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All Journal FARABI: Jurnal Matematika dan Pendidikan Matematika
Nurwan Nurwan
Universitas Negeri Gorontalo, Gorontalo-Indonesia
Computer Science & IT Decision Sciences, Operations Research & Management Mathematics

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Model Aljabar Max-Plus pada Sistem Distribusi Produk Bakery dengan Representasi Petri Net Siti Nurlaila Mustapa; Nurwan Nurwan; La Ode Nashar
FARABI: Jurnal Matematika dan Pendidikan Matematika Vol 9 No 1 (2026): FARABI: Jurnal Matematika dan Pendidikan Matematika
Publisher : Program Studi Pendidikan Matematika FKIP UNIVA Medan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.47662/farabi.v9i1.1397

Abstract

Distribution efficiency is a critical aspect of bakery product distribution systems, as delivery delays affect product freshness, operational costs, and service reliability to customers. This study aims to develop a mathematical model to analyze product distribution time at UD. Win Win Bakery by integrating Petri Nets and Max-Plus Algebra. Petri Nets are used to represent the sequential, event-based distribution process, including vehicle preparation, goods loading, distribution travel, goods unloading, and the return trip to the factory. The Petri Net structure is then transformed into a Max-Plus Algebra model and matrix to calculate the total distribution time for each team. Data were collected through observations and interviews regarding distribution schedules, routes, number of vehicles, loading time, unloading time, and travel duration. The results show significant variations in distribution times among the nine delivery teams. The longest durations were found on the Toboli–Parigi, Ampibabo, and Kotamobagu routes, indicating workload imbalance and potential bottlenecks in the distribution system. The main contribution of this study lies in the application of Max-Plus Algebra supported by Petri Nets as a structured framework to identify time inefficiencies in regional-scale distribution. The implications of this study suggest that Max-Plus Algebra can be effectively used in discrete event-based distribution systems and supports route evaluation, workload balancing, and operational decision-making in perishable product logistics.
Co-Authors La Ode Nashar Siti Nurlaila Mustapa