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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

An Integrated Framework for Risk Assessment of Safety-related Digital Instrumentation and Control Systems in Nuclear Power Plants: Methodology Refinement and Exploration

This report documents activities performed by Idaho National Laboratory (INL) during Fiscal Year (FY) 2023 for the U.S. Department of Energy (DOE) Light Water Reactor Sustainability (LWRS) Program, Risk Informed Systems Analysis (RISA) Pathway, digital instrumentation and control (DI&C) risk assessment project. In FY 2019, the RISA Pathway initiated a project to develop a risk assessment strategy for delivering a technical basis to support effective, and secure DI&C technologies for digital upgrades/designs. A risk assessment-informed framework was proposed for this strategy, which aims to (1) provide a best-estimate, risk informed capability to quantitatively estimate the safety margin obtained from plant modernization, especially for safety-related DI&C systems, (2) support and supplement existing risk informed DI&C design guides by providing quantitative risk information and evidence, (3) offer a capability of design architecture evaluation of various DI&C systems, (4) assure the long-term safety and reliability of safety-related DI&C systems, and (5) reduce uncertainty in costs and support integration of DI&C systems in the plant. To achieve these technical goals, the LWRS-developed framework provides a means to address relevant technical issues by: (1) defining a risk informed analysis process for DI&C upgrade that integrates hazard analysis, reliability analysis, and consequence analysis, (2) applying risk informed tools to address common cause failures (CCFs) and quantify corresponding failure probabilities for DI&C technologies, particularly software CCFs, (3) evaluating the impact of digital failures at the component level, system level, and plant level, and (4) providing insights and suggestions on designs to manage the risks, thus to support the development and deployment of advanced DI&C technologies in nuclear power plants (NPPs). Adding diversity within a system or components is the primary means to eliminate and mitigate CCFs, but diversity also increases system complexity and may not address all sources of systematic failures. Optimization of diversity and redundancy applications for the safety-critical DI&C systems remains a challenge. To deal with the technical issues in addressing potential software CCFs in safety-related DI&C systems of NPPs and supporting relevant design optimization, the proposed framework provides: (a) A best-estimate, risk informed capability to address new technical digital issues quantitatively, focusing on software CCFs in safety-related DI&C systems of NPPs; (b) A common and a modularized platform for DI&C designers, software developers, cybersecurity analysts, and plant engineers to predict and prevent risk in the early design stage of DI&C systems; (c) Technical bases and risk informed insights to assist users address the risk informed alternatives for evaluation of CCFs in safety-related DI&C systems of NPPs; and (d) A risk informed tool that offers a capability of design architecture evaluation of various DI&C systems to support system design decisions in diversity and redundancy applications. The research and development efforts of this project in FY 2023 are focused on refining current methods on software CCF modeling and estimation and exploring additional innovative approaches to risk assessment of DI&C systems to enable a more comprehensive and complete assessment of various safety-related DI&C design architectures. The primary audience of this report are DI&C designers, engineers, and probabilistic risk assessment (PRA) practitioners. This includes stakeholders, such as the nuclear utilities and regulators who consider the deployment and upgrade of DI&C systems, DI&C software developers and reviewers, and cybersecurity specialists. It should be noted that all the analyses are performed for the demonstration of the methodology, not for the evaluation of an actual digital control system. Results are obtained based on limited design information and testing data.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

The Gene Fitness Atlas: A Roadmap for Predicting Evolution

We developed a novel, high-throughput microfluidic device design containing “interaction zones” where progeny cell lines compete against each other allowing for accurate analysis of bacterial cell fitness. The goal of the project was to use the device for two applications: 1) gene knockout screening and 2) antibiotic resistance screening. The microfluidic platform was fabricated using photolithography and soft lithography in polydimethylsiloxane (PDMS). E.coli Keio mutants and fluorescent wildtype parent were chosen for the study. Cells were grown overnight and their loading into the devices and seeding in mother machines was optimized. For mutant screening, the least fit mutant and wildtype parent were cultured individually and then added to the microfluidic device. The mother machines which were seeded with mutant and wildtype were imaged through time lapse microscopy and the growth of cells was observed. For antibiotic screening, wildtype E.coli cells which were grown overnight were added to the device and washed with media containing the antibiotic ampicillin. The growth pattern in presence and absence of ampicillin was observed through time lapse microscopy. It was observed that over a period of four hours, both the mutant and the wildtype divided in the mother machine and pushed daughter cells out into the interaction zone. In case of the antibiotic screening experiment, the fluorescent wildtype divided both in the absence and presence of sublethal concentration of ampicillin. This study is a proof of concept demonstration of high- throughput single cell analysis of cells using a novel microfluidics device.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Port Technical Assistance Program: A Proposed Initiative to Support U.S. Ports Through Energy Innovation

This document highlights the crucial importance of the maritime sector within the United States (U.S.) economy, serving as a key node for trade and global goods transportation. U.S. ports are currently grappling with challenges posed by rising shipping demands, the health impacts of diesel fuel reliance, and the technology adoptions of global trade partners due to increasing environmental regulations. This document proposes forming a technical assistance program, led by Pacific Northwest National Laboratory (PNNL), to help U.S. ports transition to sustainable energy solutions that not only improve environmental and community outcomes, but also enhance resilience to unexpected weather events and reduce pressure on local utilities. Coordinated by PNNL, this initiative would offer a web-based platform of consolidated resources and tools for comprehensive strategic planning and cost-benefit analysis. It also seeks to establish a collaborative network between ports and national laboratories to facilitate the sharing of best practices. The document suggests that optimizing resource allocation and providing tailored support could be achieved through strategic categorization of ports within this network, with relevant attributes and examples detailed in the report. The anticipated benefits of such a program could include increased efficiency and cost savings in port operations and the advancement of scientific innovation via alternative energy research. Also, it could enhance economic growth and competitiveness in international trade by enabling ports to meet shipping demands and develop resilient critical infrastructure through informed, long-term strategies.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2021

Insights from PPL's DERMS Implementation

PPL Electric Utilities’ Keystone Solar Future Project (KSFP) is part of the U.S. Department of Energy’s Office of Energy Efficiency and Renewables, Energy Enabling Extreme Real-time Grid Integration of Solar Energy (ENERGISE) grant. The three-year project, beginning in October, 2017, funded an innovative pilot program to develop and evaluate a technology platform and framework for managing high levels of distributed energy resources (DER), and improving future DER interconnection. The KSFP aimed to bridge gaps between existing and future technology, including Distributed Energy Resource Management Systems (DERMS), by monitoring, managing, and optimizing a system with high penetration of solar and other DER. Specifically, the project worked to make Demand Management Systems (DMS) applications, devices, and real-time communications technology DER-aware to allow for advanced applications for utility operations. Here, by installing and implementing a DERMS, project designers transformed how DERs interact with PPL’s distribution system, offering learnings and results worth sharing industry-wide.

Leader, Jared↗
DOE OSTI2016

Development and Application of Virtual Nuclear Power Plant Platform Concerning Environment and Society Digitally

Virtual Nuclear Power Plant, named Virtual4DS, which is developed by the advanced nuclear energy research team (FDS Team), is a platform for full range, whole cycle safety assessment and emergency decision of nuclear power plant in the digital environment and society. The function framework of Virtual4DS is shown in Fig. 1, and it is designed to ensure an overall optimization design of nuclear power plant, achieve comprehensive evaluation of safety and control of risk, and supply the decision support for accident emergency by the accident probability analysis, environmental consequence assessment and public risk evaluation built on the core of digital reactor and the foundation of the nuclear energy big data. Therefore, Virtual4DS is eligible to be applied in reactor safety, radiation safety and environment impact, emergency and public safety. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

New high-throughput endstation to accelerate the experimental optimization pipeline for synchrotron X-ray footprinting

Synchrotron X-ray footprinting (XF) is a growing structural biology technique that leverages radiation-induced chemical modifications via X-ray radiolysis of water to produce hydroxyl radicals that probe changes in macromolecular structure and dynamics in solution states of interest. The X-ray Footprinting of Biological Materials (XFP) beamline at the National Synchrotron Light Source II provides the structural biology community with access to instrumentation and expert support in the XF method, and is also a platform for development of new technological capabilities in this field. Hee, the design and implementation of a new high-throughput endstation device based around use of a 96-well PCR plate form factor and supporting diagnostic instrumentation for synchrotron XF is described. This development enables a pipeline for rapid comprehensive screening of the influence of sample chemistry on hydroxyl radical dose using a convenient fluorescent assay, illustrated here with a study of 26 organic compounds. The new high-throughput endstation device and sample evaluation pipeline now available at the XFP beamline provide the worldwide structural biology community with a robust resource for carrying out well optimized synchrotron XF studies of challenging biological systems with complex sample compositions.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2019

Integrating Carbon Nanomaterials with Metals for Bio-sensing Applications

Age structure in most developed countries is changing fast as the average lifespan is increasing significantly, calling for solutions to provide improved treatments for age-related neurological diseases and disorders. In order to address these problems, a reliable way of recording information about neurotransmitters from in vitro and in vivo applications is needed to better understand neurological diseases and disorders as well as currently used treatments. Likewise, recent developments in medicine, especially with the opioid crisis, are demanding a swift move to personalized medicine to administer patient needs rather than population-wide averages. In order to enable the so-called personalized medicine, it is necessary to be able to do measurements in vivo and in real time. These actions require sensitive and selective detection of different analytes from very demanding environments. Current state-of-the-art materials are unable to provide sensitive and selective detection of neurotransmitters as well as the required time resolution needed for drug molecules at a reasonable cost. To meet these challenges, we have utilized different metals to grow carbon nanomaterials and applied them for sensing applications showing that there are clear differences in their electrochemical properties based on the selected catalyst metal. Additionally, we have combined atomistic simulations to support optimizing materials for experiments and to gain further understanding of the atomistic level reactions between different analytes and the sensor surface. With carbon nanostructures grown from Ni and Al + Co + Fe hybrid, we can detect dopamine, ascorbic acid, and uric acid simultaneously. On the other hand, nanostructures grown from platinum provide a feasible platform for detection of H 2 O 2 making them suitable candidates for enzymatic biosensors for detection of glutamate, for example. Tetrahedral amorphous carbon electrodes have an ability to detect morphine, paracetamol, tramadol, and O-desmethyltramadol. With carbon nanomaterial-based sensors, it is possible to reach metal-like properties in sensing applications using only a fraction of the metal as seed for the material growth. We have also seen that by using nanodiamonds as growth catalyst for carbon nanofibers, it is not possible to detect dopamine and ascorbic acid simultaneously, although the morphology of the resulting nanofibers is similar to the ones grown using Ni. This further indicates the importance of the metal selection for specific applications. However, Ni as a continuous layer or as separate islands does not provide adequate performance. Thus, it appears that metal nanoparticles combined with fiber-like morphology are needed for optimized sensor performance for neurotransmitter detection. This opens up a new research approach of application-specific nanomaterials, where carefully selected metals are integrated with carbon nanomaterials to match the needs of the sensing application in question.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Memory access optimization for particle operations in computational fluid dynamics-discrete element method simulations

Computational Fluid Dynamics - Discrete Element Method is used to model gas-solid systems in several applications in energy, pharmaceutical and petrochemical industries. Computational performance bottlenecks often limit the problem sizes that can be simulated at industrial scale. The data structures used to store several millions of particles in such large-scale simulations have a large memory footprint that does not fit into the processor cache hierarchies on current high-performance-computing platforms, leading to reduced computational performance. This paper specifically addresses this aspect of memory access bottlenecks in industrial scale simulations. The use of space-filling curves to improve memory access patterns is described and their impact on computational performance is quantified in both shared and distributed memory parallelization paradigms. The Morton space filling curve applied to uniform grids and k-dimensional tree partitions are used to reorder the particle data-structure thus improving spatial and temporal locality in memory. The performance impact of these techniques when applied to two benchmark problems, namely the homogeneous-cooling-system and a fluidized-bed, are presented. We report these optimization techniques lead to approximately two-fold performance improvement in particle focused operations such as neighbor-list creation and data-exchange, with ~ 1.5 times overall improvement in a fluidization simulation with 1.27 million particles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

SU-D-206-02: Evaluation of Partial Storage of the System Matrix for Cone Beam Computed Tomography Using a GPU Platform

Purpose: Iterative reconstruction algorithms in computed tomography (CT) require a fast method for computing the intersections between the photons’ trajectories and the object, also called ray-tracing or system matrix computation. This work evaluates different ways to store the system matrix, aiming to reconstruct dense image grids in reasonable time. Methods: We propose an optimized implementation of the Siddon’s algorithm using graphics processing units (GPUs) with a novel data storage scheme. The algorithm computes a part of the system matrix on demand, typically, for one projection angle. The proposed method was enhanced with accelerating options: storage of larger subsets of the system matrix, systematic reuse of data via geometric symmetries, an arithmetic-rich parallel code and code configuration via machine learning. It was tested on geometries mimicking a cone beam CT acquisition of a human head. To realistically assess the execution time, the ray-tracing routines were integrated into a regularized Poisson-based reconstruction algorithm. The proposed scheme was also compared to a different approach, where the system matrix is fully pre-computed and loaded at reconstruction time. Results: Fast ray-tracing of realistic acquisition geometries, which often lack spatial symmetry properties, was enabled via the proposed method. Ray-tracing interleaved with projection and backprojection operations required significant additional time. In most cases, ray-tracing was shown to use about 66 % of the total reconstruction time. In absolute terms, tracing times varied from 3.6 s to 7.5 min, depending on the problem size. The presence of geometrical symmetries allowed for non-negligible ray-tracing and reconstruction time reduction. Arithmetic-rich parallel code and machine learning permitted a modest reconstruction time reduction, in the order of 1 %. Conclusion: Partial system matrix storage permitted the reconstruction of higher 3D image grid sizes and larger projection datasets at the cost of additional time, when compared to the fully pre-computed approach. This work was supported in part by the Fonds de recherche du Quebec - Nature et technologies (FRQ-NT). The authors acknowledge partial support by the CREATE Medical Physics Research Training Network grant of the Natural Sciences and Engineering Research Council of Canada (Grant No. 432290).

60 APPLIED LIFE SCIENCES↗
DOE OSTI2026

Large Language Model for Validation, Optical Calibration, and Learning (VOCAL) Distributed Temperature Sensing Interface

Distributed temperature sensing (DTS) using fiber optic sensors (FOS) offers a promising method for temperature measurements in advanced reactors, such as sodium fast reactors and molten salt cooled reactors. To support the calibration and validation of DTS measurements, Argonne National Laboratory developed the Validation, Optical Calibration, and Learning (VOCAL) software package. This report describes the integration of a local large language model (LLM) with a retrieval-augmented generation (RAG) system into the VOCAL interface to serve as an interactive user assistant. The LLM framework enhances the VOCAL platform’s accessibility to users by explaining interface components, clarifying inputs and outputs, and answering user queries dynamically in real-time. The accuracy of the LLM assistant performance was evaluated with 20 queries regarding the interface and its parameters using experimental data from the Thermal Hydraulic Experimental Test Article (THETA) facility. Results demonstrate that the LLM achieved a 95% accuracy rate, with a BERTScore of 0.8816 and SBERT value of 0.7417. Furthermore, validation of the RAG system within the LLM framework showed optimal accuracy with k-values between 1 and 2 using the k-refinement convergence test. The prompt perturbation analysis demonstrated good initial consistency for the RAG system, exhibiting the highest accuracy under punctuation variations and the greatest sensitivity under query reordering. Notably, the model’s errors were limited to data retrieval failures rather than factual hallucinations, reinforcing its baseline reliability. The integration of LLM provides a highly accurate, userfriendly enhancement to the VOCAL platform without disrupting its core computational capabilities for FOS calibration and validation.

Hong, Evan↗
DOE OSTI2023

Theory-Enabled High-Throughput Screening of Ion Dissociation Explains Conductivity Enhancements in Diluted Ionic Liquid Mixtures

The growing demand for room-temperature ionic liquids (RTILs) for energy applications necessitates the development of an efficient screening platform. Here, in this study, we successfully developed a fully automated high-throughput RTIL screening platform specifically designed for assessing ionic conductivity. By utilizing the 96 wells of a microtiter plate as individual electrolysis cells, we measured the ionic conductivity of 22 different RTILs, encompassing various combinations of cations and anions, and benchmarked the values with existing literature. We also employed the screening platform to investigate the conductivities of RTIL mixtures with a nonaqueous solvent, ethylene glycol (EG). Specific combinations of RTILs with EG result in approximately 200% enhancement in the conductivity values compared to the pure RTILs. To understand the underlying mechanisms responsible for this enhancement, we developed a theoretical framework for ionic conductivity that considers factors such as the degree of dissociation, viscous forces, and molal volume of the RTIL-EG mixtures. The optimized electrolyte mixture was then employed in the migration-assisted moisture gradient (MAMG) CO 2 capture process to study the effects of improved ionic conductivity on the energy efficiency of the process. Notably, the enhanced conductivity of the RTIL-EG mixture led to a nearly 50% reduction in energy consumption for capturing CO 2 . These outcomes highlight the effectiveness of our strategy in screening RTILs and improving existing processes. Moreover, this fully automated high-throughput setup, combined with the developed theoretical framework, provides a comprehensive platform for screening and studying RTIL mixtures with different solvents, enabling their application in various fields.

25 ENERGY STORAGE↗
DOE OSTI2021

Mapping Conductance and Switching Behavior of Graphene Devices In Situ

Graphene is proposed for use in various nanodevice designs, many of which harness emergent quantum properties for device functionality. However, visualization, measurement, and manipulation become nontrivial at nanometer and atomic scales, representing a significant challenge for device fabrication, characterization, and optimization at length scales where quantum effects emerge. Herein, proof of principle results at the crossroads between 2D nanoelectronic devices, e-beam-induced modulation, and imaging with secondary electron e-beam induced currents (SEEBIC) is presented. A device platform compatible with scanning transmission electron microscopy investigations is introduced. Then how the SEEBIC imaging technique can be used to visualize conductance and connectivity in single layer graphene nanodevices, even while supported on a thicker substrate (conditions under which conventional imaging fails) is shown. Finally, it is shown that the SEEBIC imaging technique can detect subtle differences in charge transport through time in nonohmic graphene nanoconstrictions indicating the potential to reveal dynamic electronic processes.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Two-well injector direct-phonon terahertz quantum cascade lasers

We present an experimental study on a terahertz quantum cascade laser (THz QCL) design that combines both two-well injector and direct-phonon scattering schemes, i.e., a so-called two-well injector direct-phonon design. As a result of the two-well injector direct-phonon scheme presented here, the lasers benefit from both a direct phonon scattering scheme for the lower laser level depopulation and a setback for the doping profile that reduces the overlap of the doped region with active laser states. Additionally, our design also has efficient isolation of the active laser levels from excited and continuum states as indicated by negative differential resistance behavior all the way up to room temperature. This scheme serves as a good platform for improving the temperature performance of THz QCLs as indicated by the encouraging temperature performance results of the device with a relatively high doping level of 7.56 × 10 10 cm −2 and T max ∼ 167 K. With the right optimization of the molecular beam epitaxy growth and interface quality, the injection coupling strength, and the doping density and its profile, the device could potentially reach higher temperatures than the latest records reached for the maximum operating temperature (T max ) of THz QCLs.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

A Sparse Distributed Gigascale Resolution Material Point Method

In this paper, we present a four-layer distributed simulation system and its adaptation to the Material Point Method (MPM). The system is built upon a performance portable C++ programming model targeting major High-Performance-Computing (HPC) platforms. A key ingredient of our system is a hierarchical block-tile-cell sparse grid data structure that is distributable to an arbitrary number of Message Passing Interface (MPI) ranks. We additionally propose strategies for efficient dynamic load balance optimization to maximize the efficiency of MPI tasks. Our simulation pipeline can easily switch among backend programming models, including OpenMP and CUDA, and can be effortlessly dispatched onto supercomputers and the cloud. Finally, we construct benchmark experiments and ablation studies on supercomputers and consumer workstations in a local network to evaluate the scalability and load balancing criteria. We demonstrate massively parallel, highly scalable, and gigascale resolution MPM simulations of up to 1.01 billion particles for less than 323.25 seconds per frame with 8 OpenSSH-connected workstations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Inference-Engine v0.1.0

Given a pre-trained neural network, Inference-Engine performs maps network inputs to outputs by executing the forward pass through the provided network. Although the predominant programming language for machine-learning is Python, most high-performance computing (HPC) applications are written in Fortran, C, or C++. Inference-Engine aims to support HPC programs and is written in Fortran, a language with a large feature set supporting interoperability with C. This software exposes concurrency in a portable way by using standard language features that some modern Fortran compilers can exploit with various optimizations, including offloading computation to a Graphics Processing Unit (GPU). In particular, this software makes extensive use of Fortran's "do concurrent" parallel loop construct, implicitly parallel array statements, and pure procedures that can be invoked inside "do concurrent" blocks. Inference-Engine also supports dynamic choice of inference methods at runtime. Two current options include one method that uses Fortran's "dot_product" intrinsic function inside "do concurrent" blocks and another method that instead uses Fortran' "matmul" array intrinsic function. We plan to investigate automatic compiler offloading of "do concurrent" calculations to GPUs and compile-time substitution of optimized libraries such as the Basic Linear Algebra Library (BLAS) for "matmul" invocations. We also envision the potential for the choice of which method to use could happen at program launch based on in situ performance measurements on any given platform.

Rouson, Damian↗
DOE OSTI2025

Quantum Software Engineering (Dagstuhl Seminar 24512)

The Dagstuhl Seminar 24512 on "Quantum Software Engineering" was held from December 15 to 20, 2024. It brought together 26 participants from industry and academia from 13 different countries, including senior and junior researchers as well as practitioners in the field of Quantum Software Engineering. The aim of the seminar was to advance software engineering methods and tools for the engineering of hybrid quantum systems by promoting personal interaction and open discussion among researchers who are already working in this emerging area of knowledge. The first day of the seminar was devoted to the topic "When software engineering meets quantum mechanics", while the second day focused on "Quantum software engineering and its challenges." During both days, 16 invited presentations were given. The rest of the seminar was organized into three working groups to address the topics "Quantum Software Design, Modelling and Architecturing", "Adaptive Hybrid Quantum Systems", and "Quantum Software Quality Assurance". The seminar was a very fruitful experience for all participants both in terms of scientific outcomes and in terms of the personal relationships that were generated to jointly address future experiences.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Energy Systems Integration: NREL + EATON

Electrification of transportation fleets provides an opportunity for optimizing multiple distributed energy resource (DER) technologies, such as solar and energy storage. NREL is partnering with Eaton to evaluate control strategies for managing electric bus (E-bus) fleets for grid services. The project team will develop a replicable platform for evaluating EV fleet management and quantifying benefits from grid services.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Partner with a Third-Party Delivery Service or Not? A Prediction-and-Decision Tool for Restaurants Facing Takeout Demand Surges During a Pandemic

Amidst the COVID-19 pandemic, restaurants become more reliant on no-contact pick-up or delivery ways for serving customers. As a result, they need to make tactical planning decisions such as whether to partner with online platforms, to form their own delivery team, or both. In this paper, we develop an integrated prediction-decision model to analyze the profit of combining the two approaches and to decide the needed number of drivers under stochastic demand. We first use the susceptible-infected-recovered (SIR) model to forecast future infected cases in a given region and then construct an autoregressive-moving-average (ARMA) regression model to predict food-ordering demand. Using predicted demand samples, we formulate a stochastic integer program to optimize food delivery plans. We conduct numerical studies using COVID-19 data and food-ordering demand data collected from local restaurants in Nuevo Leon, Mexico, from April to October 2020, to show results for helping restaurants build contingency plans under rapid market changes. Our method can be used under unexpected demand surges, various infection/vaccination status, and demand patterns. Here, our results show that a restaurant can benefit from partnering with third-party delivery platforms when (i) the subscription fee is low, (ii) customers can flexibly decide whether to order from platforms or from restaurants directly, (iii) customers require more efficient delivery, (iv) average delivery distance is long, or (v) demand variance is high.

97 MATHEMATICS AND COMPUTING↗