John J. Hasenbein

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.

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.

This study evaluates the application of change point detection (CPD) methodologies in the Agricultural Quarantine Inspection Monitoring (AQIM) program to identify significant shifts in pest arrival rates. Unlike prior work that focused on optimizing sampling strategies, this paper emphasizes the numerical evaluation of CPD algorithms for detecting pest outbreaks using AQIM data. The objective is to assess whether these methods can reliably detect and signal outbreaks when pest arrival rates exceed critical thresholds. Through extensive computational experiments, we compare the accuracy, sensitivity, and robustness of CPD methods under various outbreak scenarios and data conditions. The results demonstrate that CPD techniques, particularly cumulative sum (CUSUM) and exponential moving average (EMA), achieve high detection rates and low false alarm rates, even in challenging settings such as small outbreaks. These findings highlight the feasibility of integrating CPD algorithms into AQIM operations, providing a scalable and practical approach to enhancing outbreak detection and strengthening agricultural biosecurity in the context of global trade and evolving pest risks.

We consider a single-server queue where interarrival and service times depend linearly and randomly on customer waiting times, and establish a sample-path moderate deviation principle (MDP) for the waiting time process. The waiting times for the queue can be written as a modified Lindley recursion with a random weight coefficient. Under a natural scaling of the random coefficients, we analyze the fluid behavior of the workload process and derive the stable equilibrium point, which can be zero or a positive value. The moderate-deviation-scaled process is centered around the stable equilibrium point and then represented as a linear stochastic differential equation driven by two random walks together with additional asymptotically negligible error terms and possibly a reflection at zero. The rate functions of MDPs in the two scenarios can be characterized explicitly, and they differ in that the case with zero centering term involves the linearly generalized Skorokhod reflection mapping while the case with positive centering term does not (similar to the corresponding diffusion limits). Our analysis involves the MDP for the associated linearly recursive Markov chains, invoking a perturbation of two independent random walks, and employing martingale techniques to prove the asymptotically exponentially vanishing error terms.

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.

Several stochastic programming models have been developed for critical infrastructure's resilience decision-making to extreme flood events. Generating flood scenarios for such models requires running advanced flood models on a sophisticated computing infrastructure for different parameterizations (for example, different hurricane intensity levels, tracks, etc.), which may not always be practical. To address this issue, in this study, we propose a Normal-to-Anything (NORTA) model-based flood scenario generation scheme, which requires significantly fewer computing resources. The scenarios we generate using the proposed approach preserve correlation in flood height at locations of interest, in our case, the power transmission grid's substation locations. We demonstrate our approach's efficacy with a case study using a synthetic power grid with statistical similarities with the actual Texas grid and the flood maps developed by the National Atmospheric and Oceanic Administration that represent the storm-surge risk in Texas.

Consider an M/M/s queue with the additional feature that the arrival rate is a random variable of which only the mean, variance, and range are known. Using semi-infinite linear programming and duality theory for moment problems, we establish for this setting tight bounds for the expected waiting time. These bounds correspond to an arrival rate that takes only two values. The proofs crucially depend on the fact that the expected waiting time, as function of the arrival rate, has a convex derivative. We apply the novel tight bounds to a rational queueing model, where arriving individuals decide to join or balk based on expected utility and only have partial knowledge about the market size.

Imported agricultural pests can cause substantial damage to agriculture, food security, and ecosystems. In the United States, the Agricultural Quarantine Inspection Monitoring (AQIM) program conducts random sampling to estimate the probabilities that cargo and passengers arriving at ports of entry carry pests. Assessing these risks accurately is critical to enable effective policies and operational procedures. This study introduces a pathway-level analysis with an objective function aligned with AQIM's goal, offering a new perspective compared to the current container-by-container approach, which relies on heuristics to set inspection rates. We formulate an optimization model that minimizes the mean squared error of the probability estimates that AQIM obtains. The central decision-making tradeoff that the model explores is whether it is preferable to sample more arriving containers (and fewer boxes per container) or more boxes per container (and fewer containers), given limited resources. We first derive an analytical solution for the optimal sampling strategy by leveraging several approximations. Then, we apply our model to a numerical case study of maritime cargo sampling at the Port of Long Beach. Across a wide range of parameter settings, the optimal strategy samples more containers (but fewer boxes per container) than the current AQIM protocol. The difference between the two strategies and the accuracy improvement with the optimal approach are larger if the pest statuses of boxes in the same container are more strongly correlated. We recommend that AQIM record box-level (beyond only container-level) inspection data, which could be used to estimate this correlation and other model parameters.

Robust Stability in Multiclass Queueing Networks: A New Approach In “A Hierarchical Approach to Robust Stability of Multiclass Queueing Networks,” F. Zhao, I. Gurvich, and J. Hasenbein introduce a framework to identify sufficient conditions under which a network’s stability is robust to the distributed choices of resources about their (local) prioritization of jobs. The framework produces sufficient conditions for such stability by relating it to robust optimization problems where the collection of priority policies plays the role of the uncertainty set. Interestingly, within the studied family of policies, robust stability for any policy is inherited from the stability of the special “corner” policies, which are none other than simple static-priority policies.

We present a stochastic programming model for informing the deployment of ad hoc flood mitigation measures to protect electric 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.

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 direct current (DC) and linear programming alternating current (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 alternating current (AC) power flow model. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: This work was supported by the Energy Institute, The University of Texas at Austin. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0125 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0125 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

This paper presents an extension of Naor’s analysis on the join-or-balk problem in observable M/M/1 queues. Although all other Markovian assumptions still hold, we explore this problem assuming uncertain arrival rates under the distributionally robust settings. We first study the problem with the classical moment ambiguity set, where the support, mean, and mean-absolute deviation of the underlying distribution are known. Next, we extend the model to the data-driven setting, where decision makers only have access to a finite set of samples. We develop three optimal joining threshold strategies from the perspectives of an individual customer, a social optimizer, and a revenue maximizer such that their respective worst-case expected benefit rates are maximized. Finally, we compare our findings with Naor’s original results and the traditional sample average approximation scheme. Funding: This research was supported by the National Science Foundation [Grants 2342505 and 2343869].

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.

In this paper, we investigate the resilience of alternative electric grid configurations by adopting a stylized approach based on graph theory, probabilistic analysis, and simulation. We consider two alternative classes of electricity network topology: binary trees and rectangular lattices. For each topology, we derive the probabilities that customers located at various nodes in the network will continue to have power following a disaster, depending on the locations of resources (e.g., generators, storage units) in the network. Then, these probabilities are incorporated into the problem of optimally placing resources throughout the network. This is a cost-benefit problem that weighs the benefits of placing resources closer to customers – that is, pursuing a distributed resilience strategy – against the higher total cost of deploying a greater number of smaller resource units. Our analytical and numerical results thus shed light on the general circumstances in which centralized or distributed resilience strategies are preferable. While optimal resource placements depend on various assumptions, such as the probability that power lines fail and the strength of economies of scale, we find that distributed resilience strategies are more often preferred in the binary tree topology than in the rectangular lattice topology. Rectangular lattices feature greater redundancy in terms of paths between nodes in the network, enabling the system to be fairly resilient even with centralized resources.

We propose a three-stage stochastic programming model to inform risk-averse investment in power system resilience to winter storms. The first stage pertains to long-term investment in generator winterization and mobile battery energy storage system (MBESS) resources, the second stage to MBESS deployment prior to an imminent storm, and the third stage to operational response. Serving as a forecast update, an imminent winter storm’s severity is assumed to be known at the time the deployment decisions are made. We incorporate conditional value-at-risk (CVaR) as the risk measure in the objective function to target loss, represented in our model by unserved energy, experienced during high-impact, low-frequency events. We apply the model to a Texas-focused case study based on the ACTIVS 2000-bus synthetic grid with winter storm scenarios generated using historical Winter Storm Uri data. Results demonstrate how the optimal investments are affected by parameters like cost and risk aversion, and also how effectively using CVaR as a risk measure mitigates the outcomes in the tail of the loss distribution over the winter storm impact uncertainty.

This article studies the Transmission Restoration Problem with Mobile Substation Resources, a novel mixed-integer linear programming model that prescribes the most effective usage of mobile-substation resources to enhance the resilience of a power transmission system against a particular, widespread flood event. The model is a two-stage stochastic program in which each scenario captures a different potential progression of flood heights at substations over the event horizon. The first stage concerns the pre-event selection and positioning of mobile-substation resources. The second stage concerns the coordination of mobile-substation resource deployment and permanent-substation restoration to maintain and recover service within the horizon. Experiments in the IEEE 24-Bus System and a synthetic Houston grid confirm the efficacy of the model. Even when isolated from effects related to restoration of permanent substations, the effect of four mobile transformers and eight mobile breakers for a realistic set of flood scenarios in the synthetic Houston grid was found to be an average total-cost reduction of approximately $35MM (i.e., approximately 8% of a default optimal objective value). Additionally, a novel, parallel heuristic is designed that can efficiently solve the problem as well as, with minor modifications, similar stochastic problems on pre-selection of mobile resources or placement of static ones. For a 40-scenario model instance in the IEEE 24-Bus System, the extensive form was not able to find an integer-feasible solution in six hours, yet the heuristic achieved an optimality gap no worse than 4.5% in two hours.

Consider an M/M/$s$ queue with the additional feature that the arrival rate is a random variable of which only the mean, variance, and range are known. Using semi-infinite linear programming and duality theory for moment problems, we establish for this setting tight bounds for the expected waiting time. These bounds correspond to an arrival rate that takes only two values. The proofs crucially depend on the fact that the expected waiting time, as function of the arrival rate, has a convex derivative. We apply the novel tight bounds to a rational queueing model, where arriving individuals decide to join or balk based on expected utility and only have partial knowledge about the market size.

We develop a method to estimate the quality of processing routes in a wafer fabrication process. Ranking such routes can be useful for identifying the "best" and "worst" routes when making adjustments to recipes. Route categorization is also useful in developing efficient scheduling algorithms. In particular, we propose a method for ranking routes based on count-based metrics such as the number of defects on a wafer. We start with a statistical model to produce a "local" ranking of a tool and then build a "global" ranking via a heuristic procedure. Creating a fully statistical procedure for ranking routes in semiconductor fabrication plants is virtually impossible, given the number of possible routes and the limited data available. Nonetheless, our discussions with working engineers indicate that even approximate rankings are useful for making better operational decisions.

We re-visit the global - relative to control policies - stability of multiclass queueing networks. In these, as is known, it is generally insufficient that the nominal utilization at each server is below 100%. Certain policies, although work conserving, may destabilize a network that satisfies the nominal-load conditions; additional conditions on the primitives are needed for global stability (stability under any work-conserving policy). The global-stability region was fully characterized for two-station networks in [13], but a general framework for networks with more than two stations remains elusive. In this paper, we offer progress on this front by considering a subset of non-idling control policies, namely queue-ratio (QR) policies. These include as special cases all static-priority policies. With this restriction, we are able to introduce a complete framework that applies to networks of any size. Our framework breaks the analysis of robust QR stability (stability under any QR policy) into (i) robust state-space collapse and (ii) robust stability of the Skorohod problem (SP) representing the fluid workload. Sufficient conditions for both are specified in terms of simple optimization problems. We use these optimization problems to prove that the family of QR policies satisfies a weak form of convexity relative to policies. A direct implication of this convexity is that: if the SP is stable for all static-priority policies (the "extreme" QR policies), then it is also stable under any QR policy. While robust QR stability is weaker than global stability, our framework recovers necessary and sufficient conditions for global stability in specific networks.

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.

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.

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.