Production Rhythm Matters in a Sequential Manufacturing Line
Manufacturing lines that operate continuously are not simply collections of individual machines. Each stage depends on the timing of the stages before and after it. A delay at one point can influence the movement of production lots throughout the entire line.
The issue becomes particularly important in pipeline manufacturing, where a new production lot can enter the first stage before the previous lot has completed all stages. In this situation, the time needed to finish one complete lot is not necessarily the same as the interval between successive production outputs.
The researchers examined this problem in the production of 5.56 mm cartridge cases. According to the article, the manufacturing process involves a sequence of operations ranging from material forming and quality control to drilling, heat treatment, cleaning, final inspection and coating. The production line studied consisted of 11 sequential stages.
The case study was conducted using production data from PT XYZ, an anonymized Indonesian defense manufacturing company. The authors specifically noted that previous studies had examined aspects such as cartridge-case production layout, but production periodicity using Max-Plus Algebra had not been specifically analyzed for this manufacturing system.
How Max-Plus Algebra Maps the Production Line
Rather than looking at each production stage separately, the researchers modeled the entire manufacturing flow as a discrete event system. In simple terms, the model focuses on events such as one process finishing and the next process becoming ready to start.
The researchers incorporated the sequence of production stages, processing time, production lot size and waiting time between processes into a mathematical model. Each production lot contained 20,000 cartridge cases, while the average waiting time between consecutive stages was set at 15 minutes.
The model assumed a fixed production sequence and stable processing times. It did not include unexpected events such as machine breakdowns, material shortages, operator changes or temporary production stoppages. This means the resulting cycle time describes the production system under deterministic and stable operating conditions.
The researchers then used MATLAB to calculate the system's eigenvalue and perform iterative simulations. In the Max-Plus Algebra framework, the eigenvalue represents the operating period of a repetitive system once it reaches a stable production pattern.
Fire-Hole Drilling Becomes the Production Bottleneck
The analysis produced a clear result: the minimum stable production cycle is 109.649 minutes.
Importantly, the figure does not mean that a single production lot takes only 109.649 minutes to travel from the first stage to the final stage. Instead, it represents the interval between production outputs after the pipeline has reached a stable repetitive pattern.
The model identified stage P5, fire-hole drilling, as the critical production stage. Its processing time is also 109.649 minutes per 20,000-unit lot, the longest processing time among the stages listed in the production data.
The researchers found that P5 forms the critical circuit in the mathematical model and therefore determines the overall production periodicity. In practical terms, this means improving stages that are not controlling the cycle may not substantially shorten the overall production interval if the fire-hole drilling stage remains unchanged.
The simulation reinforced this conclusion. Starting from the fifth production stage, the time difference between consecutive production lots follows the 109.649-minute cycle identified by the eigenvalue analysis.
What the Finding Means for Production Management
The result gives production managers a more targeted way to evaluate manufacturing performance. Instead of attempting to improve every stage simultaneously, the model points to the process that has the greatest influence on the stable production rhythm.
The authors suggest that efforts to reduce the minimum production cycle should initially focus on the fire-hole drilling stage. Possible areas for evaluation include production capacity, machine utilization and process balancing. However, the article emphasizes that any improvement must continue to consider operational feasibility, product quality and production safety.
The approach could also be useful beyond this particular production line. The authors position the model as a way to evaluate stable production rhythms in sequential and repetitive pipeline manufacturing systems. The mathematical framework allows production timing to be viewed as an interconnected system rather than as isolated machine operations.
At the same time, the researchers caution that the result should not automatically be treated as a prediction of real-world production under all circumstances. Machine failures, material delays, defects, rework, operator variation and changes in machine availability were excluded from the model and could alter actual production timing.
Researchers and Publication
The study was authored by Wiwit Melinasari, Edy Sulistyadi, Ida Bagus Made Putra Jandhana, and Suroto. Melinasari, Sulistyadi and Jandhana are affiliated with Universitas Pertahanan RI, while Suroto is affiliated with Universitas Jenderal Soedirman. The article lists Wiwit Melinasari as the corresponding author.
The source article does not provide the authors' academic degrees or detailed individual fields of expertise, so those details are not added here to avoid introducing unsupported information.
Research Profile
- Wiwit Melinasari: Universitas Pertahanan RI; corresponding author.
- Edy Sulistyadi: Universitas Pertahanan RI.
- Ida Bagus Made Putra Jandhana: Universitas Pertahanan RI.
- Suroto: Universitas Jenderal Soedirman.
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