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ISSN : 2005-0461(Print)
ISSN : 2287-7975(Online)

Journal of Society of Korea Industrial and Systems Engineering Vol.49 No.2 pp.142-152
DOI : https://doi.org/10.11627/jksie.2026.49.2.142

Bayesian Optimization for Weight-based Dispatching of Stocker Systems in a Display Fab

Jonghyeon Chun^*

, Bosung Kim^*

, Min Hong^**

, Soondo Hong^***†

^*Major in Industrial Data Science and Engineering, Department of Industrial Engineering, Pusan National University
^**Mobile Display Logistics Automation Team, Samsung Display
^***Department of Industrial Engineering, Pusan National University

^†Corresponding Author : soondo.hong@pusan.ac.kr

Received 08/06/2026 Finally Revised 19/06/2026 Accepted 23/06/2026

Abstract

The stocker is a critical material handling system for transporting work-in-process materials in a display fab. Efficient dispatching is particularly challenging in twin-crane systems. The cranes share a single track while jobs arrive dynamically. In this study, we consider a weight-based dispatching method that combines multiple dispatching rules. The weight set determines the relative importance of multiple dispatching rules with competing objectives such as job priority and travel time, and its effectiveness varies with system dynamics. Evaluating weight sets requires simulation in stochastic and dynamic systems, which is computationally expensive. We therefore propose a simulation optimization framework to efficiently search the best weight set. Gaussian process-based Bayesian optimization is employed to guide the search under a limited simulation budget. Experimental results show that the relative importance of dispatching rules changes across scenarios. The proposed framework consistently identifies effective weight sets across diverse operating conditions.

Key Words : Simulation Optimization , Bayesian Optimization , Dispatching , Stocker System

디스플레이 Fab 저장 물류시스템의 가중치 기반 디스패칭을 위한 베이지안 최적화 방법론

천종현^*, 김보성^*, 홍 민^**, 홍순도^***†

^*부산대학교 산업공학과 산업데이터공학융합전공
^**삼성디스플레이 중소형사업부 물류자동화팀
^***부산대학교 산업공학과

초록

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1. Introduction

Stocker systems are essential components of material handling systems (MHSs) in display fabrication facilities (fabs), responsible for storage, transport, load and unload of work-in-process (WIP) materials [8]. These systems rely on real-time lot dispatching rules to assign tasks to cranes. As operational complexity increases, it becomes necessary to consider multiple objectives simultaneously—such as prompt delivery, minimization of waiting time, and efficient crane utilization. Since no single dispatching rule can satisfy all objectives, a weighted combination of multiple rules—commonly known as weight-based dispatching—is widely adopted in dynamic environments like stocker systems [7, 9, 15].

The performance of a given weight set cannot be expressed in closed form, since it emerges from dynamic interactions. It can only be evaluated by the system under realistic operating conditions. Recent advancements in digital twin technologies enable accurate evaluation of dynamic and stochastic systems, which are black-box problems [10]. The reliability of digital twins has also been improved through calibration, allowing them to closely mirror the behavior of physical systems [12]. The resulting weight set is also readily interpretable, helping operators understand which rules matter most for each stocker.

The high computational cost of digital twin-based evaluations induces a significant challenge in searching for effective weight set within a reasonable time. Bayesian approaches can efficiently navigate solutions in large and complex search space while learning the response of weight set [11]. Bayesian optimization (BO) constructs a surrogate model that approximates the simulation output and identifies the promising weight set based on both predicted improvement and uncertainty [2]. As a result, BO reduces evaluation costs and enables efficient exploration of large and complex search spaces [4, 13].

In this study, we propose a weight optimization framework that integrates BO with a simulation to efficiently optimize weight set. As shown in <Figure 1>, conventional stocker systems rely on real-time lot dispatching by the controller system. In the proposed framework, the simulation evaluates candidate weight sets under given operating scenarios, and BO guides the search toward an effective set with fewer evaluations. This reduces the computational cost of optimization and shortens the time needed to update weight set as operating conditions change.

The contributions of our study are as follows. First, we propose a simulation optimization framework for weight-based dispatching in a twin-crane stocker system. Second, we apply Gaussian Process (GP)-based BO framework to optimize the weight set under a limited simulation budget, and show that proposed framework outperforms GA and surrogate alternatives. Third, we analyze how the optimized weight sets change across operating scenarios, showing that the relative importance of dispatching rules varies with workload and hand-off conditions.

The remainder of this paper is organized as follows. Section 2 reviews related literature on weight-based dispatching and simulation optimization. Section 3 formally defines the weight-based dispatching in the context of stocker systems. Section 4 presents the proposed BO framework. Section 5 provides experimental results, and Section 6 concludes the paper and presents future research.

2. Literature Review

Weight-based dispatching has been widely adopted to address multiple objectives simultaneously in various industries. Dabbas et al. [9] introduce a multiple combined dispatching criteria by using linear combination of each rules with relative weight set. Ang et al. [1] propose a weight-based dispatching strategy for a single-machine environment with sequence-dependent setups, designed to balance conflicting performance objectives. Chiou et al. [7] implement a parameterized weight-based dispatching rule in the Logic IC Sort stage of a semiconductor wafer fab, reduces tardiness compared with single dispatching rule. Qin et al. [17] propose a dynamic dispatching method with fuzzy logic and a Hungarian algorithm to adjust the weight set of each rule.

To improve the effectiveness of weight-based dispatching, researchers have focused on optimizing the weight set. Zhang et al. [18] propose a fixed order of dispatching rules and optimize the criteria for rule selection with response surface method. Chen and Matis [6] propose a rule that computes a priority index as a linear combination of slack and processing time. Operators control how strongly the rule gives precedence to high priority jobs. Lee et al. [15] propose a sequential search using decision trees and hierarchical clustering to search for effective weight set.

Simulation forms the backbone of digital twin and supports analysis and decision-making in complex and stochastic systems. Simulation optimization extends this capability to efficiently utilize costly simulations under limited budgets. Chang et al. [5] model interactions between various machines in a semiconductor fab via simulation. They employ Genetic Algorithm (GA) to find the optimal combination of dispatching rules for each machine. Candelieri et al. [4] used BO to solve scheduling problems in water distribution systems and achieved an effective solution with limited evaluations. Kang et al. [13] applies BO to optimize vehicle dwelling policies for Overhead Hoist Transport (OHT) in a semiconductor fab. Pearce et al. [16] address stochastic simulation optimization with common random numbers, modeling the random seed in the GP surrogate to exploit correlated noise and reduce variance in the search. Karkaria et al. [14] combine a digital twin with machine learning and BO to optimize process parameters in additive manufacturing, dynamically searching for optimal process profiles. They reduce the number of simulation calls while achieving superior solutions compared to conventional methods.

Previous studies address the weight optimization problem mainly with metaheuristics or response surface methods, which require many simulation evaluations. Others apply BO to operational decisions such as scheduling and dwelling policies. This study applies GP-based BO to the weight optimization problem for a twin-crane stocker system under a limited simulation budget.

3. System and Problem Description

In this section we first describe stocker systems and lot dispatching rules. We formulate the weight-based dispatching rule (WDR) procedure and define the associated weight set optimization problem.

3.1 Stocker System and Lot Dispatching Rule

In a display fab, the stocker system performs storing, transporting, loading and unloading WIPs. It consists of two or more cranes, storage shelves, and input and output (I/O) ports interfacing with machines and other material handling systems as shown in <Figure 2>.

The Material Controller System (MCS) requests jobs to deliver cassettes containing display panels. The Stocker Control System (SCS) assigns each job to a crane based on lot dispatching rules. Each crane transports a cassette from its source to a target location. Since both cranes operate on the same pathway, they cannot pass each other. As shown in <Figure 2>, both cranes share the common zone where interference may occur. Jobs whose source and target are located in exclusive zones require a hand-off operation. The hand-off may lead to additional interference in the common zone. Therefore, effective lot dispatching is essential to minimize such conflicts.

Lot dispatching determines which job is assigned to an idle crane based on a given rule. Each lot dispatching rule is designed with a specific objective and evaluates jobs accordingly. The six lot dispatching rules considered in this study are denoted R1 through R6, as defined in <Table 1>. R1 ~ R3 are rules that reduce crane travel time, R4 prioritizes urgent jobs, and R5 preserves the order of requests to limit excessive waiting. R6 accounts for blocking between the two cranes. Each rule reflects a single objective, and no individual rule simultaneously satisfies the competing objectives of a stocker system. This motivates the weighted combination of rules.

In the next subsection, we mathematically define the WDR and formulate the optimization problem for selecting the best-performing weight set under dynamic operating conditions.

3.2 Weight-based Dispatching Rule

The WDR combines multiple dispatching rules to satisfy diverse operational objectives. Procedure of WDR is presented below.

Let $I = {1, \dots, 6}$ denote the set of dispatching rules and $J$ denote the set of candidate jobs when a crane becomes idle. Each candidate job $j \in J$ is evaluated by each dispatching rule $i \in I$ . Let $R_{i j}$ be the raw evaluation value assigned to job j by rule i. The values are normalized to enable fair comparison across different lot dispatching rules:

\tilde{R_{i j}} = \frac{R_{i j} - \min_{k \in J} R_{i k}}{\max_{k \in J} R_{i k} - \min_{k \in J} R_{i k}}

(1)

where $R_{i j}$ denotes the evaluation value of job j under lot dispatching rule i, and $\tilde{R_{i j}}$ is the normalized value.

The normalized value of each job-rule pair is multiplied by the weight assigned to that rule, reflecting its relative importance. The weighted values are aggregated to represent the priority of each job:

V_{j} (w) = \sum_{i \in I} w_{i} \cdot \tilde{R_{i j}}

(2)

where $w_{i}$ is the pre-defined weight of dispatching rule i, and $V_{j} (w)$ is the weighted-sum priority score of job j.

The job with the largest weighted-sum priority score is selected as follows:

j^{*} = \underset{j \in J}{argmax} V_{j}

(3)

3.3 Weight optimization problem

Weight set must be appropriately determined, since the importance of lot dispatching rules varies with the operational environment [15]. Digital twin enables simulation-based evaluation of the weight set under dynamic operational scenarios. In this study, the simulation is regarded as a black-box function $f (w)$ that returns the performance metrics corresponding to weight set $w = {w_{1}, w_{2}, \dots, w_{| w |}}$ .

The objective of weight optimization is the mean flow time. The flow time is the total time from job creation to completion, and it consists of four components: Waiting time, Travel time, Loading/Unloading time, Blocking time. Waiting time is the duration a job spends in the queue before assignment to a crane. Travel time is the time the crane spends moving to pick up and deliver the job. Loading/Unloading time is the time spent handling the cassette at the source and target. Blocking time is the excess transport time caused by interference between cranes.

The weight optimization problem can be formulated as:

\begin{matrix} \min_{w} f (w), \\ s.t. 0 \leq w_{i} \leq 1, w_{i} \in R, \end{matrix}

(4)

where $f (w)$ denotes the mean flow time evaluated by the simulation.

4. Methodology

4.1 Proposed Framework

We propose a simulation optimization framework for determining the dispatching weights, as shown in <Figure 3>. The framework operates in a repeated decision-making cycle: it takes an operating scenario derived from historical or forecasted data and generates the optimal weight set for the upcoming horizon.

The weight optimization module requires cost-efficient and rapid optimization, since the search relies on expensive simulations. To this end, we adopt BO as a sample-efficient method for the weight optimization.

4.2 Bayesian Optimization

The weight optimization is a simulation-based black-box problem over a low-dimensional continuous space of rule weights, where each candidate requires an expensive simulation model and only a limited number of evaluations are available. To solve this problem, we employ GP-based BO, a sample-efficient method for black-box optimization that is effective in low-dimensional continuous spaces [3].

<Figure 4> illustrates the BO procedure. It starts with collecting initial data and building a surrogate model. The acquisition function selects the next evaluation point, which is assessed by the simulation. This loop continues until the stopping criteria are met.

Initial data collected using Latin Hypercube Sampling (LHS) is used to construct the surrogate model, which predicts the simulation outcomes.

The GP surrogate employs a kernel composed of a constant kernel, a radial basis function (RBF) kernel, and a white-noise kernel. The constant and RBF kernels capture the smooth response of the simulation output over the weight space, and the white-noise kernel accounts for the stochastic variation of the simulation. We estimate the kernel hyperparameters by maximizing the log-marginal likelihood of the observed data.

The acquisition function selects the next evaluation point $x_{n + 1}$ based on the surrogate model’s predictions, $μ (x)$ and $σ (x)$ . This study employs the most common acquisition function, Expected Improvement (EI). EI chooses the next point $x_{n + 1}$ as:

x_{n + 1} = \underset{x \in X}{argmax} EI (x)

(5)

We set $y^{+}$ as current best solution, $φ$ and $Φ$ as probability density function (PDF) and cumulative density function (CDF), $Z$ as standard normal distribution, and $ξ$ as an exploration parameter that controls the trade-off between exploitation and exploration. We set $ξ = 0$ in this study. The EI quantifies expected gain over $y^{+}$ defined as:

EI (x) = \{\begin{matrix} (y^{+} - μ (x) - ξ) Φ (Z) + σ (x) φ (Z) & if σ (x) > 0, \\ 0 & if σ (x) = 0 . \end{matrix}

(6)

Z = \{\begin{matrix} \frac{y^{+} - μ (x) - ξ}{σ (x)} & if σ (x) > 0, \\ 0 & if σ (x) = 0 . \end{matrix}

(7)

By selecting $x_{n + 1}$ to maximize EI, BO adaptively balances exploitation and exploration. Exploit promising regions with $μ (x)$ and explore uncertain regions with $σ (x)$ . This balance enables BO to efficiently navigate the search space and find $w^{*}$ with fewer simulations.

5. Experiment and Results

5.1 Experimental Design

We evaluate the proposed framework on three scenarios that differ in arrival rate and hand-off ratio, as defined in <Table 2>. Job inter-arrival times are exponentially distributed, and the hand-off ratio is the proportion of jobs that require a hand-off operation. Scenario 1 is a baseline with a low arrival rate and a low hand-off ratio. Scenario 2 increases the arrival rate, and Scenario 3 further increases the hand-off ratio to cause more frequent crane interference. The three scenarios therefore correspond to light, heavy, and high interference conditions.

For each scenario, we conduct 20 replications with a budget of 100 simulation evaluations per run, consisting of 30 LHS initial samples and 70 sequential search evaluations. The search domain is the continuous weight space ${[0, 1]}^{6}$ , over which we maximize the EI acquisition function using L-BFGS-B with a multi-start strategy.

In this study, we use four performance metrics. Flow time measures the duration from job creation to completion. Tact time measures the duration from assignment to completion, waiting time measures the duration from job creation to assignment, and blocking time measures the excess transport time caused by crane interference.

The experiments use a simulation model built from the real-world in-line stocker layout and parameters of a display fab, validated against the operational data of the field system. The experiments were run on a system with Tecnomatix Plant Simulation 22, Python 3.11, Ryzen 5 PRO 4650G with Radeon Graphics 3.70 GHz, 16GB RAM.

5.2 Experimental Results

We conduct two comparative studies. First, we compare the proposed BO against a GA baseline and single dispatching rules, to assess the benefit of weight optimization over fixed rules and simulation optimization method. Second, we compare the GP with surrogate alternatives, Artificial Neural Network (ANN), Support Vector Regression (SVR), and Random Forest (RF).

We use cumulative minimum flow time to confirm which algorithms obtain an efficient weight set within a limited number of simulation runs. The GA takes the 10 best samples as its initial population and runs for seven generations with 10 offspring each, using the remaining 70 evaluations. In each generation, GA selects parents by tournament selection, generates offspring through blend crossover and Gaussian mutation, and keeps the 10 best individuals of the combined parents and offspring. The GA parameter settings are summarized in <Appendix 1>.

<Figure 5> shows the cumulative minimum flow time of GP and GA across the three scenarios; the initial samples are excluded, and only the sequential search phase is shown. Both methods share the same evaluation budget and the same initial samples, after which they search candidate weight sets sequentially. GP outperforms the GA in flow time by 1.05% in S1, 1.53% in S2, and 2.78% in S3 within 50 simulation runs, and by 0.68% in S1, 1.17% in S2, and 2.32% in S3 within 100 simulation runs. The effectiveness of GP over GA grows as workload intensity increases.

<Figure 6>, <Figure 7>, and <Figure 8> show the distributions of tact time, waiting time, and blocking time for single dispatching rules, GA, and GP. The flow time difference arose mainly from waiting time. Relative to GA, GP reduced tact time by only 0.19% but waiting time by 2.41%. The improvement of the proposed method is due to reduced waiting time rather than travel time. As workload intensity increases from S1 to S3, the difference in waiting time between GP and the comparison methods grew, and GP also showed a lower and more tightly distributed waiting time, indicating more stable performance under heavier workloads. Among the single rules, R1 achieved the lowest tact time and waiting time, and R6 achieved the lowest blocking time. GP still reduced waiting time by 11.09% relative to R1. R6 showed a lower blocking time than GP, but GP reduced tact time and waiting time by 2.11% and 23.75% relative to R6. A rule that minimizes a single operational criterion therefore does not always lead to shorter flow time, whereas GP reduces flow time by balancing multiple criteria through the weighted combination.

<Figure 9> compares GP with the surrogate alternatives; the initial samples are excluded, and only the sequential search phase is shown. The hyperparameters of the surrogate models were tuned by grid search. GP reached a lower cumulative best flow time than ANN, RF, and SVR in every scenario. In S1, GP improved on ANN, RF, and SVR by 1.42%, 0.42%, and 0.27%; in S2, by 2.91%, 1.27%, and 0.85%; and in S3, by 3.55%, 2.20%, and 1.60%, respectively. RF and SVR performed close to GP in S1, but the gap widened as workload intensity increased from S1 to S3.

To confirm the statistical significance, we apply a two-sided Wilcoxon signed-rank test to the paired flow time of the 20 replications in each scenario. As shown in <Table 3>, GP significantly outperforms GA, ANN, and RF in all three scenarios (adjusted p < 0.05). The difference between GP and SVR is not significant in Scenario 1 (p = 0.19) but becomes significant in Scenarios 2 and 3. The result shows that GP is more effective than the other methods for the weight optimization problem, finding better weight sets under limited budget.

<Figure 10> shows the relative importance of the optimal weight set of GP in each scenario. For interpretation, the weights are normalized to sum to one. R1 holds a large importance across all scenarios. From S1 to S3, the relative weight of R6 increases from 0.35 to 0.43. As the proportion of jobs requiring a hand-off grows, R6 becomes more important. The relative importance of dispatching rules thus changes with the operating environment, and the proposed framework detects this change and adjusts the weights adaptively.

6. Conclusion

In this study, we proposed a weight optimization framework that integrates BO with a simulation optimization framework for a twin-crane stocker system in a display fab. The framework evaluates candidate weight sets on the simulation model and uses a GP surrogate to search for an effective weight set within a limited evaluation budget.

Experiments on three scenarios show that GP-based BO reached a lower flow time than a GA baseline, the single dispatching rules, and surrogate alternatives, and its advantage grew as workload intensity increased. The results also confirm that the relative importance of dispatching rules changes with the operating environment, and that the proposed framework detects this change and adjusts the weight set adaptively. Moreover, the optimized weight set shows which rules matter most, giving operators an interpretable result.

We suggest the following directions for future research. First, the framework can be extended from a single stocker to multiple stockers. Second, the weight set can be re-optimized online as operating conditions change, rather than fixed horizon. Third, the framework can be extended to multi-objective BO that simultaneously considers flow time, utilization rate, and tact time, allowing operators to balance competing operational goals.

Acknowledgement

This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (RS-2026-25471656), and by Samsung Display Co., LTD.

Figure

<Figure 1>.

A Simulation Optimization Framework for Weight Optimization of Stocker System

<Figure 2>.

Simplified Stocker System

<Figure 3>.

Simulation-based Weight Optimization Framework

<Figure 4>.

Procedure of Proposed Bayesian Optimization

<Figure 5>.

Cumulative Minimum Flow Times of the Simulation Optimization Alternatives over the Increased Number of Simulation Runs: (a) Scenario 1; (b) Scenario 2; (c) Scenario 3.

<Figure 6>.

Average Tact Times of Dispatching Rules Across Scenario (a) Scenario 1; (b) Scenario 2; (c) Scenario 3.

<Figure 7>.

Average Waiting Times of Dispatching Rules Across Scenario (a) Scenario 1; (b) Scenario 2; (c) Scenario 3.

<Figure 8>.

Average Blocking Times of Dispatching Rules Across Scenario (a) Scenario 1; (b) Scenario 2; (c) Scenario 3.

<Figure 9>.

Cumulative Minimum Flow Times of the GP and the Three Surrogate Alternatives over the Increased Number of Simulation Runs: (a) Scenario 1; (b) Scenario 2; (c) Scenario 3.

<Figure 10>.

Relative Importance of Dispatching Rules Across Scenario

Table

<Table 1>.

Lot Dispatching Rules of Stocker System

Rule	Definition
R1	Assign higher value to a job that source is closer to current crane location.
R2	Assign higher value to a job that has a shorter source-target distance.
R3	Assign higher value to a job that has a shorter processing time.
R4	Assign higher value to a job that has higher priority.
R5	Assign higher value to a job that arrived earlier.
R6	Assign higher value to a job that reduces interference between cranes.

<Table 2>.

Scenario Configurations

Scenario	Arrival rate (jobs/h)	Hand-off ratio (%)
1	70	20
2	80	20
3	80	30

<Table 3>.

Holm-adjusted p-values of pairwise comparisons on mean flow time within each scenario; (a) Scenario 1, (b) Scenario 2, (c) Scenario 3.

^*p

(a)
GP	0.0061*	<0.0001*	0.1938	0.0319*
GA	-	0.0004*	0.2087	0.2087
ANN	-	-	0.0009*	<0.0001*
RF	-	-	-	0.2311
(b)
Scenario 2	GA	ANN	SVR	RF
GP	0.0024*	<0.0001*	0.0041*	0.0008*
GA	-	<0.0001*	0.2919	0.5706
ANN	-	-	<0.0001*	<0.0001*
RF	-	-	-	0.2919
(c)
Scenario 3	GA	ANN	SVR	RF
GP	<0.0001*	<0.0001*	0.0024*	0.0011*
GA	-	0.0769	0.2477	0.5957
ANN	-	-	0.0014*	0.0365*
RF	-	-	-	0.4621

<Appendix 1>.

GA Parameter Settings

Parameter	Setting
Population size	10
Generations	7
Selection	Tournament (size 3)
Crossover	Blend crossover
Crossover rate	0.90
Mutation	Gaussian
Mutation rate	0.20
Mutation scale	0.12
Survivor selection	Elitism

Reference

Ang, A.T., Sivakumar, A.I., and Qi, C., Criteria selection and analysis for single machine dynamic on-line scheduling with multiple objectives and sequence-dependent setups, Computers & Industrial Engineering, 2009, Vol. 56, No. 4, pp. 1223-1231.
Bhosekar, A., and Ierapetritou, M., Advances in surrogate based modeling, feasibility analysis, and optimization: A review, Computers & Chemical Engineering, 2018, Vol. 108, pp. 250-267.
Binois, M., and Wycoff, N., A survey on high-dimensional Gaussian process modeling with application to Bayesian optimization, ACM Transactions on Evolutionary Learning and Optimization, 2022, Vol. 2, No. 2, pp. 1-26.
Candelieri, A., Perego, R., and Archetti, F., Bayesian optimization of pump operations in water distribution systems, Journal of Global Optimization, 2018, Vol. 71, No. 1, pp. 213-235.
Chang, X., Dong, M., and Yang, D., Multi-objective real-time dispatching for integrated delivery in a Fab using GA based simulation optimization, Journal of Manufacturing Systems, 2013, Vol. 32, No. 4, pp. 741-751.
Chen, B., and Matis, T. I., A flexible dispatching rule for minimizing tardiness in job shop scheduling, International Journal of Production Economics, 2013, Vol. 141, No. 1, pp. 360-365.
Chiou, C.-W., Chen, W.-M., and Wu, M.-C., A combined dispatching criteria approach to scheduling dual flow-shops, International Journal of Production Research, 2013, Vol. 51, No. 3, pp. 927-939.
Chung, J., A simulation and scheduling method for analyzing the peak time capacity of the dual-robot in-line stocker, Journal of Simulation, 2024, Vol. 18, No. 5, pp. 835-850.
Dabbas, R.M., Chen, H.-N., Fowler, J.W., and Shunk, D., A combined dispatching criteria approach to scheduling semiconductor manufacturing systems, Computers & Industrial Engineering, 2001, Vol. 39, No. 3-4, pp. 307-324.
dos Santos, C. H., Campos, A. T., Montevechi, J. A. B., de Carvalho Miranda, R., and Costa, A. F. B., Digital Twin simulation models: a validation method based on machine learning and control charts, International Journal of Production Research, 2024, Vol. 62, No. 7, pp. 2398-2414.
Frazier, P.I., Bayesian optimization, Recent advances in optimization and modeling of contemporary problems, City, Informs, 2018, pp. 255-278.
Kang, B., Park, C., Kim, H., and Hong, S., A digital twin calibration for an automated material handling system in a semiconductor fab, Journal of Manufacturing Systems, 2025, Vol. 80, pp. 1013-1028.
Kang, B., Park, C., Kim, H., and Hong, S., Bayesian optimization for the vehicle dwelling policy in a semiconductor wafer fab, IEEE Transactions on Automation Science and Engineering, 2024, Vol. 21, No. 4, pp. 5942-5952.
Karkaria, V., Goeckner, A., Zha, R., Chen, J., Zhang, J., Zhu, Q., Cao, J., Gao, R.X., and Chen, W., Towards a digital twin framework in additive manufacturing: Machine learning and bayesian optimization for time series process optimization, Journal of Manufacturing Systems, 2024, Vol. 75, pp. 322-332.
Lee, J.-H., Kim, Y., Kim, Y.B., Kim, B.-H., Jung, G.-H., and Kim, H.-J., A sequential search method of dispatching rules for scheduling of LCD manufacturing systems, IEEE Transactions on Semiconductor Manufacturing, 2020, Vol. 33, No. 4, pp. 496-503.
Pearce, M. A. L., Poloczek, M., and Branke, J., Bayesian optimization allowing for common random numbers, Operations Research, 2022, Vol. 70, No. 6, pp. 3457-3472.
Qin, W., Zhang, J., and Sun, Y., Dynamic dispatching for interbay material handling by using modified Hungarian algorithm and fuzzy-logic-based control, The International Journal of Advanced Manufacturing Technology, 2013, Vol. 67, No. 1, pp. 295-309.
Zhang, H., Jiang, Z., and Guo, C., Simulation-based optimization of dispatching rules for semiconductor wafer fabrication system scheduling by the response surface methodology, The International Journal of Advanced Manufacturing Technology, 2009, Vol. 41, No. 1, pp. 110-121.

(a)
Scenario 1	GA	ANN	SVR	RF
GP	0.0061*	<0.0001*	0.1938	0.0319*
GA	-	0.0004*	0.2087	0.2087
ANN	-	-	0.0009*	<0.0001*
RF	-	-	-	0.2311
(b)
Scenario 2	GA	ANN	SVR	RF
GP	0.0024*	<0.0001*	0.0041*	0.0008*
GA	-	<0.0001*	0.2919	0.5706
ANN	-	-	<0.0001*	<0.0001*
RF	-	-	-	0.2919
(c)
Scenario 3	GA	ANN	SVR	RF
GP	<0.0001*	<0.0001*	0.0024*	0.0011*
GA	-	0.0769	0.2477	0.5957
ANN	-	-	0.0014*	0.0365*
RF	-	-	-	0.4621