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Simply put, OCBA ensures that computational resources are distributed efficiently by allocating more simulation effort to design alternatives that are harder to evaluate or more likely to be the best. This allows researchers and decision-makers to achieve accurate results faster and with fewer resources.
OCBA has also been shown to enhance partition-based random search algorithms for solving deterministic global optimization problems.<ref name="Chen2014">{{cite journal | last1=Chen | first1=Wei | last2=Gao | first2=Siyang | last3=Chen | first3=Chun-Hung | last4=Shi | first4=Lei | title=An Optimal Sample Allocation Strategy for Partition-Based Random Search | journal=IEEE Transactions on Automation Science and Engineering | year=2014 | volume=11 | issue=1 | pages=177–186 | url=https://www.researchgate.net/publication/260721040 | publisher=IEEE | doi=10.1109/TASE.2013.2251881 | bibcode=2014ITASE..11..177C }}</ref> Over the years, OCBA has been applied in manufacturing systems design, healthcare planning, and financial modeling. It has also been extended to handle more complex scenarios, such as balancing multiple objectives,<ref name="Lee2012">{{cite journal | last1=Lee | first1=Loo Hay | last2=Li | first2=Li Wei | last3=Chen | first3=Chun-Hung | last4=Yap | first4=C. M. | title=Approximation Simulation Budget Allocation for Selecting the Best Design in the Presence of Stochastic Constraints | journal=IEEE Transactions on Automatic Control | year=2012 | volume=57 | issue=12 | pages=2940–2945 | doi=10.1109/TAC.2012.2204478 | doi-broken-date=
== Intuitive Explanation ==
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* <math>\delta_{i,j}=\mu_i-\mu_j</math>.
The budget allocation problem with the EOC objective measure is given by Gao et al. (2017)<ref>{{cite journal | url=https://pubsonline.informs.org/doi/abs/10.1287/opre.2016.1581 | doi=10.1287/opre.2016.1581 | title=A New Budget Allocation Framework for the Expected Opportunity Cost | date=2017 | last1=Gao | first1=Siyang | last2=Chen | first2=Weiwei | last3=Shi | first3=Leyuan | journal=Operations Research | volume=65 | issue=3 | pages=787–803 | url-access=subscription }}</ref>
: <math>
\begin{align}
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* '''Monte Carlo Tree Search (MCTS):'''
** A 2020 study proposed an OCBA-based tree policy for MCTS, optimizing computational resource allocation to maximize the probability of correct action selection. This approach maximizes the probability of correct action selection under limited sampling budgets by dynamically balancing exploration of less-sampled actions and exploitation of promising ones.<ref>{{cite journal | last1=Li | first1=Yunchuan | last2=Fu | first2=Michael C. | last3=Xu | first3=Jie | title=An Optimal Computing Budget Allocation Tree Policy for Monte Carlo Tree Search | journal=
* '''Online Serving Systems:'''
** The Distributed Asynchronous Optimal Computing Budget Allocation (DA-OCBA) framework applies OCBA principles in a cloud computing environment for simulation optimization. By utilizing idle docker containers and enabling asynchronous execution of simulation tasks, DA-OCBA improves the efficiency of simulation optimization in large-scale systems. The framework demonstrates significant computational savings and scalability, making it particularly useful in applications such as cloud-based resource allocation systems.<ref>{{cite journal | last1=Wang | first1=Yu | last2=Tang | first2=Wei | last3=Yao | first3=Yan | last4=Zhu | first4=Fang | title=DA-OCBA: Distributed Asynchronous Optimal Computing Budget Allocation Algorithm of Simulation Optimization Using Cloud Computing | journal=Symmetry | year=2019 | volume=11 | issue=10 | pages=1297 | doi=10.3390/sym11101297 | doi-access=free | bibcode=2019Symm...11.1297W }}</ref>
*'''Digital Twinning and Decision Support Systems for Maintaining A Resilient Port:'''
**As real-world physical systems become increasingly more elaborate and subject to wide-ranging external factors and disruptions, it becomes necessary to develop mechanisms to both monitor changes and coordinate the successful operation of all the aspects of the system. A 2021 paper proposes OCBA as a means of ensuring the successful allocation of resources to reduce the impact of hazards and environmental factors that may block the timely transfer of cargo across ports. By implementing OCBA within a digital twin-based framework, decision makers will be able to use real-time data to optimize the number of simulation runs for each recovery alternative.<ref>{{cite journal | doi=10.1016/j.dss.2021.113496 | title=Analytics with digital-twinning: A decision support system for maintaining a resilient port | date=2021 | last1=Zhou | first1=Chenhao | last2=Xu | first2=Jie | last3=Miller-Hooks | first3=Elise | last4=Zhou | first4=Weiwen | last5=Chen | first5=Chun-Hung | last6=Lee | first6=Loo Hay | last7=Chew | first7=Ek Peng | last8=Li | first8=Haobin | journal=Decision Support Systems | volume=143 | article-number=113496 }}</ref>
These recent innovations demonstrate OCBA's growing versatility and effectiveness in optimizing resource allocation for diverse applications.
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=== Applications ===
'''Predictive Multi-Fidelity Models:''' Gaussian Mixture Models (GMMs) predict relationships between low- and high-fidelity simulations, enabling OCBA to focus on the most promising alternatives. Multi-fidelity models combine insights from low-fidelity simulations, which are computationally inexpensive but less accurate, and high-fidelity simulations, which are more accurate but computationally intensive. The integration of GMMs into this process allows OCBA to strategically allocate computational resources across fidelity levels, significantly reducing simulation costs while maintaining decision accuracy.<ref>{{cite journal |last1=Peng |first1=Y. |last2=Xu |first2=J. |last3=Lee |first3=L. H. |last4=Hu |first4=J. |last5=Chen |first5=C. H. |title=Efficient Simulation Sampling Allocation Using Multifidelity Models |journal=IEEE Transactions on Automatic Control |year=2019 |volume=64 |issue=8 |pages=3156–3169 |doi=10.1109/TAC.2018.2886165 |
'''Dynamic Resource Allocation in Healthcare:''' A Bayesian OCBA framework has been applied to allocate resources in hospital emergency departments, balancing service quality with operational efficiency. By minimizing expected opportunity costs, this approach supports real-time decision-making in high-stakes environments.<ref>{{cite journal | title=Optimizing Resource Allocation in Service Systems via Simulation: A Bayesian Formulation | journal=Production and Operations Management | year=2023 | doi=
'''Sequential Allocation using Machine-learning Predictions as Light-weight Estimates (SAMPLE):''' SAMPLE is an extension of OCBA that presents a new opportunity for the integration of machine learning with digital twins for real-time simulation optimization and decision-making. Current methods for applying machine learning on simulation data may not produce the optimal solution due to errors encountered during the predictive learning phase since training data can be limited. SAMPLE overcomes this issue by leveraging lightweight machine learning models, which are easy to train and interpret, then running additional simulations once the real-world context is captured through the digital twin.<ref>{{cite journal | doi=10.1080/17477778.2022.2046520 | title=Real-time digital twin-based optimization with predictive simulation learning | date=2024 | last1=Goodwin | first1=Travis | last2=Xu | first2=Jie | last3=Celik | first3=Nurcin | last4=Chen | first4=Chun-Hung | journal=Journal of Simulation | volume=18 | pages=47–64 }}</ref>
== References ==
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