An Optimization Protocol for MRI Examination Resource Allocation Based on Demand Forecasting and Linear Programming

Zhongbin Zhou 1

Hanyu Zhou 2

Yuanyuan Qiao 1

Zhihan Gao 1

Ying Yang 1

1 The 6 th Medical Center of PLA General Hospital 100048 Beijing China

2 China Unicom Beijing Branch 100006 Beijing China

Zhongbin Zhou¹,Hanyu Zhou²,Yuanyuan Qiao¹, Zhihan Gao¹, Ying Yang^1*

¹ The 6th Medical Center of PLA General Hospital, Beijing, 100048, China

² China Unicom Beijing Branch, Beijing, 100006, China

Keywords:

MRI

ARIMA model

NAR model

Integer Linear Programming

Optimization Protocol

ABSTRACT

Objective

The accessibility of medical services in Mainland China had been on the rise, leading to a surge in the number of Magnetic Resonance Imaging (MRI) scans. This increase had caused substantial delays in MRI examination queues at large hospitals. With MRI equipment and exams being costly, over-purchasing machines could lead to underutilization of resources. It was, therefore, crucial to devise a comprehensive method that could shorten patient wait times and optimize the use of medical resources within hospitals.

Method

The research had utilized daily MRI examination application data from a hospital covering the period from July 1, 2017, to November 30, 2022. The Autoregressive Integrated Moving Average (ARIMA) model and the AutoRegressive Integrated Moving Average with exogenous (ARIMAX) model were developed using SAS (version 9.3) software. Moreover, Non-AutoRegressive (NAR) and Non-AutoRegressive with exogenous (NARX) models were built using MATLAB (version R2015b) to forecast future MRI examination demands. The predictive accuracy of these models was then assessed and compared. Based on the prediction outcomes, an Integer Linear Programming model was employed to calculate the optimal number of MRI examinations per machine per day, targeting cost reduction. An optimization flowchart for MRI examination resource allocation was developed by integrating critical process components, thus streamlining and systematizing the optimization process to improve efficiency.

Results

Analysis of the data revealed a weekly cyclical trend in MRI examination applications. Among the ARIMA, ARIMAX, NAR, and NARX models evaluated for their predictive skills, the NARX model emerged as the most accurate for forecasting. An Integer Linear Programming (ILP) model was utilized to plan the number of examinations for each MRI machine, effectively reducing costs. An optimization flowchart was developed to integrate key factors in MRI examination resource allocation, streamlining and systematizing the optimization process to enhance work efficiency.

Conclusion

This study offers a comprehensive protocol for optimizing MRI examination resource allocation, combining the predictive power of the NARX model, the planning capabilities of the Integer Linear Programming model, and the integration of other relevant factors via an optimization flowchart.

Clinical trial number:

not applicable.

1.Background

Magnetic Resonance Imaging (MRI) examinations were becoming increasingly important in determining treatment plans in contemporary medical institutions. A significant number of patients required MRI results before undergoing diagnostic and therapeutic procedures. In the past few decades, as the medical standard in mainland China gradually improved, there was a significant increase in the number of patients undergoing MRI examinations. The significant increase in the number of MRI examinations led to prolonged queuing phenomena in many large hospitals across the mainland, which not only delayed the diagnosis and treatment of various diseases but also had the potential to adversely affect treatment outcomes. Therefore, there was a need for a set of optimization solutions designed to reduce the waiting time for patients and to coordinate medical resources .

The distribution of demand for Magnetic Resonance Imaging (MRI) examinations was characterized by complexity and was subject to the influence of various factors, including seasonal variations and holiday periods. Scholarly literature pertaining to the prediction of patient demand predominantly concentrated on forecasting the volume of emergency patients [1–6], with a comparative paucity of research directed towards the prediction of daily MRI examination demand.

Conventional time series analysis models, including the Grey model, the Markov model, and the Autoregressive Integrated Moving Average (ARIMA) model, predominantly hinged on the linear attributes of the data. Wen-Ting Zha introduced an Autoregressive Integrated Moving Average with exogenous variables (ARIMAX) model to investigate the impact and forecast the incidence of mumps in China attributable to meteorological factors [7], while Jing Yang applied the ARIMAX model to predict the incidence of tuberculosis in China by utilizing Baidu search index data [8]. The ARIMA model did not account for the nonline arities present in time series data [9]. Given the limitations of the ARIMA model, there was a growing interest in the application of neural network models for time series forecasting [10–13], as they were capable of considering the nonlinear relationships within the data. Artificial Neural Networks (ANN) offered an innovative approach to parameter estimation in both linear and nonlinear models. The ANN’s capacity for learning and generalizing behaviors allowed it to adapt to variable and dynamic environments, thereby endowing predictive tools with greater flexibility than traditional statistical models [14]. The Nonlinear AutoRegressive with eXogenous inputs (NARX) model was recognized as an effective methodology for addressing continuous nonlinear problems [15], and unlike other neural network architectures, the NARX model’s output functioned as input for subsequent predictions in a feedback loop [16].

Academic articles on the application of integer programming models to MRI examination planning were relatively scarce. A study reported that a Norwegian hospital had employed Integer Programming models to yield optimal solutions for MRI block scheduling issues and had furnished managerial insights for decision-makers [17]. Nevertheless, Integer Programming models were more frequently applied to the optimization of dietary regimens [18–22].

This investigation utilized Integer Programming models to forecast the demand for MRI examinations and to optimize work schedules. Subsequently, an optimization protocol for the allocation of MRI examination resources was developed, which integrated additional process components.

2. Materials and methods

2.1. Materials

The dataset employed in this research was extracted from the daily MRI examination application records of a specific hospital in Chinese Mainland, spanning from July 1, 2017, to November 30, 2022. The institution in question is a prominent public general hospital located in the Chinese Mainland. Owing to the influence of the COVID-19 pandemic and the associated containment measures implemented in mainland China, there was a marked reduction in MRI applications between January 13, 2020, and March 14, 2021. Therefore, data from this time period was excluded from the analysis. Ultimately, it was determined that 1,522 MRI examination data were included in this study. In this study, we observed a significant decrease in MRI examination requests at the hospital on weekends and public holidays. Public holidays in mainland China are not fixed and are determined differently from those in other countries, often aligning with the Chinese lunar calendar, including festivals such as the Spring Festival, Dragon Boat Festival, and Mid-Autumn Festival. On these occasions, the Chinese mainland government adjusts the regular weekend schedule to extend continuous holiday periods by designating certain Saturdays and Sundays as workdays, while conversely designating certain weekdays as holidays. To mitigate the effect of holiday data on predictive accuracy, this study excluded data that were subject to alterations in workday status due to holiday influence. Furthermore, it was observed that the number of MRI examination requests on the first day following a holiday exhibited a significant increase compared to regular weekdays. Hence, the predictive models developed in this study incorporated this variable as a significant influencing factor within the research framework.

2.2. ARIMA and ARIMAX Models

The ARIMA model constitutes a linear time-series forecasting approach that employs the linear combination of previously observed stationary series and error terms. Conventionally, the ARIMA model is specified as ARIMA(p, d, q)(P, D, Q), wherein p, q, and d denote the orders of autoregression, moving average, and differencing, respectively, while P, D, and Q represent the respective orders of seasonal autoregression, seasonal moving average, and seasonal differencing. The examination of data autocorrelation and seasonality is conducted through the deployment of autocorrelation function (ACF) and partial autocorrelation function (PACF) plots. Model selection is guided by the Akaike information criterion (AIC) and the Bayesian information criterion (BIC), aiming to strike a balance between model fit and complexity [23]. The ARIMAX model is an extension of the ARIMA model that incorporates exogenous regression terms. The incorporation of these regression terms enhances the predictive accuracy of the model, with such terms generally comprising variables that exhibit a high degree of correlation with the forecasted variable.

2.3. NAR and NARX Models

The NAR model represents a nonlinear time series forecasting approach that expands upon the conventional linear autoregressive (AR) model, facilitating a more effective capture of nonlinear dynamics within the time series data and potentially yielding more precise predictive outcomes in specific contexts. The underlying rationale of the NAR model is based on the utilization of historical data across multiple time steps to establish a nonlinear functional relationship with the current time step for the purpose of time series forecasting. The NARX neural network model is an advancement of the NAR neural network model, distinguished by its nonlinear autoregressive properties with exogenous inputs. It operates by predicting a given time series based on the past values of that series, the feedback input, as well as an additional time series, referred to as the external or exogenous time series.[24–25]

2.4. Assessment of Predictive Performance

We utilized three metrics, namely Mean Squared Error (MSE), Mean Absolute Percentage Error (MAPE), and Mean Absolute Error (MAE), to evaluate the performance of the model. Lower values of these metrics indicate superior model performance. Typically, the MSE is susceptible to the influence of individual large errors, whereas MAPE and MAE provide a reliable measure of the discrepancy between predicted and actual values [26–28].

$\:\text{M}\text{S}\text{E}=\frac{{\sum\:}_{i=1}^{n}({{\text{x}}_{\text{i}}-{\widehat{\text{x}}}_{\text{i}})}^{2}}{\text{n}}$

$\:\text{M}\text{A}\text{E}=\frac{{\sum\:}_{i=1}^{n}{|\text{x}}_{\text{i}}-{\widehat{\text{x}}}_{\text{i}}|}{\text{n}}$

$\:\text{M}\text{A}\text{P}\text{E}=\frac{{\sum\:}_{i=1}^{n}\frac{{|\text{x}}_{\text{i}}-{\widehat{\text{x}}}_{\text{i}}|}{{\text{x}}_{\text{i}}}\times\:100}{\text{n}}$

X_i is the actual value,

$\:{\widehat{\text{x}}}_{\text{i}}$

is the predicted value, i = 1…n, and n is the number of observation.

2.5. Linear Programming

Linear programming can address optimization issues in production processes, logistics transportation, and resource allocation, aiding managers in determining solutions to these problems. A linear programming model comprises three elements: the objective function, decision variables, and constraints. The solution to the model involves identifying the values of the decision variables that optimize the objective function (either to a maximum or minimum), while concurrently ensuring that these values satisfy the specified constraints.In the context of linear programming, when all decision variables are required to take on non-negative integer values, such a problem is termed integer linear programming. The traditional approach to solving integer programming problems is the branch-and-bound method. This constitutes a mathematical technique capable of addressing various types of problems. The underlying principle of the branch-and-bound method is that the entire set of feasible solutions can be partitioned into smaller subsets. These subsets can be systematically evaluated until the optimal solution is identified.

2.6. Construct a flowchart for the optimization process

The development of an optimized process for the allocation of resources in MRI examinations was the focus of this study. The optimization process was constructed by means of flowcharts, which are graphical representations of processes or systems. Flowcharts employ icons composed of fundamental shapes to depict the various components, steps, and logical relationships inherent in a process or system, thereby enhancing comprehension and analysis. The creation of a flowchart entailed a six-step process: initially, defining the objective of the diagram; secondly, establishing the scope of the process; thirdly, gathering pertinent information; fourthly, constructing the basic framework; fifthly, delineating the elements of the flowchart; and finally, engaging in optimization and refinement.

2.7. Statistical analysis

The data analysis was performed with the employment of Microsoft Excel (2007) for purposes of data organization and statistical delineation. The ARIMA model was crafted utilizing SAS version 9.3. Concurrently, the development of the Artificial Neural Network (ANN) model was achieved through the use of MATLAB version R2015b.

3. Results

3.1 The temporal distribution of demand for MRI examinations

Figure 1 presented the daily MRI examination application data from July 1, 2017, to November 30, 2022. Excluding the impact of the COVID-19 pandemic, the data plot revealed a pronounced cyclical pattern in the number of MRI examination applications. Notably, public holidays in mainland China significantly influenced the volume of MRI examination applications.

Fig. 1

Temporal Distribution Chart of Magnetic Resonance Imaging (MRI) Examination Request Volume

3.2. Prediction results of each model

We developed an ARIMA model to predict the demand for MRI examinations. The ARIMA model was divided into two types: one with exogenous influencing factors (ARIMAX) and one without (ARIMA). The occurrence of holidays and the first working day after a holiday were considered as exogenous factors. Model parameters were determined based on the Autocorrelation Function (ACF) plot, Partial Autocorrelation Function (PACF) plot, and Akaike Information Criterion (AIC) and Schwarz Bayesian Criterion (SBC) values. Both ARIMA and ARIMAX predictions utilized the ARIMA(0,2,1)(0,2,7)₁₂ model, which yielded better prediction results. Figures 2, 3 showed the residual correlation diagnostics for ARIMA model and ARIMAX model, respectively. Figures 4, 5 showed the residual normality diagnostics for ARIMA model and ARIMAX model, respectively. Figures 6, 7 showed the forecasts for ARIMA model and ARIMAX model, respectively.

Fig. 2

Rdsidual Correlation Diagnostics for ARIMA model

Fig. 3

Rdsidual Correlation Diagnostics for ARIMAX model

Fig. 4

Residual Normality Diagnostics for ARIMA model

Fig. 5

Residual Normality Diagnostics for ARIMAX model

Fig. 6

Forecasts for ARIMA model

Fig. 7

Forecasts for ARIMAX model

We also developed a NAR neural network method for predicting the demand for MRI examinations. Among them, the NAR model was also divided into two types: one with external influencing factors (NARX) and the other without (NAR). Similarly, we also included factors such as whether a day was holiday or the first working day after a holiday as external influencers. The sequence length and the number of hidden layers were determined by analyzing the histogram of the errors between the predicted values and the actual values, as well as by assessing the R-squared value of the predictive model. In this study, the sequence length of the model was set to 7, and the number of hidden layers was set to 12. Figure 8 showed the synoptic schematic of the NAR and NARX prediction model. Figures 9, 10 showed the Error Histogram with 20 Bins for NAR and NARX prediction model, respectively. Figures 11, 12 showed the Regression plots of the NAR and NARX model trained with the Bayesian Regularization algorithm, respectively.

Fig. 8

Synoptic schematic of the NAR and NARX prediction model

Fig. 9

Error Histogram with 20 Bins for NAR prediction model

Fig. 10

Error Histogram with 20 Bins for NARX prediction model

Fig. 11

Regression plots of the NAR model trained with the Bayesian Regularization algorithm.

Fig. 12

Regression plots of the NARX model trained with the Bayesian Regularization algorithm.

3.3. Comparison of prediction accuracy

We conducted calculations of the MSE, MAE, MAPE, and the Pearson Correlation Coefficient (R value) to quantify the level of association between the predicted and actual values for the previously mentioned four models. Table 1 shows the prediction accuracy of various methods. This was done to facilitate a comparative analysis of the predictive accuracy across the different models.

Table 1

Prediction accuracy of various methods
	MSE	MAE	MAPE	R
ARIMA model	1370.43	18.29	0.1661	0.9282
ARIMAX model	1289.08	17.70	0.1613	0.9273
NAR model	433.20	14.67	0.1608	0.9287
NARX model	333.09	14.04	0.2108	0.9549

Upon comparison, it was evident that the NARX model exhibited superior prediction performance relative to the other models. Consequently, this study employed the NARX model to forecast the inspection demand from October 24th to October 30th, 2022. Table 2 shows the results predicted by the NARX model.

Table 2

Prediction results
	24/10 Mon.	25/10 Tues.	26/10 Wed.	27/10 Thur.	28/10 Fri.	29/10 Sat.	30/10 Sun.
MRI examination demand	196	174	149	151	143	48	48

3.4. Programming for daily inspection volume

According to the predictions from the NARX model, the daily actual inspection workload was allocated using Integer Linear Programming to minimize the inspection costs. This hospital had three MRI machines, and through the analysis of historical data, the following parameters were derived for professional assessment. Machine number 1 (MR1) had a daily maximum workload of 72 sessions, machine number 2 (MR2) had a daily maximum workload of 58 sessions, and machine number 3 (MR3) had a daily maximum workload of 41 sessions. The cost per inspection session for MR1 was 280 yuan, for MR2 was 250 yuan, and for MR3 was 220 yuan. An additional labor cost of 30 yuan was incurred for each inspection performed on holidays, and a cost of 60 yuan was added for each day that the patient’s examination was extended.

Model Decision Variables:

x11, x12, x13, x14, x15, x16, x17, x21, x22, x23, x24, x25, x26, x27, x31, x32, x33, x34, x35, x36, x37.

Objective Function:

MIN(cost)=-140*x11-80*x12 + 20*x13 + 80*x14 + 100*x15 + 160*x16 + 220*x17- 170*x21-110*x22-20x23 + 40*x24 + 70*x25 + 130*x26 + 190*x27-200*x31-140*x32 -50*x33 + 10*x34 + 40*x35 + 100*x36 + 160*x37

X11: Represented the inspection volume on the first day for MA1,

X12: Represents the inspection volume on the second day for MA1,

X21: Represents the inspection volume on the first day for MA2,

X31: Represents the inspection volume on the first day for MA3, …

Constraints: The daily inspection volume per machine should not exceed the daily maximum workload, the daily inspection volume should not exceed the cumulative applied volume, and all inspection applications must be completed on the last working day.

Table 3 shows the optimal solution for linear programming, which is the daily required inspection volume for each MRI machine from October 24th to October 30th.

Table 3

Daily inspection volume
	24/10 Mon.	25/10 Tues.	26/10 Wed.	27/10 Thur.	28/10 Fri.	29/10 Sat.	30/10 Sun.
MR1	72	72	72	64	45	0	0
MR2	58	58	58	51	58	7	7
MR3	41	41	41	41	41	41	41

3.5. Constructing an optimized flowchart for MRI examination resource allocation

The optimization process for MRI examination resource allocation encompassed several key elements, including the collection and processing of historical data, prediction of examination demands, cost estimation, linear programming, formulation of examination plans, post-examination benefit analysis, scheme evaluation, and information feedback. Each step of the optimization process was vital and should undergo a continuous cycle of improvement. Figures 13 shows the optimization process flowchart of MRI examination resource allocation. In accordance with the flowchart, the initial step involved the collection and processing of recent MRI examination data for analytical purposes. Subsequently, a suitable predictive method was chosen and applied based on the specific context to forecast the demand for examinations during the ensuing cycle. Thereafter, considering the diverse costs associated with examinations, labor expenses, and the operational capabilities of the equipment, daily examination quantities were calculated and determined through linear programming techniques. Ultimately, based on the computed examination quantities, an examination plan for the subsequent cycle was formulated and executed accordingly. In parallel, regular evaluations of the plan’s implementation were conducted, with feedback being generated from these assessments to address any issues identified within the process.

Fig. 13

the optimization process flowchart of MRI examination resource allocation

4.Discussion

4.1. The significance of optimizing the allocation of medical resources

The optimization of resource allocation pertaining to substantial medical apparatus and the mitigation of patient queuing durations represent pivotal challenges that demand immediate attention within the context of major healthcare institutions in China. The present investigation elucidates a set of strategic approaches aimed at facilitating the harmonized scheduling of extensive medical equipment, thereby diminishing the duration of patient wait times.

4.2. The prediction methods for the volume of MRI examination application requests

it is essential to analyze the the distribution of data when choosing a pridiction method. The distribution diagram of the MRI examination application data from this study revealed that the number of applications was cyclical, with a pattern of distribution every 7 days, reaching its peak on Mondays, and exhibiting a consistent pattern of change from Monday to Friday. Applications were comparatively fewer on weekends, that is, Saturdays and Sundays. During Chinese public holidays, when days off were observed, regardless of the day of the week, there is a noticeable decrease in the number of applications. Consequently, some patients were postponed their MRI examination, which leads to a sudden increase in the number of applications on the first working day following the holiday period.

it is essential to analyze the applicability of each model When choosing a prediction model.The ARIMA model was characterized by its simplicity of use, broad applicability, and strong interpretability of parameters, enabling it to reflect the inherent characteristics of time series data. However, it was sensitive to noise and was limited to modeling linear trends, resulting in suboptimal performance for non-linear trends. The NAR model, on the other hand, exceled in handling non-linear and non-stationary sequences, offering good adaptability and predictive capabilities. It could automatically learn and capture dynamic features within the sequence, with its structure and parameters adjustable and optimizable according to specific problems. The drawback of the NAR model was that its performance was highly dependent on the selection of network structure and parameters, necessitating extensive tuning and optimization. This increased the risk of overfitting the training data, necessitating the use of regularization and validation techniques to enhance its generalization ability.

This study was based on the time series of MRI examination application numbers, utilizing the ARIMA, ARIMAX, NAR, and NARX models to predict future MRI

examination demand. By calculating the MSE,MAE,MAPE and R values,we compared the prediction accuracy of various models.The comparison revealed that the NAR model performs better than the ARIMA model, and models with exogenous influencing factors outperformed those without. Consequently, for the data in this study, it was more suitable to introduce exogenous factors such as “holiday status” and to employ nonlinear time series methods for prediction.

4.3. The application of integer linear programming in medical resource allocation

This study employed Integer Linear Programming to reasonably plan the actual number of inspections required for each MR per day ,in order to achieve the goal of minimizing costs.Managers could effectively allocate resources and optimize inspection processes according to the outcomes of linear programming, thereby enhancing overall efficiency to its maximum potential. The integer linear programming approach is straightforward to implement. Once the daily demand for a week was determinded,the actual number of inspections required for each MRI could be planned.

4.4. The significance of applying optimized flowcharts

The creation of optimized flowcharts involved the systematic integration of relevant elements, thereby processualizing and institutionalizing the optimization scheme for the allocation of MRI examination resources. The establishment of these flowcharts offered a lucid depiction of the relationships and functions associated with each component, facilitating the identification of bottlenecks or issues. Moreover, they served as a normative and directive mechanism, guiding individuals in executing their tasks in the appropriate sequence and manner, thereby preventing errors and omissions, and enhancing work efficiency and uniformity.

4.5. The limitations of this study

This study has several limitations. Due to the incomplete availability of existing data, it was not possible to incorporate potential influencing factors on MRI examination demand into the model, such as weather conditions, temperature, healthcare insurance policies, and infectious disease outbreaks. Furthermore, in the aspect of examination volume planning, the impact of MRI maintenance on overall planning has not been considered.

Declarations

Ethics approval and consent to participate

The Medical Ethics Committee of the 6th Medical Center of PLA General Hospital waived informed consent given the lack of intervention and the anonymity of the data.

Consent for publication

Not applicable

Data Availability

The data used to support the findings of this study are restricted by The 6th Medical Center of PLA General Hospital in order to protect patient privacy. Data are available from The 6th Medical Center of PLA General Hospital for researchers who meet the criteria for access to confidential data. If data access is needed, please contact Zhongbin Zhou with the email: to_zzb@163.com.

Competing Interests

The authors declare that they have no competing interests.

Funding

No funding.

Authors’contributions

Zhongbin Zhou wrote the main manuscript text,Hanyu Zhou processed and analyzed data, All authors reviewed the manuscript.

Acknowledgements

This work was not supported by outside funds.

Author Contribution

All authors contributed to the conceptualization and design of the study. Author ZHOU Zhongbin conducted the literature review and data collection, and played a pivotal role in the analysis and interpretation of the data. Author ZHOU Hanyu was responsible for the statistical analysis and helped to draft the methods and results sections of the paper. Author YANG ying contributed to the acquisition of the administrative, technical, and material support necessary for the research. All authors participated in the revision of the manuscript and approved the final version for submission.

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Table 1 Prediction accuracy of various methods

	MSE	MAE	MAPE	R
ARIMA model	1370.43	18.29	0.1661	0.9282
ARIMAX model	1289.08	17.70	0.1613	0.9273
NAR model	433.20	14.67	0.1608	0.9287
NARX model	333.09	14.04	0.2108	0.9549

Table 2 Prediction results

	24/10 Mon.	25/10 Tues.	26/10 Wed.	27/10 Thur.	28/10 Fri.	29/10 Sat.	30/10 Sun.
MRI examination demand	196	174	149	151	143	48	48

Table 3 Daily inspection volume

	24/10 Mon.	25/10 Tues.	26/10 Wed.	27/10 Thur.	28/10 Fri.	29/10 Sat.	30/10 Sun.
MR1	72	72	72	64	45	0	0
MR2	58	58	58	51	58	7	7
MR3	41	41	41	41	41	41	41

Yes

Abstract

ABSTRACT Objective: The accessibility of medical services in Mainland China had been on the rise, leading to a surge in the number of Magnetic Resonance Imaging (MRI) scans. This increase had caused substantial delays in MRI examination queues at large hospitals. With MRI equipment and exams being costly, over-purchasing machines could lead to underutilization of resources. It was, therefore, crucial to devise a comprehensive method that could shorten patient wait times and optimize the use of medical resources within hospitals. Method: The research had utilized daily MRI examination application data from a hospital covering the period from July 1, 2017, to November 30, 2022. The Autoregressive Integrated Moving Average (ARIMA) model and the AutoRegressive Integrated Moving Average with exogenous (ARIMAX) model were developed using SAS (version 9.3) software. Moreover, Non-AutoRegressive (NAR) and Non-AutoRegressive with exogenous (NARX) models were built using MATLAB (version R2015b) to forecast future MRI examination demands. The predictive accuracy of these models was then assessed and compared. Based on the prediction outcomes, an Integer Linear Programming model was employed to calculate the optimal number of MRI examinations per machine per day, targeting cost reduction. An optimization flowchart for MRI examination resource allocation was developed by integrating critical process components, thus streamlining and systematizing the optimization process to improve efficiency. Results: Analysis of the data revealed a weekly cyclical trend in MRI examination applications. Among the ARIMA, ARIMAX, NAR, and NARX models evaluated for their predictive skills, the NARX model emerged as the most accurate for forecasting. An Integer Linear Programming (ILP) model was utilized to plan the number of examinations for each MRI machine, effectively reducing costs. An optimization flowchart was developed to integrate key factors in MRI examination resource allocation, streamlining and systematizing the optimization process to enhance work efficiency. Conclusion: This study offers a comprehensive protocol for optimizing MRI examination resource allocation, combining the predictive power of the NARX model, the planning capabilities of the Integer Linear Programming model, and the integration of other relevant factors via an optimization flowchart.