Parameter Identification for Synchronous Two-Machine Exponential Production Line Model

Abstract

Production system modeling refers to the process of constructing valid and high-fidelity mathematical models that are capable of capturing the behavior of job flow in the manufacturing systems. During the modeling process, model parameter identification is the most critical step. This step, however, often involves a significant amount of complex and nonstandardized work. To tackle this problem, we propose to reversely compute the production system model parameters based on standard manufacturing system performance metrics. In this paper, we consider a two-machine production line model, in which the machines follow the exponential reliability model and have identical processing speed, and formulate a constrained optimization problem with the objective of finding the optimal machine parameters which can fit the system performance metrics the best. To solve this problem, barrier method with BFGS quasi-Newton algorithm and cyclic coordinate descent method with proximal point update are developed. The accuracy of these two methods in estimating machine parameters and performance metrics are computed and compared through extensive numerical experiments. Although barrier method is much more efficient in terms of computation time, the risk of getting trapped in local optima exists due to the lack of convexity. On the other hand, the numerical experiments demonstrate that the coordinate descent method reaches the global optimal solution for all the cases. Therefore, an ensemble strategy is recommended to ensure a high accuracy in parameter estimation with acceptable computation time.