TY - JOUR

T1 - Matrix-augmentation approach for machine repair problem with generally distributed repair times during working breakdown periods

AU - Wu, Chia Huang

AU - Yang, Dong Yuh

AU - He, Ting En

N1 - Publisher Copyright:
© 2023 International Association for Mathematics and Computers in Simulation (IMACS)

PY - 2023

Y1 - 2023

N2 - In the manufacturing industry, production facilities for product manufacturing often contain unreliable operating machines and standbys. The machines can break down and result in productivity loss, and have to be repaired by the repairmen. To evaluate the system performance in operations and production management accurately, a general mathematical model is proposed to investigate the machine repair problem with an unreliable repairman, working breakdowns, and multiple vacations. A novel matrix-augmentation approach is introduced to simplify the analysis process and to derive the stationary distribution of the number of failed machines in the system when the classical supplementary variable technique cannot evolve the steady-state probability recursively. Furthermore, explicit formulas of various performance metrics are developed and numerically computed corresponding to various repair time distributions during working breakdown periods. Finally, an optimization problem with multiple objective functions is formulated with two different objective functions: the expected cost and machine availability. The NSGA-II algorithm is applied to perform numerical experiments and to provide Pareto-efficient solutions for managers and decision-makers.

AB - In the manufacturing industry, production facilities for product manufacturing often contain unreliable operating machines and standbys. The machines can break down and result in productivity loss, and have to be repaired by the repairmen. To evaluate the system performance in operations and production management accurately, a general mathematical model is proposed to investigate the machine repair problem with an unreliable repairman, working breakdowns, and multiple vacations. A novel matrix-augmentation approach is introduced to simplify the analysis process and to derive the stationary distribution of the number of failed machines in the system when the classical supplementary variable technique cannot evolve the steady-state probability recursively. Furthermore, explicit formulas of various performance metrics are developed and numerically computed corresponding to various repair time distributions during working breakdown periods. Finally, an optimization problem with multiple objective functions is formulated with two different objective functions: the expected cost and machine availability. The NSGA-II algorithm is applied to perform numerical experiments and to provide Pareto-efficient solutions for managers and decision-makers.

KW - Generally distributed repair times

KW - Matrix-augmentation method

KW - Multiple vacations

KW - NSGA-II

KW - Working breakdown

UR - http://www.scopus.com/inward/record.url?scp=85175086123&partnerID=8YFLogxK

U2 - 10.1016/j.matcom.2023.09.026

DO - 10.1016/j.matcom.2023.09.026

M3 - Article

AN - SCOPUS:85175086123

SN - 0378-4754

JO - Mathematics and Computers in Simulation

JF - Mathematics and Computers in Simulation

ER -