arXiv subjects

Erhan Kutanoglu

Publications and source records attributed to Erhan Kutanoglu.

9 recordsLinked to original sources

arXiv2026

Multi-Objective Planning for Healthcare Facility Resilience: Mitigate Now or Respond Later?

Flooding can damage healthcare facilities, interrupt local care capacity, and trigger costly patient evacuations. Addressing these risks requires long-term resilience investments under uncertainty. We develop a bi-objective two-stage stochastic optimization model that jointly determines permanent facility hardening and scenario-dependent evacuation decisions. The first objective minimizes expected evacuation, physical damage, and business-interruption costs. The second minimizes a service-disruption impact index that combines the duration and scale of service loss with a place-based social-vulnerability weight. We develop an exact Benders decomposition and a scalable Lagrangian-dual method with tailored primal recovery, embedding both within an adaptive procedure for constructing informative Pareto frontiers. A case study of 3,752 hospitals and nursing homes in Texas evaluates the framework under climate-informed tropical-cyclone flood scenarios. The results show that minimizing economic losses alone can systematically allocate less protection to facilities located in socially vulnerable areas, while moderate movement along the Pareto frontier can substantially reduce disruption impacts at limited additional expected cost. The exact decomposition solves all tested instances, including larger stress tests for which the extensive formulation becomes memory-limited, while the Lagrangian method provides substantially faster high-quality solutions.

math.OC↗

arXiv2026

Industrial electrification in the era of data centers: A Bayesian Optimization approach for grid-aware large load allocation

Large loads from industrial electrification and data centers are reshaping the planning and operation of the power grid. Identifying optimal large load siting decisions while accounting for transmission congestion is key to reducing expansion cost and operational risks. In this paper, we propose a leader-follower bilevel optimization framework to identify optimal large load allocation strategies. The leader determines the allocation of large loads, while the followers determine grid expansion cost and transmission utilization. This modeling approach explicitly integrates strategic planning with detailed short-term operational decisions. Moreover, we develop a Bayesian Optimization approach to efficiently solve the bilevel optimization problem by treating the followers as a black box. We use the framework to study large-scale load allocation from electrified oil refineries and data centers on a synthetic power grid that resembles key characteristics of the Texas (ERCOT) system. The results show that these large loads compete for electricity, and under high-load scenarios, data center demand is distributed across the entire grid, avoiding regions with high demand from industrial electrification.

eess.SY↗

arXiv2026

Grid Capacity Expansion under Data Centers and Electrified Manufacturing Large Loads

In this paper, we consider the expansion of power grids under emerging large loads from data centers and electrified manufacturing. We develop a multi-period grid capacity expansion model to determine optimal investment profiles for power generation, storage, and transmission capacity while accounting for hourly power dispatch, such that electricity demand is satisfied and the total planning and operation cost is minimized. We also propose a new modeling approach regarding the spatial distribution of demand from large loads. The model is used to analyze the expansion of a synthetic grid that follows key characteristics of the ERCOT system over a seven-year planning horizon, under loads from data centers and electrified oil refining, which account for 17.5% and 4.7% of total annual electricity demand by the end of the planning horizon. The optimal investment policy leads to an 83.6% increase in generation capacity and exploits the short construction times of solar and storage as well as the operational flexibility of thermal generators. Finally, sensitivity analysis reveals that the construction time of grid assets substantially impacts investment timing, generation technology mix, and transmission capacity expansion. The proposed modeling framework is general and can be extended to other grid systems, enabling the exploration of diverse demand scenarios, policy assumptions, and regional characteristics.

eess.SY↗

arXiv2026

Using a generative model for out-of-sample testing of two-stage stochastic programs

Stochastic programming models for decision-making under uncertainty often suffer from scenario scarcity, where obtaining representative samples of uncertain parameters requires expensive simulations or measurements. This work presents a framework that leverages the Normal-to-Anything (NORTA) generative model to enhance the reliability of two-stage stochastic programming solutions through comprehensive out-of-sample testing when scenario data is limited. The NORTA model efficiently generates synthetic scenarios that preserve both marginal distributions and correlation structures from limited available data, offering a computationally tractable alternative to expensive physics-based simulations. We demonstrate the approach through a case study on power grid resilience planning against flood events in Texas, where we use 16 high-fidelity flood scenarios to generate 800 additional synthetic scenarios for validation. The results show that NORTA-generated scenarios accurately capture essential statistical properties, with the out-of-sample performance of first-stage decisions closely matching expectations from the original stochastic programming model. This framework enables decision-makers to assess the robustness of their solutions when obtaining additional real-world data is prohibitively expensive. The approach bridges machine learning and operations research by providing a practical solution to scenario generation challenges in stochastic programming.

math.OC↗

arXiv2025

Co-optimization of Short- and Long-term Decisions for the Transmission Grid's Resilience to Flooding

We present and analyze a three-stage stochastic optimization model that integrates output from a geoscience-based flood model with a power flow model for transmission grid resilience planning against flooding. The proposed model coordinates the decisions made across multiple stages of resilience planning and recommends an optimal allocation of the overall resilience investment budget across short- and long-term measures. While doing so, the model balances the cost of investment in both short- and long-term measures against the cost of load shed that results from unmitigated flooding forcing grid components go out-of-service. We also present a case study for the Texas Gulf Coast region to demonstrate how the proposed model can provide insights into various grid resilience questions. Specifically, we demonstrate that for a comprehensive yet reasonable range of economic values assigned to load loss, we should make significant investments in the permanent hardening of substations such that we achieve near-zero load shed. We also show that not accounting for short-term measures while making decisions about long-term measures can lead to significant overspending. Furthermore, we demonstrate that a technological development enabling to protect substations on short notice before imminent hurricanes could vastly influence and reduce the total investment budget that would otherwise be allocated for more expensive substation hardening. Lastly, we also show that for a wide range of values associated with the cost of mitigative long-term measures, the proportion allocated to such measures dominates the overall resilience spending.

math.OC↗

arXiv2024

On Simplices with a Given Barycenter That Are Enclosed by the Standard Simplex

We present an optimization model defined on the manifold of the set of stochastic matrices. Geometrically, the model is akin to identifying a maximum-volume $n$-dimensional simplex that has a given barycenter and is enclosed by the $n$-dimensional standard simplex. Maximizing the volume of a simplex is equivalent to maximizing the determinant of its corresponding matrix. In our model, we employ trace maximization as a linear alternative to determinant maximization. We identify the analytical form of a solution to this model. We prove the solution is optimal and present necessary and sufficient conditions for it to be the unique optimal solution. Additionally, we show the identified optimal solution is an inverse $M$-matrix, and that its eigenvalues are the same as its diagonal entries. We demonstrate how the model and its solutions apply to the task of synthesizing conditional cumulative distribution functions (CDFs) that, in tandem with a given discrete marginal distribution, coherently preserve a given CDF.

math.OC↗

arXiv2023

Comparisons of two-stage models for flood mitigation of electrical substations

We compare stochastic programming and robust optimization decision models for informing the deployment of ad hoc flood mitigation measures to protect electrical substations prior to an imminent and uncertain hurricane. In our models, the first stage captures the deployment of a fixed quantity of flood mitigation resources, and the second stage captures the operation of a potentially degraded power grid with the primary goal of minimizing load shed. To model grid operation, we introduce adaptations of the DC and LPAC power flow approximation models that feature relatively complete recourse by way of an indicator variable. We apply our models to a pair of geographically realistic flooding case studies, one based on Hurricane Harvey and the other on Tropical Storm Imelda. We investigate the effect of the mitigation budget, the choice of power flow model, and the uncertainty perspective on the optimal mitigation strategy. Our results indicate the mitigation budget and uncertainty perspective are impactful whereas choosing between the DC and LPAC power flow models is of little to no consequence. To validate our models, we assess the performance of the mitigation solutions they prescribe in an AC power flow model.

math.OC↗

arXiv2023

Scenario-based Optimization Models for Power Grid Resilience to Extreme Flooding Events

We propose two scenario-based optimization models for power grid resilience decision making that integrate output from a hydrology model with a power flow model. The models are used to identify an optimal substation hardening strategy against potential flooding from storms for a given investment budget, which if implemented enhances the resilience of the power grid, minimizing the power demand that is shed. The same models can alternatively be used to determine the optimal budget that should be allocated for substation hardening when long-term forecasts of storm frequency and impact (specifically restoration times) are available. The two optimization models differ in terms of capturing risk attitude: one minimizes the average load shed for given scenario probabilities and the other minimizes the worst-case load shed without needing scenario probabilities. To demonstrate the efficacy of the proposed models, we further develop a case study for the Texas Gulf Coast using storm surge maps developed by the National Oceanic and Atmospheric Administration and a synthetic power grid for the state of Texas developed as part of an ARPA-E project. For a reasonable choice of parameters, we show that a scenario-based representation of uncertainty can offer a significant improvement in minimizing load shed as compared to using point estimates or average flood values. We further show that when the available investment budget is relatively high, solutions that minimize the worst-case load shed can offer several advantages as compared to solutions obtained from minimizing the average load shed. Lastly, we show that even for relatively low values of load loss and short post-hurricane power restoration times, it is optimal to make significant investments in substation hardening to deal with the storm surge considered in the NOAA flood scenarios.

math.OC↗

arXiv2023

A two-stage stochastic programming model for electric substation flood mitigation prior to an imminent hurricane

We present a stochastic programming model for informing the deployment of ad hoc flood mitigation measures to protect electrical substations prior to an imminent and uncertain hurricane. The first stage captures the deployment of a fixed number of mitigation resources, and the second stage captures grid operation in response to a contingency. The primary objective is to minimize expected load shed. We develop methods for simulating flooding induced by extreme rainfall and construct two geographically realistic case studies, one based on Tropical Storm Imelda and the other on Hurricane Harvey. Applying our model to those case studies, we investigate the effect of the mitigation budget on the optimal objective value and solutions. Our results highlight the sensitivity of the optimal mitigation to the budget, a consequence of those decisions being discrete. We additionally assess the value of having better mitigation options and the spatial features of the optimal mitigation.

math.OC↗