Welch-Powell Mathematical Algorithm Successfully Optimizes Course Schedules and Eliminates Instructor Conflicts at HKBP Nommensen University

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FORMOSA NEWS - PematangSiantar - The classic problem of course scheduling, which frequently causes conflicting timetables for professors, has found a smart and structured scientific solution. Three researchers from HKBP Nommensen University Pematangsiantar have successfully tested a discrete mathematics approach to generate an automated, conflict-free, and highly efficient academic schedule ready for higher education deployment.

This study was conducted by Ropitta Anjelina Manik, Dr. Juli Antasari Sinaga, M.Pd., and Gayus Simarmata from the Computer Science Program, Faculty of Mathematics and Natural Sciences (FMIPA), HKBP Nommensen University. Published in June 2026, their research proves that a graph coloring method utilizing the Welch-Powell Algorithm combined with the Python programming language effectively simplifies class organization while completely eliminating overlapping teaching hours for faculty members who manage multiple courses.

The Complex Challenge of Manual Academic Scheduling

Developing a university course schedule is an incredibly complex task due to the necessity of aligning numerous variables simultaneously, including courses, available instructors, classroom capacities, and specific time slots. In practice, manual scheduling remains common across many institutions. Consequently, department administrators frequently encounter overlapping assignments—such as an instructor mistakenly assigned to two different classes at the exact same hour—or classroom booking conflicts.

To address this recurring issue, Ropitta Anjelina Manik and her team modeled the academic system using graph theory. In this mathematical model, each individual course is represented as a vertex (simpul), while scheduling conflicts resulting from a shared instructor are designated as edges (sisi) connecting those vertices. Two courses taught by the same instructor cannot share the same time slot, meaning they must be assigned distinct "colors" to separate them.

Streamlining Scheduling Conflicts with Welch-Powell and Python

The methodology of this applied quantitative study was conducted within the Computer Science Program at FMIPA, HKBP Nommensen University Pematangsiantar. The data utilized encompassed the entire academic population of the even semester for the 2025/2026 Academic Year, which included 34 active instructors and 40 core and elective courses.

The system's operational workflow begins by inputting all course details and corresponding instructor codes into a Python program. Next, the program calculates the degree of each vertex, which represents the total number of scheduling conflicts that a specific course shares with others. Following this step, the Welch-Powell Algorithm automatically sorts the courses in descending order, starting from the vertex with the highest degree of conflict down to the lowest.

The course facing the highest potential for conflict is prioritized and assigned the first color. Subsequently, the same color is distributed to other courses that are not adjacent (meaning they do not share an instructor and have no conflict). This coloring process loops dynamically, introducing new colors until all 40 courses are labeled. In this computational setup, each distinct color produced directly corresponds to a specific day of the week.

Main Findings: Semester-by-Semester Class Distribution

By executing the automated process using Python's specialized NetworkX and Matplotlib libraries, the research effectively grouped the 40 courses into 6 distinct colors, mapping out an optimal schedule across Monday to Saturday. The structured weekly course distribution by semester is organized as follows:

• 2nd Semester: Requires 4 colors (Red, Blue, Green, Purple), meaning all mandatory classes for this level can be systematically completed within 4 days, specifically Monday through Thursday.
• 4th Semester: Requires 5 colors (Red, Blue, Green, Purple, Yellow), allowing the workload to be efficiently balanced across 5 working days, from Monday to Friday.
• 6th Semester: Requires 6 colors (Red, Blue, Green, Purple, Yellow, Orange), which means classes span across 6 full days from Monday to Saturday due to intensive practical labs and cutting-edge elective subjects such as Machine Learning, Ethical Hacking, and the Internet of Things.
• 8th Semester: Requires only 2 colors (Red, Blue), allowing final-year students to attend formal campus lectures just 2 days a week (Monday and Tuesday), leaving the remaining days free to focus entirely on their undergraduate thesis.

Thanks to this rigorous mathematical mapping, no instructor is double-booked for the same time slot, resulting in highly optimized time management across the faculty.

Broad Implications for the Higher Education Sector

The successful deployment of the Python-based Welch-Powell Algorithm yields significant benefits for university administration. For department heads and academic registrars, this automated method shrinks the scheduling process from days of tedious manual cross-checking to a matter of seconds.

For both students and faculty members, a beautifully structured timetable directly elevates the quality of teaching and learning while preventing canceled classes due to sudden physical room or time overlaps. Furthermore, this scalable computational model is flexible enough to be adopted by other departments or massive university faculties dealing with larger academic datasets, establishing a reliable digital blueprint for modern educational logistics.

Researcher Profiles

• Ropitta Anjelina Manik — Lead researcher and graduate of the Computer Science Program, Faculty of Mathematics and Natural Sciences, HKBP Nommensen University Pematangsiantar. Specializes in Python programming, discrete mathematics, and information system optimization.
• Dr. Juli Antasari Sinaga, M.Pd. — Permanent Faculty Lecturer at HKBP Nommensen University. Expert in mathematics education, graph theory applications, and quantitative research methodologies.
• Gayus Simarmata — Academic researcher at HKBP Nommensen University actively developing applied computing research for science and technological systems.

Research Source Reference:

• Journal Article Title: Application of the Welch-Powell Graph Coloring Algorithm for Optimizing Course Scheduling Using Python (Case Study: Computer Science Program, Faculty of Mathematics and Natural Sciences, HKBP Nommensen University, Pematangsiantar)
• Journal Name: Indonesian Journal of Advanced Research (IJAR), Vol. 5, No. 6, Year 2026, Pages: 869-892.
• Official DOI: https://doi.org/10.55927/ijar.v5i6.16577
• https://journal.formosapublisher.org/index.php/ijar