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Vaccine X
Vaccine X
Vaccine: X
2590-1362
Elsevier

S2590-1362(24)00123-2
10.1016/j.jvacx.2024.100550
100550
Regular paper
Queuing analysis for improving performance in bacterial vaccine quality control process
Martha Sallyta Ayu ab
Yunani Akhmad c
Setiabudi Wega d
Harsanto Budi budi.harsanto@unpad.ac.id
b⁎
a PT. Biofarma (Persero), Indonesia
b Faculty of Economics and Business, Universitas Padjadjaran, Indonesia
c Faculty of Communication and Business, Telkom University, Indonesia
d Institute of Infection, University of Liverpool, United Kingdom
⁎ Corresponding author. budi.harsanto@unpad.ac.id
22 8 2024
10 2024
22 8 2024
20 10055029 6 2023
19 8 2024
20 8 2024
© 2024 The Author(s)
2024
https://creativecommons.org/licenses/by-nc/4.0/ This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
The aim of the research is to analyze and improve the performance of the vaccine quality control queuing system to reduce delays and achieve the firm’s long-term goal on vaccine production capacity. The research focuses on the Bacterial Vaccine Quality Control (BVQC) at the largest vaccine manufacturers in Indonesia and Southeast Asia. The vaccines handled by BVQC include TT, DTP, BCG, BioTT, BioTd, DT, Td, and DTP-Hb-Hib. The BVQC operates a queuing system with eight servers, each assigned a fixed task. The existing system experienced delays ranging from 13 % to 61 % from January to June 2022. After identifying the queuing characteristics of the existing system, improvement proposals were suggested by modifying the assignment of the servers. This proposal was then simulated in November 2022, resulting in improved performance with no delays, a reduction in the length of the queue in the system (Lq) from 2.88 to 2.59, and a reduction in the average time spent in the system (Ws) from 0.0099 to 0.0044. The research suggests that modifying server assignments can be an effective method for improving the performance of a queuing system in vaccine quality control. This can lead to reduced delays, optimized queue lengths, and improved overall efficiency, potentially enhancing the firm’s ability to meet vaccine demand in the future.

Keywords

Vaccine production
Queue analysis
Bacterial vaccine quality control
Indonesia
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pmcIntroduction

Queuing analysis is a mathematical approach widely used to understand and improve the performance of waiting systems in various industries, including manufacturing and service sectors [1], [2]. Its application in healthcare, including vaccine production, is particularly relevant given the growing global demand for vaccines and the importance of ensuring its efficiency and speed [3], [4]. In the context of queuing analysis, the vaccine production quality control process is a crucial step, as it ensures the safety and quality of the final product before it is released for distribution [5].

The aim of the research is to analyze and improve the performance of the vaccine quality control queuing system in order to reduce delays and achieve the firm’s long-term goal on vaccine production capacity. This study focuses on the Bacterial Vaccine Quality Control (BVQC) process at the largest vaccine manufacturer in Indonesia and Southeast Asia. Southeast Asia is an emerging region in terms of health and economy [6], [7]. The vaccines handled by BVQC include TT, DTP, BCG, BioTT, BioTd, DT, Td, and DTP-Hb-Hib. The BVQC has a queuing system with eight servers, each assigned a fixed task. The system experienced delays of 13 %, 61 %, 22 %, 27 %, 8 %, and 14 % in January, February, March, April, May, and June 2022 respectively.

The importance of improving efficiency in the Bacterial Vaccine Quality Control (BVQC) process has been acknowledged by the Indonesian government through Presidential Instruction No. 6 of 2016. This instruction highlights the need to accelerate the development of the pharmaceutical and medical device industry sector to ensure that people can access drugs, including vaccines, sera, and life science products, easily, sustainably, and affordably [8].

The issue of delays could impact the company’s Long-Term Strategic Plan (RJPP) in meeting vaccine production goals. We considered several strategies for this improvement includes Value Stream Mapping (VSM) technique to identify non-value-added activities in the process streamlining[9], scheduling techniques to prioritize the sequence of arrivals [10], and queuing theory to analyze and optimize system performance [10]. After evaluating these strategies and considering the characteristics of the problems faced, queuing theory was selected. Based on this, strategic improvements were made using queuing theory as the analytical foundation. Thus, the aim of the research is to analyze and improve the performance of the vaccine quality control queuing system to reduce delays and achieve the firm’s long-term goal on vaccine production capacity.

Material and methods

This study uses three stages, which include: (a) analysis of existing queuing systems, (b) improvement by modifying the configuration and then analyzing the results, and (c) comparison before and after improvement.

In the first stage, the existing queuing system is analyzed by observing the existing configuration and its performance. For queue performance analysis, the data collected is c = number of servers, λ = number of test arrivals per month, and μ = number of tests served per month. The data is collected directly through observation and company data. The performance metrics measured include:

The probability that the system is idle:(1) P0=1∑n=0n=c-11n!λμn+1c!λμccμcμ-λ

Average number of test types in the queuing system:(2) Ls=λμλ/μcc-1!Mμ-λ2P0+λμ

The average time spent by one type of testing in the entire queuing system:(3) Ws=Lsλ

Average number of test types waiting in a queue:(4) Lq=Lsλμ

The average time one type of test spends waiting in a queue until it is served:(5) Wq=Lqλ

In the second stage, the configuration modification is carried out by considering the existing queueing performance and consulting with the BVQC manager. The aim of this improvement is to minimize delays. The improvement is then implemented concretely to obtain factual performance measurements after the improvement is carried out. Further performance measurements after the improvement are made by applying the same calculation formulas as in the first stage.

In the third stage, a comparison is made between the performance before and after the improvement was carried out. The goal of this comparison is to understand the changes in performance that have occurred as a result of the improvement. The comparison based on the same performance metrics that were used in the first and second stage. This comparison provides insights into the effectiveness of the improvement.

Results

Existing queuing systems and performance

The current queue service assignment is an existing server where each server is assigned a task in the form of a fixed type of testing service as shown in Fig. 1. The flow process of existing server is shown in Fig. 2.Fig. 1 Types of Delegated Testing for Each Server.

Fig. 2 Flow process of existing server arrangement.

For example, if there is a sample in which there is a type of pH test, the one that will complete this service is server 4. Next, the server performs the testing service process to fill in the result documentation. The completed result document is sent to the manager for review based on the type of sample. For example, PFB samples, sending results to managers must wait for thimerosal testing first because PFB samples have two types of testing, namely pH and thimerosal. The manager reviews the test results and sends the test result documents to the sender. The queueing system performance can be seen in Table 1.Table 1 Queuing Systems Performance.

Queuing System Performance Measures	P0	Ls	Ws	Lq	Wq	U	I	
(Existing Server)	0.0027	2.88	4.75 min	8.29	12.96 min	0.36	0.64	

Improved queuing systems and performance

The assignment of the proposed service poses is a modified server, testing by a ready operator. The flow process of modified server is shown in Fig. 3.Fig. 3 Flow process of modified server arrangement.

From Fig. 3, it is evident that server 3, which was previously part of the main queuing system, has been reclassified as a supporting server due to service imbalances causing delays. Analysis of the difficulty level and testing volume, with scores of 167, 704, 89, 592, 1296, and 787 for servers 1 through 7 respectively, highlighted Server 3 as having the lowest performance score, making it the primary candidate for modification. Server 3 was reassigned to focus on documentation tasks, performance improved across all measurements of the queuing system. This strategic shift not only addressed the initial delays but also opens the possibility of reassigning server 3 to other areas within the company in the future, potentially allowing administrative staff to handle documentation tasks and further optimizing resource use.

The service process flow describes the arrival of several samples, each requiring different types of testing. The manager logs the incoming samples and assigns them to the appropriate server. The server then performs the testing and completes the result documentation. Once the results are documented, they are sent to the manager for review based on the sample type. For instance, PFB samples require results from thimerosal testing before the pH test results are reviewed, as PFB samples involve both types of testing. The manager reviews the test results and sends the final documents back to the sender. For example, if a PFB sample originated from the production department, the manager sends the results back to that section. The performance of the modified queuing system is shown in Table 2.Table 2 Queuing Systems Performance of modified server arrangement.

Queuing System Performance Measures	P0	Ls	Ws	Lq	Wq	U	I	
(Modified Server)	0.0029	2.59	2.11 min	6.71	5.28 min	0.37	0.63	

Performance comparison between existing and modified server arrangement is shown in Table 3. Performance measures of the modified queuing system including (P0) the probability of absence of test types in the previous system of 0.0027 increased to 0.0029; (Ls) the average number of tests in the system 2.88 decreased by 2.59; (Ws) the average time spent by one type of testing in the entire previous system was 4,75 min and after repairs it changed to 2,11 min; (Lq) the average number of test types in the previous queue was 8.29 and after repairs it changed to 6.71; (Wq) the average time one test spends waiting in a queue until it is served previously is 12.96 min and after repairs change to 5, 28 min; (U) the opportunity for the service to be busy doing the test type 0.36 and after the repair is made it changes to 0.37; (I) the service opportunity was idle 0.74 and after improvement changed to 0.73.Table 3 Performance comparison.

Queuing System Performance Measures	P0	Ls	Ws	Lq	Wq	U	I	
(Existing Server)	0.0027	2.88	4.75 min	8.29	12.96 min	0.36	0.64	
(Modified Server)	0.0029	2.59	2.11 min	6.71	5.28 min	0.37	0.63	
Remarks	Improved	Improved	Improved	Improved	Improved	Improved	Improved	

Discussion

The difference of the Existing server queue system with Modified server is that in the server queue discipline, previously the service adopted the Service in Random Order (SIRO) queue where each server had a full will for which service to do first regardless of which type of test came first and which type of test had a faster QC time. In the repair queue system, the service adopts a Priority Services (PRI) queue where control over the test queue is with the manager, servers that are ready are assigned by the manager by taking into account the QC time and test efficiency limits. By adopting the Priority Services (PRI) queue service, the work on the type of testing is more controlled as evidenced by a decrease in the delay rate by up to 0 %. More controlled testing work means that sample testing types are controlled by the manager, in this case the server focuses on performing services without co-managing which types of tests will be served first. More controlled service testing types means that managers can directly control the length of time it takes for the server to serve test types and managers can directly control the results that have been done so that the service runs more optimally.

One key improvement is observed in the average number of tests in the system (Ls). The existing server queue system had an average of 2.88 tests in the system, whereas the modified server queue system reduced this number to 2.59. This improvement suggests that the modified system achieved better efficiency in managing the testing workload, resulting in a more streamlined process.

Another significant improvement is seen in the average time spent by one type of testing in the entire system (Ws). The existing server queue system required an average time of 4.75 min per test, whereas the modified server queue system reduced this time to 2.11 min. This reduction in testing time indicates increased productivity and faster turnaround for the testing process.

Moreover, the average number of test types in the queue (Lq) decreased from 8.29 in the existing server queue system to 6.71 in the modified server queue system. This reduction indicates a decrease in the waiting time for tests in the queue, allowing for a more efficient utilization of resources and a faster overall testing process.

The average time a test spends waiting in the queue until it is served (Wq) also significantly decreased from 12.96 min in the existing server queue system to 5.28 min in the modified server queue system. This reduction in waiting time implies better management of the testing queue, minimizing delays and improving the overall timeliness of the process.

The proposed modification of adopting a Priority Services (PRI) queue system, where the manager controls the test queue and assigns ready servers based on QC time and test efficiency limits, has contributed to these improvements. By implementing this queue system, the testing work becomes more controlled, allowing managers to prioritize tests efficiently and optimize the service workflow[11].

Regarding the impact on human resource costs, implementing the recommended improvement strategy will not increase these costs. Instead, it will optimize existing resources and processes without incurring additional expenses. The modifications mainly involve reconfiguring and reallocating the current queuing system rather than adding new servers, so there should be no increase in human resource costs.

As for decision-making efficiency, the performance analysis before and after the changes shows that the modifications have positively impacted the queuing system. This indicates that decision-making efficiency has been maintained or even improved due to better configuration and reduced bottlenecks. These findings align with previous research on queuing systems, which has demonstrated the significance of proper queue management in enhancing system performance and efficiency. For example, a study by [12] investigated priority disciplines and schedules with and without interruptions are essential in transport systems to reduce queuing delay and increase efficiency. Cost-effective and resource-efficient improvements align with the concept of sustainability-oriented innovation, which is currently receiving increased attention in the across multiple industries [13].

Furthermore, a study by Safdar et al. [14] highlighted the importance of optimizing resource utilization and reducing waiting times in the healthcare industry through effective queue management strategies. Their findings emphasized optimized queue management system can help improve patient flow in the absence of an appointment system. The proposed model provides vital information in the form of “required” number of personnel which allows the administrators to control the queue pre-emptively minimizing wait times, with optimal yet dynamic staff allocation

Conclusion

The queuing analysis results indicate that the proposed modifications to the bacterial vaccine quality control process, including the adoption of a Priority Services (PRI) queue system, have resulted in significant improvements in various performance measures. The modified server queue system has demonstrated enhanced efficiency, reduced waiting times, and improved utilization of testing resources. These findings align with existing research in the field of queuing systems, emphasizing the importance of effective queue management in optimizing service performance. The article contributes to the existing literature on queuing systems and their application in improving process performance. It provides a specific case study in the context of bacterial vaccine quality control, highlighting the importance of efficient queue management for enhancing overall system performance.

By comparing the existing server queue system with the proposed modified server queue system, the study demonstrates the positive impact of adopting a Priority Services (PRI) queue system on reducing waiting times, improving resource utilization, and streamlining the testing process. The findings of the article have practical implications for the pharmaceutical industry, particularly in the domain of quality control for vaccine production. The adoption of a modified server queue system, as proposed in the study, can be implemented in real-world laboratory settings to improve the efficiency and effectiveness of the quality control process. By implementing a Priority Services (PRI) queue system, managers can prioritize tests based on their urgency, QC time, and test efficiency limits, ensuring that critical tests are performed promptly and optimizing the utilization of available resources.

The proposed modifications allow managers to have better control over the testing queue, enabling them to make timely decisions based on test priorities. This can significantly improve the response time to critical tests and facilitate prompt decision-making regarding the release or further investigation of vaccine batches. Timely decision-making is crucial in ensuring the safety and efficacy of vaccines while maintaining production efficiency. Future research in the field of queuing analysis for improving performance in the quality control process of bacterial vaccines can focus on advanced queueing models that consider varying service times, arrival rates, and priority levels for different tests.

Integration of real-time data can enable dynamic queuing models, while optimization algorithms can optimize resource allocation and test scheduling. Additionally, exploring queuing analysis in a multi-site setting, incorporating machine learning and artificial intelligence techniques, and conducting comparative studies can further enhance the efficiency, responsiveness, and decision-making capabilities of the quality control process. By addressing these areas, future research can contribute to the development of more effective and streamlined quality control processes in the pharmaceutical industry. Future research could also consider the use of machine learning (ML) and artificial intelligence (AI), which have not been addressed in this paper. Integrating ML and AI could further optimize the system and enhance operational efficiencies by providing advanced data analysis and predictive capabilities.

Funding Sources

This research did not receive any specific funding. The APC was covered by Universitas Padjadjaran.

CRediT authorship contribution statement

Sallyta Ayu Martha: Conceptualization, Data curation, Formal analysis, Methodology, Software, Writing – original draft, Writing – review & editing. Akhmad Yunani: Methodology, Supervision, Validation, Writing – original draft. Wega Setiabudi: Validation, Writing – original draft. Budi Harsanto: Conceptualization, Data curation, Methodology, Supervision, Validation, Writing – original draft, Writing – review & editing.

Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Sallyta Ayu Martha reports a relationship with Biofarma that includes: employment.

Data availability

Due to the sensitive nature of the vaccine production, the raw data remain confidential.
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