Measuring Production Periodicity in a 5.56 mm Cartridge Case Manufacturing System Using Max-Plus Algebra

Wiwit Melinasari (Universitas Pertahanan RI)
Edy Sulistyadi (Universitas Pertahanan RI)
Ida Bagus Made Putra Jandhana (Universitas Pertahanan RI)
Suroto (Universitas Jenderal Soedirman)

Indonesian Journal of Advanced Research (IJAR)
Vol. 5 No. 8 (2026): August 2026

This study measures production periodicity in a 5.56 mm cartridge case manufacturing system using Max-Plus Algebra. The manufacturing system was modeled as a deterministic discrete event system consisting of eleven sequential stages, one lot of 20,000 units, and inter-process waiting time as a model parameter. A max-plus state-space model was formulated to capture temporal dependencies among stages, followed by eigenvalue analysis and iterative simulation in MATLAB. The results show a minimum production cycle time of 109.649 minutes, with the fire-hole drilling stage identified as the critical production stage. The model clarifies the stable production period of a pipeline manufacturing system and supports stage-focused production evaluation.