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In Computer Science, '''Optimal Computing Budget Allocation (OCBA)''' is a simulation optimization method designed to maximize the Probability of Correct Selection (PCS) while minimizing computational costs. First introduced by Dr. Chun-Hung Chen in the mid-1990s, OCBA determines how many simulation runs (or how much computational time) or the number of replications each design alternative needs to identify the best option while using as few resources as possible.<ref name="Chen1995">{{cite conference | last=Chen | first=Chun-Hung | title=An Effective Approach to Smartly Allocate Computing Budget for Discrete Event Simulation | book-title=Proceedings of the 34th IEEE Conference on Decision and Control | year=1995 | pages=2598–2605 | url=https://ieeexplore.ieee.org/document/478499 | publisher=IEEE }} </ref><ref name="Chen2011">{{cite book | last1=Chen | first1=Chun-Hung | last2=Lee | first2=Loo H. | title=Stochastic Simulation Optimization: An Optimal Computing Budget Allocation | series=World Scientific Series on Nonlinear Science Series A | publisher=World Scientific | year=2011 | volume=82 | doi=10.1142/7437 | isbn=978-981-4282-64-2 | url=https://www.worldscientific.com/worldscibooks/10.1142/7437?srsltid=AfmBOoqKrPtEAQwx9OAUZIJMIuye75kDLYKHtuoFV7_RhJAsW6O0DA8A#t=aboutBook }}</ref> It works by focusing more on alternatives that are harder to evaluate, such as those with higher uncertainty or close performance to the best option.

{{Technical|date=May 2021}}

{{Orphan|date=October 2013}}}}

In [[computer science]], '''Optimal computing budget allocation''' ('''OCBA''') is an approach to maximize the overall [[simulation]] efficiency for finding an optimal decision.<ref>Fu, M, C. H. Chen, and L. Shi, “[http://simulation.su/uploads/files/default/2008-fu-chun-hung-shi.pdf Some Topics for Simulation Optimization],” Proceedings of 2008 Winter Simulation Conference, pp. 27–38, Miami, FL, December 2008.</ref> It was introduced in the mid-1990s by Dr. Chun-Hung Chen.

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 determines the number of [[Replication (statistics)|replications]] or the simulation time that is needed in order to receive acceptable or best results within a set of given parameters.<ref>Chen, and Loo H. Lee. [https://books.google.com/books?hl=en&lr=&id=wtVpDQAAQBAJ&oi=fnd&pg=PR5&dq=%22Stochastic+simulation+optimization+an+optimal+computing+budget+allocation%22&ots=evSr8zuuWn&sig=crRw81au6-FEK8S0DeoDzlEFR_w#v=onepage&q=%22Stochastic%20simulation%20optimization%20an%20optimal%20computing%20budget%20allocation%22&f=false Stochastic simulation optimization an optimal computing budget allocation]. Singapore Hackensack, NJ: World Scientific, 2011. Print..</ref> This is accomplished by using an [[Asymptote|asymptotic]] framework to analyze the structure of the optimal allocation.<ref>Chen, C. H. "[https://ieeexplore.ieee.org/abstract/document/478499/ An Effective Approach to Smartly Allocate Computing Budget for Discrete Event Simulation]," Proceedings of the 34th IEEE Conference on Decision and Control, pp. 2598–2605, December 1995.</ref>

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=1 July 2025 | url=https://ieeexplore.ieee.org/document/5371030 }}</ref> feasibility determination,<ref name="Szechtman2008">{{cite conference | last1=Szechtman | first1=R. | last2=Yücesan | first2=E. | title=A New Perspective on Feasibility Determination | book-title=Proceedings of the 2008 Winter Simulation Conference | year=2008 | pages=273–280 | url=https://informs-sim.org/wsc08papers/005.pdf }}</ref> and constrained optimization.<ref name="Gao2017">{{cite journal | last1=Gao | first1=Shu | last2=Xiao | first2=Hongsheng | last3=Zhou | first3=Enlu | last4=Chen | first4=Wei | title=Robust Ranking and Selection with Optimal Computing Budget Allocation | journal=Automatica | year=2017 | volume=81 | pages=30–36 | doi=10.1016/j.automatica.2017.03.015 | url=https://www.sciencedirect.com/science/article/abs/pii/S0005109817301070 }}</ref>

OCBA has also been shown effective in enhancing partition-based random [[Search algorithm|search algorithms]] for solving [[deterministic global optimization]] problems.<ref>Chen, W., S. Gao, C. H. Chen and L. Shi, "[https://www.researchgate.net/profile/Siyang_Gao2/publication/260721040_An_Optimal_Sample_Allocation_Strategy_for_Partition-Based_Random_Search/links/582584b808aeb45b58927ed5/An-Optimal-Sample-Allocation-Strategy-for-Partition-Based-Random-Search.pdf An Optimal Sample Allocation Strategy for Partition-based Random Search]," IEEE Transactions on Automation Science and Engineering, 11(1), 177–186, 2014.</ref>

== Intuitive explanationExplanation ==

OCBA'sThe goal of OCBA is to provide a systematic approach to efficiently run a large number of [[Simulation|simulations]] includingby focusing only on the critical alternatives, in order to select the best alternative.

In other words, OCBA focuses onprioritizes only part the most critical alternatives, which minimizesminimizing [[computation time]] and reducesreducing the variances of these critical [[Estimator|estimators]]’ variances. The expected resultoutcome is maintainsmaintaining the required level of [[Accuracy and precision|accuracy]], while requiring lessfewer amount ofcomputational workresources.<ref>{{cite web|last=Chen|first=Chun-Hung|title=Optimal Computing Budget Allocation (OCBA) for Simulation-based Decision Making Under Uncertainty|url=http://seor.gmu.edu/~cchen9/ocba.html|access-date=9 July 2013|url-status=dead|archive-url=https://archive.istoday/20131001025704/http://seor.gmu.edu/~cchen9/ocba.html|archive-date=1 October 2013}}</ref>

[[File:Comparing 5 different alternatives with respect to Cost.png|Figure 1: Preliminary simulation results show alternatives 2 and 3 have lower average delay times. OCBA suggests focusing further simulation resources on alternatives 2 and 3 while stopping simulations for alternatives 1, 4, and 5 to save costs without compromising accuracy.|thumb|400x400px]]

For example, we can create a simple simulation between five alternatives. The goal is to select an alternative with minimum average delay time. The figure below shows preliminary simulation results ( i.e. having run only a fraction of the required number of simulation replications). It is clear to see that alternative 2 and 3 have a significantly lower delay time (highlighted in red). In order to save computation cost (which is time, resources and money spend on the process of running the simulation) OCBA suggests that more replications are required for alternative 2 and 3, and simulation can be stopped for 1, 4, and 5 much earlier without compromising results.

[[File:Comparing 5 different alternatives with respect to Cost.png|framed|Observing the above graphic, it is clear that alternative 2 and 3 have the lowest cost. OCBA suggests to run further simulations on only alternatives 2 and 3 in order to minimize computation cost]]

For example, we can createconsider a simple simulation betweeninvolving five alternatives., Thewhere the goal is to select anthe alternativeone with the minimum average delay time. TheFigure figure below1, shows preliminary simulation results ( i.e., having run only a fraction of the required number of simulation replications). It is clear to see that alternativeAlternatives 2 and 3 clearly have a significantly lower delay timetimes (highlighted in red). In order toTo save computation costcost—which (which isincludes time, resources, and money spendspent on the process of running the simulation) OCBAsimulations—OCBA suggests that more replications areshould requiredbe forallocated alternativeto alternatives 2 and 3, andwhile simulationsimulations canfor be stopped foralternatives 1, 4, and 5 can be stopped much earlier without compromising resultsaccuracy.

== Core Optimization Problem ==

Simulation is widely used for designing large, complex, stochastic systems, where analytical solutions are often infeasible. However, simulations can be computationally expensive because multiple simulation runs are needed to account for stochastic variability. The challenge lies in efficiently allocating limited computational resources to identify the best design alternative with high confidence.

The primary objective of OCBA is to maximize the Probability of Correct Selection (PCS), which represents the likelihood of identifying the best-performing design alternative among a finite set of options. This goal must be achieved while adhering to a limited computational budget. PCS is calculated based on the number of simulation replications allocated to each design.

The main objective of OCBA is to maximize the [[probability]] of correct selection (PCS). PCS is subject to the sampling budget of a given stage of sampling&nbsp;''τ''.

The problem is mathematically formulated as:

: <math>

\begin{align}

<big><math display="block"> \max_{\tau_1,\tau_2,\ldots,\tau_k} &\mathrm{ PCS} \\</math></big>

\text{subject to } &\sum_{i=1}^k \tau_i=\tau,\\

Subject to:

& \tau_i \ge 0, i=1,2,...,k.\qquad (1)

\end{align}

<big><math> \sum_{i=1}^k \tau_i = \tau, \quad \tau_i \geq 0, ; i=1,2,...,k </math></big>

</math>

where:

<math>k</math>: Total number of design alternatives

<math>\tau_i</math>: Number of simulation replications allocated to the <math>i</math>-th design

<math>\tau</math>: Total computational budget

OCBA optimizes the allocation of simulation replications by focusing on alternatives with higher variances or smaller performance gaps relative to the best alternative. The ratio of replications between two alternatives, such as <math>N_2</math> and <math>N_3</math>, is determined by the following formula:

<big><math display="block"> \frac{N_2}{N_3} = \frac{\left( \frac{\sigma_2}{\delta_{1,2}} \right)^2}{\left( \frac{\sigma_3}{\delta_{1,3}} \right)^2} </math></big>

Here:

<math>\sigma_i</math>: The variance of the performance of alternative <math>i</math>.

<math>\delta_{1,i}</math>: The performance gap between the best alternative (<math>1</math>) and alternative <math>i</math>.

<math>N_i</math>: The number of simulation replications allocated to alternative <math>i</math>.

This formula ensures that alternatives with smaller performance gaps (<math>\delta_{1,i}</math>) or higher variances (<math>\sigma_i</math>) receive more simulation replications. This maximizes computational efficiency while maintaining a high Probability of Correct Selection (PCS), ensuring computational efficiency by reducing replications for non-critical alternatives and increasing them for critical ones.<ref>Chen, C. H., J. Lin, E. Yücesan, and S. E. Chick, "Simulation Budget Allocation for Further Enhancing the Efficiency of Ordinal Optimization," Journal of Discrete Event Dynamic Systems, 2000.</ref> Numerical results show that OCBA can achieve the same simulation quality with only one-tenth of the computational effort compared to traditional methods.<ref name="Chen2011">{{cite book | last1=Chen | first1=Chun-Hung | last2=Lee | first2=Loo H. | title=Stochastic Simulation Optimization: An Optimal Computing Budget Allocation | series=World Scientific Series on Nonlinear Science Series A | publisher=World Scientific | year=2011 | volume=82 | doi=10.1142/7437 | isbn=978-981-4282-64-2 | url=https://www.worldscientific.com/worldscibooks/10.1142/7437?srsltid=AfmBOoqKrPtEAQwx9OAUZIJMIuye75kDLYKHtuoFV7_RhJAsW6O0DA8A#t=aboutBook }}</ref>

In this case <math>\sum_{i=1}^k \tau_i=\tau</math> stands for the total computational cost.<ref>Chen, and Loo H. Lee. [https://books.google.com/books?hl=en&lr=&id=wtVpDQAAQBAJ&oi=fnd&pg=PR5&dq=%22Stochastic+simulation+optimization+an+optimal+computing+budget+allocation%22&ots=evSr8zuuWn&sig=crRw81au6-FEK8S0DeoDzlEFR_w#v=onepage&q=%22Stochastic%20simulation%20optimization%20an%20optimal%20computing%20budget%20allocation%22&f=false Stochastic simulation optimization an optimal computing budget allocation]. Singapore Hackensack, NJ: World Scientific, 2011. Print.</ref>

== Some extensions of OCBA ==

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According to Szechtman and Yücesan (2008),<ref>Szechtman R, Yücesan E (2008) [https://calhoun.nps.edu/bitstream/handle/10945/38580/031.pdf?sequence=3 A new perspective on feasibility determination]. Proc of the 2008 Winter Simul Conf 273–280</ref> OCBA is also helpful in feasibility determination problems. This is where the decisions makers are only interested in differentiating [[Logical possibility|feasible]] alternatives from the infeasible ones. Further, choosing an alternative that is simpler, yet similar in performance is crucial for other decision makers. In this case, the best choice is among top-r simplest alternatives, whose [[performance]] rank above desired levels.<ref>Jia QS, Zhou E, Chen CH (2012). [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3653338/ efficient computing budget allocation for finding simplest good designs]. IIE Trans, To Appear.</ref>

In addition, Trailovic<ref>Trailovic Tekin E, Sabuncuoglu I (2004) Simulation optimization: A comprehensive review on theory and applications. IIE Trans 36:1067–1081</ref> and Pao<ref>Trailovic L, Pao LY (2004) [http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.15.1213&rep=rep1&type=pdf Computing budget allocation for efficient ranking and selection of variances with application to target tracking algorithms], IEEE Trans Autom Control 49:58–67.</ref> (2004) demonstrate an OCBA approach, where we find alternatives with minimum [[variance]], instead of with best mean. Here, we assume unknown variances, voiding the OCBA rule (assuming that the variances are known). During 2010 research was done on an OCBA algorithm that is based on a t distribution. The results show no significant differences between those from t-distribution and [[normal distribution]]. The above presented extensions of OCBA is not a complete list and is yet to be fully explored and compiled.<ref name="ChenChen2011">Chen,{{cite C.book H.,| M.last1=Chen Fu,| L.first1=Chun-Hung Shi,| andlast2=Lee L.| first2=Loo H. Lee,| “Stochastic Systemstitle=Stochastic Simulation Optimization,”: FrontiersAn ofOptimal ElectricalComputing andBudget ElectronicAllocation Engineering| inseries=World China,Scientific 6(3),Series 468–480,on Nonlinear Science Series A | publisher=World Scientific | year=2011 | volume=82 | doi=10.1142/7437 | isbn=978-981-4282-64-2 | url=https://www.worldscientific.com/worldscibooks/10.1142/7437?srsltid=AfmBOoqKrPtEAQwx9OAUZIJMIuye75kDLYKHtuoFV7_RhJAsW6O0DA8A#t=aboutBook }}</ref>

== Multi-objectiveObjective OCBA ==

Multi-objectiveObjective Optimal Computing Budget Allocation (MOCBA) is the OCBA concept that applies to multi-objective problems. In a typical MOCBA, the PCS is defined as

<math display="block">\Pr\{CS\} \equiv \Pr \left\{ \left( \bigcap_{i \in S_p} E_i \right) \bigcap \left( \bigcap_{i \in \overline{S}_p} E_i^c \right) \right\}, </math>

in which

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<math>\rho_i = \alpha_{j_i} / \alpha_i.</math>

== Constrained optimization==

Similar to the previous section, there are many situations with multiple performance measures. If the multiple performance measures are equally important, the decision makers can use the MOCBA. In other situations, the decision makers have one primary performance measure to be [[program optimization|optimized]]{{dn|date=June 2021}} while the secondary performance measures are constrained by certain limits.

The primary performance measure can be called the main objective while the secondary performance measures are referred as the constraint measures. This falls into the problem of [[constrained optimization]]. When the number of alternatives is fixed, the problem is called constrained ranking and selection where the goal is to select the best feasible design given that both the main objective and the constraint measures need to be estimated via [[stochastic]] simulation. The OCBA method for constrained optimization (called OCBA-CO) can be found in Pujowidianto et al. (2009) <ref>Pujowidianto NA, Lee LH, Chen CH, Yap CM (2009) [https://core.ac.uk/download/pdf/48657520.pdf Optimal computing budget allocation for constrained optimization]. Proc of the 2009 Winter Simul Conf 584–589.</ref> and Lee et al. (2012).<ref>Lee LH, Pujowidianto NA, Li LW, Chen CH, Yap CM (2012) [https://ieeexplore.ieee.org/abstract/document/6189041/ Approximation simulation budget allocation for selecting the best design in the presence of stochastic constraints], IEEE Trans Autom Control 57:2940–2945.</ref>

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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>Gao,{{cite S., W. Chenjournal and| L. Shi, "[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, 63,| volume=65 | issue=3 | pages=787–803, 2017.| url-access=subscription }}</ref>

: <math>

\begin{align}

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An [[implicit assumption]] for the aforementioned OCBA methods is that the true input distributions and their [[Parameter|parameters]] are known, while in practice, they are typically unknown and have to be estimated from limited historical data. This may lead to uncertainty in the estimated input distributions and their parameters, which might (severely) affect the quality of the selection. Assuming that the uncertainty set contains a finite number of [[Scenario|scenarios]] for the underlying input distributions and parameters, Gao et al. (2017)<ref>Gao, S., H. Xiao, E. Zhou and W. Chen, "[https://www.sciencedirect.com/science/article/pii/S0005109817301425 Robust Ranking and Selection with Optimal Computing Budget Allocation]," Automatica, 81, 30–36, 2017.</ref> introduces a new OCBA approach by maximizing the probability of correctly selecting the best design under a fixed simulation budget, where the performance of a design is measured by its worst-case performance among all the possible scenarios in the uncertainty set.

== Web-basedRecent demonstrationApplications of OCBA ==

Optimal Computing Budget Allocation (OCBA), has continued to evolve, demonstrating its adaptability and efficiency in addressing complex decision-making problems across various domains.

== Web-based demonstration of OCBA ==

* '''Simulation-Based Ranking and Selection:'''

The following link provides an OCBA demonstration using a simple example. In the demo, OCBA performs and allocates computing budget differently as compared with traditional equal allocation approach.

** A 2023 study introduced a budget-adaptive allocation rule for OCBA, dynamically adjusting simulation budgets to maximize the probability of correct selection. This approach was validated through synthetic examples and case studies, showcasing its efficiency in identifying optimal system designs.<ref>{{cite conference | last=Chen | first=Chun-Hung | title=An Effective Approach to Smartly Allocate Computing Budget for Discrete Event Simulation | book-title=Proceedings of the 34th IEEE Conference on Decision and Control | year=1995 | pages=2598–2605 | url=https://ieeexplore.ieee.org/document/478499 | publisher=IEEE }} </ref>

* '''Data-Driven Decision Making:'''

== See also ==

** In 2022, researchers developed a data-driven OCBA method that addresses input uncertainty by updating distribution estimates with streaming data. This method ensures consistent and asymptotically optimal selection of the best design, enhancing decision-making in dynamic environments.<ref name="Chen2011">{{cite book | last1=Chen | first1=Chun-Hung | last2=Lee | first2=Loo H. | title=Stochastic Simulation Optimization: An Optimal Computing Budget Allocation | series=World Scientific Series on Nonlinear Science Series A | publisher=World Scientific | year=2011 | volume=82 | doi=10.1142/7437 | isbn=978-981-4282-64-2 | url=https://www.worldscientific.com/worldscibooks/10.1142/7437?srsltid=AfmBOoqKrPtEAQwx9OAUZIJMIuye75kDLYKHtuoFV7_RhJAsW6O0DA8A#t=aboutBook }}</ref>

* http://seor.vse.gmu.edu/~cchen9/ocba.html

* '''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=IEEE Transactions on Automatic Control | date=2020 | volume=67 | issue=6 | page=2685 | doi=10.1109/TAC.2021.3088792 | arxiv=2009.12407 | bibcode=2022ITAC...67.2685L }}</ref>

* '''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.

== Emerging Research Area: Integration of Machine Learning with OCBA ==

The integration of Machine Learning (ML) with Optimal Computing Budget Allocation (OCBA) represents a promising area of research, leveraging ML’s predictive capabilities to enhance the efficiency and accuracy of simulation optimization. By incorporating ML models, OCBA can dynamically adapt resource allocation strategies, addressing complex decision-making problems with greater computational efficiency.

=== 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 |bibcode=2019ITAC...64.3156P }}</ref>

'''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=10.1111/poms.13825 | last1=Chen | first1=Weiwei | last2=Gao | first2=Siyang | last3=Chen | first3=Wenjie | last4=Du | first4=Jianzhong | volume=32 | pages=65–81 | doi-access=free }}</ref> Additionally, the integration of OCBA with real-time digital twin-based optimization has further advanced its application in predictive simulation learning, enabling dynamic adjustments to resource allocation in healthcare settings.<ref>{{cite journal | last1=Goodwin | first1=Timothy | last2=Xu | first2=Jie | last3=Celik | first3=Niyazi | last4=Chen | first4=Chun-Hung | title=Real-Time Digital Twin-Based Optimization with Predictive Simulation Learning | journal=Journal of Simulation | year=2024 | volume=18 | issue=1 | pages=47–64 | doi=10.1080/17477778.2022.2046520 | url=https://www.tandfonline.com/doi/full/10.1080/17477778.2022.2046520 | url-access=subscription }}</ref> Furthermore, a contextual ranking and selection method for personalized medicine leverages OCBA to optimize resource allocation in treatments tailored to individual patient profiles, demonstrating its potential in personalized healthcare.<ref>{{cite journal | last1=Gao | first1=Siyang | last2=Du | first2=Jianzhong | last3=Chen | first3=Chun-Hung | title=A Contextual Ranking and Selection Method for Personalized Medicine | journal=Manufacturing and Service Operations Management | year=2024 | volume=26 | issue=1 | pages=167–181 | doi=10.1287/msom.2022.0232 | arxiv=2206.12640 | url=https://pubsonline.informs.org/doi/10.1287/msom.2022.0232 }}</ref>

'''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 ==

{{Reflist}}

<!--- See [[Wikipedia:Footnotes]] on how to create references using<ref></ref> tags which will then appear here automatically -->

{{Reflist}}

== External links ==

* [http://seor.vse.gmu.edu/~cchen9/ocba.html Optimal Computing Budget Allocation (OCBA) for Simulation-based Decision Making Under Uncertainty (Simulation Optimization)]

* [http://carschimp.com/blog/ocba/ Russian translation] of OCBA page by [http://carschimp.com Carschimp]

* [http://sciposts.com/ocba/ Ukrainian translation] of OCBA page by [http://sciposts.com/ sciposts]

[[Category:Stochastic optimization]]