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All Journal Indonesian Journal of Mathematics and Applications
Muthuvalu, Mohana Sundaram
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Computer Science & IT Education Mathematics Other

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Dynamical Analysis and Data-Driven Parameter Estimation of a Multi-Stage Toyota Manufacturing System Using Machine Learning Habibah, Ummu; Hidayat, Fatah; Ardiana, Dita; Andawaningtyas, Kwardiniya; Karim, Corina; Marjono; Maulana, Avin; Kurniawaty, Mila; Muthuvalu, Mohana Sundaram; Gunaningtyas, Almira Jorydanta
Indonesian Journal of Mathematics and Applications Vol. 4 No. 2 (2026): Indonesian Journal of Mathematics and Applications
Publisher : Universitas Brawijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21776/ub.ijma.2026.004.02.4

Abstract

Efficient buffering and material flow synchronization are foundational to maintaining high-volume throughput in modern automotive assembly networks, such as the Toyota Production System (TPS). However, real-time control utility optimization and predictive scheduling are often constrained by hidden or variable workshop capacities (μᵢ). This paper proposes a comprehensive data-driven parameter estimation and continuous-time dynamical analysis framework to model a multi-stage automotive manufacturing queueing network under Just-In-Time (JIT) control policies. The plant is formalized using a continuous state-space model governed by ordinary differential equations (ODEs), incorporating a non-linear minimum (min) operator at multi-input junctions to capture the vehicle-engine synchronization (marriage process). Local stability analysis rigorously establishes that the network converges asymptotically toward a unique steady-state equilibrium vector X̄, behaving as a globally attractive Stable Node capable of neutralizing severe initial line imbalances. To make the model adaptive to factory floor environments, a machine learning least-squares optimization loop backed by MATLAB’s adaptive numerical solvers is deployed to identify hidden processing capacities from noisy, discrete work-in-progress (WIP) time-series data. Goodness-of-fit validations against synthetic datasets contaminated with 2% Gaussian white noise demonstrate exceptional tracking fidelity, yielding minimal residual thresholds (RMSE ≤ 0.029). The results confirm that integrating continuous-time differential equations with data-driven optimization establishes a robust, highly scalable, and structurally stable digital twin framework for real-time manufacturing system calibration and throughput optimization.
Co-Authors Ardiana, Dita Fatah Hidayat Gunaningtyas, Almira Jorydanta Karim, Corina Kwardiniya Andawaningtyas Marjono Maulana, Avin Mila Kurniawaty Ummu Habibah, Ummu