau_{loss}$	Loss Threshold (for the disruption propagation network)	100 mUSD
-	Max. Disruption Path Length	3 edges

Acknowledgments

This work is partially supported by University of Virginia Strategic Investment Fund Awards: SIF160, SIF186, the Contagion Science P2PE fund SIF176A, NSF grants CCF-1918656 and CNS-2317193. The research is also partly supported by the National Security Data & Policy Institute, Contracting Activity 2024-24070100001.

Technical Appendix

Additional results Figure 10 shows the gas flow from producer firms to more fine-grained consumer regions. For clarity, we combined some of the regions into a single region based on low prominence pertaining to gas flows, in the previous plot in main text (Figure 1). We visualize these flows as Sankey diagrams in Figure 12.

In Figure 13, we show how the size of the disruption propagation network, i.e., the number of nodes included, varies with increasing loss threshold, $\tau_{loss}$. This shows that with a low enough $\tau_{loss}$, a large majority ($>75\%$) of the network participates in the disruption propagation. Yet, this number quickly decreases as $\tau_{loss}$ increases, ultimately retaining only those nodes which propagate major flow losses. In Figure 15, we show the top 10 propagation paths for the firm, Korea electronics.

Additional details on methods We report the hyperparameter settings used in our methods in Table 4. For the input coefficient threshold used in our network construction, we report the tradeoff between accuracy in the resulting solutions and time taken to solve in Table 5. Next, we study various settings of $W_{max}$ and $\lambda_3$ and report the accuracy vs. time to solve for the solutions in Table 6.

Threshold	Aggregate Error %	Mean Error % (MAPE)	Median Error %
0.001	0.596	0.508	0.028
$10^{-5}$	0.003	0.002	0.0001
$10^{-7}$	$5.85 \times10^{-6}$	$2.98 \times10^{-6}$	0.0

$\epsilon_{s,i} \leq W_{max}$	Penalty Scale ($\lambda_3$)	Total Production	Wasted Input Flows ($\sum\epsilon_{s,i}$)	Time to solve
0	No slack allowed	187,105,695	0 (0.00%)	8 hrs
N.B.	0	187,792,119	2883500 (1.54%)	10 min
N.B.	$10^{-6}$	187,792,119	635486.47 (0.34%)	10 min
N.B.	1	187,792,100	629593.56 (0.34%)	20 min
100	$10^{-6}$	187,250,102	147,036 (0.08%)	20 min
10	$10^{-6}$	187151721	43416 (0.02%)	1.50 hr