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APPLICATION OF COOPERATIVE GAME THEORY: SOLVING THE PROBLEM OF TRAVELING BETWEEN FIVE CITIES IN JAVA Ariyanto, Muhammad Aditya Tri; Setiawan, Rubono
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0797-0814

Abstract

Intercity travel between Surabaya, Madiun, Surakarta, Semarang, Cirebon, and Jakarta is increasingly facilitated by integrated infrastructure such as toll roads, railways, and airports. Among travelers, forming informal coalitions with others heading in the same direction has become a practical way to reduce individual travel expenses. This study aims to analyze the cost-efficiency of coalition-based intercity travel compared to solo travel, utilizing cooperative game theory to determine fair contribution values among travelers. This study aims to analyze the cost-efficiency of coalition-based intercity travel compared to solo travel, utilizing cooperative game theory to determine fair contribution values among travelers. A case study was conducted in an urban setting involving individuals who travel intercity using various transportation modes. Data were collected through semi-structured interviews. The study applied the Shapley value method within cooperative game theory to model and evaluate each participant’s contribution in a travel coalition. An algorithm was developed to calculate Shapley values for different coalition scenarios. Initial expenditures were: Player A (IDR 210,000), B (IDR 240,000), C (IDR 60,000), D (IDR 400,000), and E (IDR 165,000). First calculation (5-player coalition): A spent IDR 122,750, B IDR 147,750, C IDR 77,750, D IDR -52,250, and E IDR 104,000. Player C opted out, as joining the coalition would cost more than traveling individually (IDR 60,000). Second calculation (4-player coalition): A spent IDR 113,750, B IDR 133,750, D IDR 53,750, and E IDR 98,750. The study’s findings are based on a small sample with specific subject criteria and cannot be generalized to broader intercity travel scenarios. This research demonstrates the practical application of game theory—specifically the Shapley value—in modeling travel coalitions and optimizing cost distribution, offering insights for policy makers and transport planners in collaborative travel schemes.
Analisis Soal Latihan Transformasi Linier Dalam Buku Ajar Aljabar Linier Berdasarkan Teori Prakseologi Sujatmiko, Ponco; Aryuna, Dyah Ratri; Pramudya, Ikrar; Mardiyana, Mardiyana; Setiawan, Rubono
Jurnal Ilmiah Pendidikan Matematika Al Qalasadi Vol 9 No 2 (2025): JURNAL ILMIAH PENDIDIKAN MATEMATIKA AL QALASADI
Publisher : Prodi Pendidikan Matematika, Fakultas Tarbiyah dan Ilmu Keguruan IAIN Langsa

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.32505/qalasadi.v9i2.12872

Abstract

Undergraduate students often struggle to shift froam procedural to conceptual understanding when learning linear transformation. They tend to focus on mechanical procedures while neglecting the underlying concepts. Textbooks play a crucial role in developing conceptual understanding through well-structured and meaningful exercises. Praxeological theory, which maps the relationship among mathematical tasks, techniques, supporting technologies, and underlying theories, provides a comprehensive framework for such analysis. This study aims to analyze linear transformation exercises in Elementary Linear Algebras (11th edition) by Howard Anton and Chris Rorres using a qualitative content analysis based on the praxeological framework. The findings reveal that most exercises have the potential to foster deep conceptual understanding, particularly when learning activities do not stop at the technical stage. Practically, the study offers insights for lecturers and textbook developers in designing exercises that balance procedural demands and conceptual reasoning, thereby enhancing meaningful learning of linear algebra in higher education.
Study on the Suitability of Mathematics Learning Media to Increase Interest of Vocational Students Through Media Learning Exhibition Activity Setiawan, Rubono; Chrisnawati, Henny Ekana
Journal of Mathematics and Mathematics Education Vol 13, No 2 (2023): Journal of Mathematics and Mathematics Education (JMME)
Publisher : Universitas Sebelas Maret

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20961/jmme.v13i2.79592

Abstract

In this research, an evaluation was carried out to determine the suitability of different hands-on and digital learning tools designed to stimulate students' enthusiasm for mathematics, especially those in Vocational High Schools (SMK). These physical and digital educational resources were showcased during an exhibition, which was part of community engagement initiatives at SMK Warga Surakarta. During this event, a team of students and professors elucidated the functioning of these educational tools. Following this, math teachers from SMK, the intended users, provided assessments and analyses regarding the suitability of the demonstrated educational tools. Information collected from the exhibition, observations, validation records, and specifics about the educational tools were presented in a detailed and qualitative manner. Additionally, feedback for enhancements and advancements to elevate the quality of educational tools was gathered. Based on the qualitative descriptive analysis undertaken, both the physical and digital educational tools presented were deemed valid, fitting, and practical for the learning process, effectively augmenting students' interest.