The potential of the P-graph for optimizing public service processes

The European Union defines the public services sector in detail and sets out the public sector’s operational requirements in fields such as health, education, social care, and transport to meet the diverse needs of European citizens. It refers to the fact that the changing social, demographic, and political context will make improving the quality of public services increasingly challenging. In addition to quality and affordability, new aspects such as digitization, broad accessibility, and sustainability are also coming to the fore (Eurofound 2023). On the development of digitization, the EU clearly states the need to improve the quality of digital public administration between and within Member States (European Council 2023).

To improve quality, public services are expected to reduce bureaucracy for citizens and businesses (Interoperable Europe Act, European Parlaiment, 2023). Improving quality also involves considering environmental and sustainability objectives within public services. The number of sustainability reports on (and by) the private sector has increased significantly over the last decade. However, few reports and studies have been produced by public service organizations (Unerman et al. 2007). In the private sector, the GRI (Global Reporting Initiative) index is most commonly used for sustainability reporting, including environmental impact, labor practices, human rights, societal impact, product responsibility, and more (Global Reporting 2023). The ESG (Environmental, Social, and Governance) indicator (Berg et al. 2020) is a tool for measuring sustainability that has been developed over a long debate and revision process and is still used today, primarily to assess the sustainability and ethics of private sector investment. The Environmental component measures the company’s environmental impact, while the Social component examines the relationship with employees, customers, and partners. The Governance component focuses on decision-making, governance, and legal compliance within the company (Shen et al. 2023). While many studies in the private sector use GRI and ESG methods for sustainability assessments, there are few publications regarding the public sector. Domingues et al. (2015) developed a conceptual framework for assessing and communicating the sustainability of local public services using the GRI indicators. They found that public services play a crucial role in setting themselves as sustainable service providers in the market, setting an example for citizens and market actors. Accordingly, they developed an EU eco-label for the public sector based on the GRI indicators. In this paper, we aim to draw attention to the fact that few studies have been carried out in the public sector using the GRI indicators. Only the following contents will be considered in the research, as they are interpretable in the context of the enrolment process for staff: Economic Aspects (EA), Economic Development (ED), Financial Performance (FP), Ethics and Social Responsibility (ESR), Labor Practices and Decent Work (LPDW), and Social and Service Responsibility (SSR). Researchers and policymakers have developed models to enhance public sector quality, focusing on New Public Management (NPM) and Neo-Weberian State approaches. The public administration sector in Hungary is closest to the Neo-Weberian model, as the apparatus is highly centralized. The image of the service state outlined in the Magyary Programme and the Public Administration Development Strategy is closest to the Neo-Weberian model. Referencing the traditional Weberian model of bureaucracy, Rónay (2014) describes state operations as mechanistic, detached, and rule-based. Zoltán Magyary posited that the sole purpose of public administration is to benefit the populace and the nation, as outlined by Balaskó and Molnár (2014). This approach to public service is propelled by factors such as the reinvigoration of the state’s role, enhanced integration within the system of public administration, and improved coordination of planning and service delivery across various sectors and administrative entities (Kovács 2019). Typical forms may include one-stop shops or public service cooperation between local authorities (Kovács 2019). The NPM model is a modern public administration concept that emphasizes meeting the real needs of citizens and, therefore, adopts different management techniques. It aims to improve processes to be more efficient and effective. The foundations of NPM were laid in the 1980s, mainly in England, Australia, and especially New Zealand (Stark 2002). According to Kettl (1995), NPM can be understood as competition between public and private service providers, giving citizens more choices.

The NPM model has also been subject to several criticisms. For example, the government’s role is reduced, and private actors’ involvement is increased. One criticism has been that such schemes create quasi-autonomy by creating agent-like structures. Public services are thus subject to marketization, outsourcing part of their functions. Introducing new management techniques and benchmarking do not necessarily improve processes (O’Toole 1997). Overall, the current public service model in Hungary is relatively far from the EU’s customer-friendly expectations, and this is often true of bureaucratic processes in universities (in our case study, the enrolment process is only partially digitized and is highly bureaucratic and complex). The complete documentation for all students is also available in hard copy on the registrars department, which cannot be said to be a sustainable process. The final step of the enrolment process is done on a printed document, so the expectation of digitization is only partially met. The existing enrolment procedure lacks environmental soundness and sustainability, making it insufficient for staff and students.

Several models have been used in public service endeavors to increase efficiency. Optimization studies can be found across diverse research domains, spanning engineering, economics, operations research, and beyond. These studies leverage mathematical modeling techniques to identify the most efficient or effective solution to complex real-life problems (Ordu and Der 2023). In engineering, optimization is applied to design processes, logistics, and resource allocation, aiming to minimize costs, maximize performance, or achieve specific objectives. In economics, optimization models are utilized to optimize production, pricing strategies, and resource utilization, ultimately enhancing profitability and efficiency. Operations research employs optimization to optimize supply chain management, transportation systems, and scheduling, improving overall system performance and productivity (Ikuobase and Okpako 2020) The widespread use of optimization underscores its importance in addressing critical challenges across various industries and disciplines. By harnessing mathematical modeling and computational methods, optimization studies offer invaluable insights and solutions to intricate real-life problems, driving innovation, efficiency, and competitiveness in today’s complex world. The interview questions were developed through a primary unstructured interview. The first two interviews were with a very overburdened staff member and the deputy office manager. The deputy manager also shared a document with us describing the process. Based on the first interviews and the document, we prepared an in-depth interview guide, which we conducted with 50% of the staff. For the selection of the participants in the research, it was considered to interview less, average and significantly overworked staff. We built our model based on the process steps, time data and case numbers shared with us in the interviews. In order to improve the university enrolment process, this case study will examine the efficacy of several mathematical models, including P-graph, Process Chain Network, Business Process Modeling, and Service Blueprinting. The goal is to determine which approach produces the best results.

This paper examines the university enrolment process as a public service process. Research Goal: To apply a new model to study the public service process (Fig. 1.)

Research Questions:

In our research, we conducted in-depth interviews with the deputy head of the study department involved in the university enrollment process, and four administrators of the department to understand the enrollment process (Table 1). Data collection was conducted between August and November 2023. We were provided with the descriptions, diagrams, and rules used for the enrollment process, which were included in our model. At the beginning of the research process, the enrolment process was found to consist of two central arcs.

First, after successful admission, the university receives data and documentation about students from the central admission database. After that, the university administrators start processing the documentation and send additional data requests to the students if some data are incorrect or missing. The goal at this stage is to enter all students into the database for course administration. This part of the process must be completed within 2–3 weeks in case of all students before the official contract signing happens during an organized mass meeting. Besides signing the contract, additional documentation is collected on paper from the students during this meeting.

The second major arc of the process starts here with the processing of the paper-based documentation to enter additional information about the students into the database that was not provided before. This process is partially digital and partially paper-based and altogether requires lengthy, repetitive paper and digital corrections by administrators. The process is also highly bureaucratic, complicated, and opaque. For this second part, the administrators also have a limited timeframe, as they must be ready when the semester starts. Additionally, nearly 60% of the enrolled students cannot complete all paperwork correctly the first time, requiring several rounds of additional data requests per student. As a result, to complete the process in time and administer more than 4000 enrollment students, administrators have to work overtime. A total of 14,000 students attend the investigated Hungarian university, approximately 4500 enroll in the fall semester and 2000 in the spring. The number of enrollments has been similar over the past 6–7 years, so no significant fluctuations can be observed. The reason for the fluctuation is not that the number of enrolled students changes frantically, but that the staff has difficulty getting used to the changing stress and overload. And those who survive the first 2 years will stay longer, but in the first two years, the turnover is approx. 20%.' Often, weekend work is also required. The process is stressful for the stakeholders. At least 1–2 years of experience is required for effective administration, and the staff turnover is significant. The research developed four different models—one for each evaluation method (SBP, BPM, PCN, P-graph). Visualizations of each model are shown in Figs. 2 through 5.

The models used to analyze the enrolment process are presented below. The purpose of presenting these models is to compare the models used to study the public sector and to identify which model is best suited to improve the quality of the process. To develop a model that can be widely and effectively applied in public services in the future.

As shown in Fig. 2 created by the Camunda Modeler Software, in the Service Blueprinting (SBP) method, the leading customer actions consist of admission to the university, providing data and documentation, personal appearance to sign the contract, and finally receiving student status. The contact signing process is the stage of visible employee action in the student administration office. Backstage action consists of waiting for admission information, receiving data and admission information, pre-processing documentation, calling students for contract signing, processing signed contracts and additional data, and finishing administration. The administrators’ official digital system supports the whole process. Figure 3 shows the university enrolment process’s Business Process Model (BPM), created by the Camunda Modeler Software. The BPM model offers more flexibility and deeper insights into the process from an organizational perspective, clearly separating the process steps of the administrators and the students and adding two more layers to provide additional perspective on the enrolment process’s paper-based and electronic information processing tasks.

The process seems similar: after entering the admission process, students must provide data and documentation, which the administrator collects and processes through several steps. In many cases, additional information requests are sent to students if the initially provided information is inaccurate or if some information is missing. These steps are required to register the students in the university system and start course administration. In a later stage, an official contract is also signed, and additional information and documentation are requested to continue the administrative process, again with additional information request steps if necessary, until the process is finished and the students receive official student status at the university.

The Process Chain Network method (PCN) in Fig. 4 is designed to present process elements involved in the service process based on needs and satisfaction, adding another layer and perspective to help understand the enrolment process. The PCN model also examines and includes customer satisfaction or dissatisfaction at different points of the service. Our research and model show that the administrators and the customers are dissatisfied at several points during the process.

From the administrator’s perspective, dissatisfaction occurs during data processing due to the short timeframe and incomplete documentation coming from different sources, which lead to additional data requests, prolonging the process. The workload of administrators is high, with each administrator being expected to process the documentation of hundreds of students quickly, which often leads to significant levels of administrator dissatisfaction. On the customer side, the primary source of dissatisfaction is also connected to the data-providing steps, as they are obliged to provide separate sets of documentation on paper and in digital form to multiple sources in several rounds instead of one comprehensive data collection. Unfortunately, these independent elements slow down the process. Eliminating redundancies and inefficiencies in the data processing process could significantly increase administrator and customer satisfaction. New digital administration solutions or other efficiency-enhancing methods would help students and administrators alike. Figure 5 shows the P-Graph representation of the university enrolment process.

The graph representation of the process created by the P-graph Sudio software contains resources, operating units, and intermediate actions. In this context, the administrators, their capacity, and the students are the process’s resources. In the first stage, administrators either process the documentation provided by students or request additional information because of incorrect or missing information and process it afterward. During the second stage, administrators process the paper-based documentation provided during the contract signing, following a similar process pattern. However, the time allocated for these different stages differs, as the paper-based documentation processing takes longer than its electronic counterpart. Students often make mistakes at each stage, requiring additional data request rounds. The time limitation of the whole process also has to be considered at both stages separately.

Available administrative human resources (A_n) of the P-graph representation can be calculated as the following:

In this process, there are 15 administrators (N_a) working 8 h a day (H), five days (D) per week (W). We aim to maximize our process output, considering the finished documentation process as the final product. We are calculating with N_S = 4000 student input documentation. As a constraint, the administrators have three weeks for the first stage with A₁ = 1800 h of human resources and two weeks for the second stage with A₁ = 1200 h of human resources.

The third input resource is the required labor hours (L_n) per documentation. According to administrators, the average processing time of a documentation is 30 min (P₁) in the first digital stage and 45 min (P₂) in the second paper-based stage per student. As administrators also have other daily tasks, we consider that they can allocate 60% (\(\sigma \)) of their time to the enrolment process. Of course, we also have to keep in mind the right unit of time measurement in the numerator and denominator as well. As a result, in this scenario, administrators have L₁ = 2160 labor hours capacity for the first stage and L₂ = 960 labor hours capacity for the second stage, acting as constraints (Table 1).

There is an additional significant limitation in this scenario regarding the administrators, as we assume that all of them work every day and manage to do all their other tasks, breaks, and opening hours during the other 40% of their time. Also, while the administrators’ experience suggests that 60% of the documentation is incorrect in some way in the second stage, we assumed a moderate 10–20% error rate for this scenario initially.

According to the model results, administrators could process 1646 documents during the first stage and 612 documents maximum during the second stage, far from the initially considered 4000 student documents.

Suppose we set the scenario to require all documents to be processed within the given administrator constraints. In that case, the model provides no feasible solutions, suggesting that administrators must work overtime every day and even on weekends to complete this process by the given deadlines. We would need at least twice as many administrators or a more effective document processing system to achieve the target goal within the given timeframe.

This paper aimed to present four methods that had not previously been used to examine and visualize the university enrolment process but could effectively describe and analyze it, highlighting why the P-graph approach is more suitable to this complex service process than other methods.

First, we presented an overall literature review of public administration theories, with a particular focus on the connection and importance of GRI and ESG methods for sustainability assessments, highlighting the potential research gap and emphasizing why these processes should be reconsidered and transformed according to modern standards and expectations, in order to satisfy the customers and also to support the administrators’ work, making it more effective and efficient. We first presented the Service Blueprinting, Business Process Modeling, and Process Chain Network methods. These three practical tools had never been used in the Hungarian public administration literature to analyze complex university enrolment service processes. These methods can help map and visualize public services, analyze the service process, and identify possible problems responsible for inefficiency and ineffectiveness. As preliminary results of our research, we presented the application of all three methods to the university enrolment process, showing how these methods provide deeper insights into various aspects of the process. We also demonstrated how each method gave us a new perspective on the enrolment process steps and interactions between the administrators and customers, highlighting dissatisfaction in the process for each party. Improving the quality of university enrollment as a public service process can be achieved through the combined application of Service Blueprinting, Business Process Modeling, Process Chain Network, and P-graphs. Service Blueprinting allows universities to visualize the enrollment journey, identify pain points, and streamline both customer-facing interactions and backstage operations. Business process modeling helps in analyzing and optimizing enrollment processes, standardizing procedures, and supporting automation initiatives. Process Chain Network analysis enables universities to identify interdependencies, enhance coordination between departments, and optimize resource allocation across the enrollment network. Additionally, P-graphs address uncertainty, optimize decision-making through scenario analysis, and prioritize interventions based on sensitivity analysis, ensuring that efforts are focused on improving enrollment outcomes effectively and efficiently. Overall, these methodologies offer comprehensive approaches to enhancing the quality of university enrollment services, ultimately benefiting both students and the institution. Determining which is the best method to study public service processes depends on various factors such as the specific nature of the service, the objectives of the analysis, available resources, and the complexity of the process. However each of these methods have their own strengths and limitations and none of them are universally superior compared to each other. For public service processes, methodologies like Service Blueprinting, Business Process Modeling, Process Chain Network, and P-graphs are used due to their ability to provide a holistic view, identify inefficiencies, and optimize workflows. Service blueprinting excels in understanding customer experiences and interactions, making it valuable for services with a strong customer-facing component. Business process modeling offers a structured approach to analyze and streamline processes, which is beneficial for identifying bottlenecks and standardizing procedures. Process chain network analysis, on the other hand, emphasizes interdependencies and collaboration across various stages of service delivery, making it particularly useful for services involving multiple stakeholders or departments. P-graphs complement these methodologies by providing a robust framework for addressing uncertainty and optimizing decision-making in the analysis and improvement of public service processes. By incorporating probabilistic information and conducting sensitivity analysis, P-graphs enhance the ability to make informed decisions and drive continuous improvement in public service delivery. Ultimately, as this research shows it is beneficial to combine multiple methods to leverage their respective strengths and ensure a more comprehensive understanding of the public service process under study. To enhance the sustainability, environmental friendliness, and overall quality of public service processes, Service Blueprinting, Business Process Modeling, Process Chain Network, and P-graphs offer valuable strategies. Service Blueprinting helps identify environmental impacts and integrates sustainability measures into the service design, enhancing the customer experience. Business Process Modeling allows for the analysis and optimization of resource efficiency, guiding the implementation of sustainable practices throughout the process. Process Chain Network analysis fosters collaboration and identifies supply chain impacts, enabling targeted interventions to minimize environmental footprints. P-graphs assess sustainability risks, optimize investments, and support continuous monitoring and adaptation of sustainability initiatives, ensuring long-term environmental sustainability and qualitative improvement in public service delivery. Overall, integrating these methodologies enables governments and organizations to promote sustainability while delivering high-quality services to citizens. As we can see from the visualizations of the enrolment process, the procedure starts with the successful admission of a student to the university, which triggers administrative data processing after the initial information about the students is provided to administrators. After this, the students must provide additional documentation not included in the first transfer to continue the enrolment process. This data request can happen multiple times if the provided information is incomplete or wrong while each administrator simultaneously processes several hundred students’ documentation. In addition, administrators have a narrow timeframe for this early processing step. The steps required to register students in the university system and start course administration must be done quickly. In a later stage, an official contract is also signed, and additional information and documentation are requested to continue the administrative process, again with additional information request steps if necessary, until the process is finished and the students receive official student status at the university. The results of the P-graph model also highlight the overall complexity and inefficiency of this administrative process. Our results establish that administrators could not complete their work during regular working hours by the deadline, even if they did nothing else and took no breaks. They must work overtime to complete this critical process by the deadline. This overwork results in elevated stress levels and a high turnover rate. From the perspective of SSR, LPDW and ESR, the analyzed administrative process can be considered highly ineffective in its current form, resulting in the dissatisfaction of every stakeholder, especially administrators. Efficiency could be increased by reconsidering the process steps, allocating human resources, and providing feasible deadlines with more reasonable timeframes. From the perspective of EA, ED and FP the number of unnecessary document requests could be reduced by introducing a new method for initial data collection with more advanced digitalization and by the minimization or complete elimination of paper-based documentation processing.

In our article, we used the university enrolment process as an example of a complex process to show the usefulness of the four analytical methods—Service Blueprinting, Business Process Modeling, Process Chain Network, and P-graph methodology—in highlighting the different aspects and layers of this process. We have demonstrated why it is essential to approach a complex process with a sophisticated tool to find optimal means of achieving higher efficiency, effectiveness, and satisfaction on both the customer and administrator side. Each model offers an additional point of view regarding the enrolment process, providing insights and details about the process steps, stakeholders, and their interactions. The Service Blueprinting and Business Process Modeling methods help us understand the process’s main steps and the stakeholders’ interactions. The Process Chain Network also provides us insights regarding stakeholders’ satisfaction, while P-graph addresses uncertainty and optimizes decision-making. Researchers should consider several internal factors to understand the process above and increase efficiency. In the reviewed process, administrators have strict deadlines from which they cannot deviate. According to our interviews, this combination of heavy workloads and fast-approaching deadlines puts pressure on the workforce, which leads to high stress and dissatisfaction. The P-graph model confirmed the extent of this problem, which was also acknowledged by the administrators during the validation of the created models, and it demonstrated that the administrators could not be expected to operate effectively within the given time and resource constraints without putting in considerable overtime. To meet ESG and GRI standards regarding SSR, LPDW and ESR managers should reconsider several process steps, and additional resources should be allocated to administrators. Regarding the EA, ED and FP aspects, the number of nonessential steps could be reduced by ensuring the accuracy of arriving documentation with advanced digitalization tools and the elimination of paper-based documentation requirements.

Additionally, to allow the process to adapt to sudden changes, the enrollment process necessitates a flexible and agile approach. Organizations can achieve this by continuously monitoring and evaluating the enrollment process, employing scenario planning and simulation to anticipate external factors, designing processes with built-in flexibility, and engaging in rapid prototyping and collaborative decision-making. Additionally, investment in technology solutions, such as automation and digitization, can enhance process resilience, while training and capacity building initiatives prepare employees to effectively navigate changes. By embracing these strategies, organizations can respond adeptly to sudden changes in the enrollment process, ensuring continuity, resilience, and quality in service delivery. Our research found that every analytical technique was effective in assessing the current issue and could be extended to address more intricate processes within Hungarian public services. It was possible to pinpoint critical areas where enhancements could lead to reduced processing times, enhanced adaptability, and heightened overall efficiency and performance. It can be said that the phenomenon under study is the enrolment process, and the problems and possible solutions presented are applicable to all universities in Hungary, as the enrolment process has the same disadvantages and areas for improvement in all Hungarian universities. Currently, the administrators do double work, because they do the task on paper and also digitize (scan) it, but this solution is not a real digitization. We propose that universities take advantage of AI and digitization to create a more efficient system, supported by online solutions, and truly digitize the periodic (semi-annual) process. We recommend our study to the attention of university decision makers, by taking into account and applying our results it will be possible to make the enrolment process in all Hungarian universities more flexible and faster, thus making the stakeholders more satisfied. In subsequent studies, our attention will be directed toward the university enrollment process, where we aim to gather comprehensive data on each case, focusing on processing durations and intricacies. We plan to employ a combination of analytical techniques and simulations to thoroughly examine the data obtained. These measures will enable us to identify additional inefficiencies in the enrolment process. The long-term impact of the model we have developed is clear, as the enrolment process will be much faster and more flexible. This will free up additional resources for staff to be used for other processes or tasks. In the long-term, students will also be more satisfied as the currently very complex task will be simplified and will not take up their free time. Full digitization will eliminate the need to store documents on paper, thus reducing the environmental footprint. As the amount of documents that need to be stored in the long-term will be reduced, there will be no need for large warehouses, which will also reduce the ecological footprint.