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# Models and numerical algorithms for re-manufacturing systems

Abstract (Summary)
(Uncorrected OCR) Abstract of thesis entitled MODELS AND NUMERICAL ALGORITHMS FOR RE-MANUFACTURING SYSTEMS submitted by YUEN Wai-On for the degree of Master of Philosophy at The University of Hong Kong in July 2004 Due to the world? limited resources and disposal capacities, manufacturers and inventory managers are now very concerned about the recycling of products to reduce the amount of waste generated. In this thesis, stochastic queueing networks are proposed to model the re-manufacturing process of the returns. To obtain the system performance, one has to solve the system steady-state probability distribution. This results in a problem of solving linear equations. In this thesis, several models were proposed to model the re-manufacturing process. The first model assumes that the re-manufacturing time is negligible and excessive returns are disposed. Closed form solution for the system steady-state probability distribution was obtained. The model was then extended to allow lateral transshipment of returns. In this case, approximated closed form solution of the system steady-state probability distribution was also obtained. In the second model, the queueing capacity for the returns was introduced. The model is a generalization of the first model. The system steady-state probability distribution was solved by using an iterative method, the Preconditioned Conjugate Gradient Squared (PCGS) method with circulant-based preconditioners. It was proved that the preconditioned linear system has singular values clustered around one when the queueing capacity of returns tends to infinity. Fast convergence rate of PCGS was demonstrated by numerical examples. Next, a hybrid re-manufacturing system comprising a manufacturing process and a re-manufacturing process was considered. A direct method based on Fast Fourier Transform (FFT) and the Sherman-Morrison-Woodbury formula was proposed to solve the system steady-state probability distribution efficiently. The computational cost of the proposed method was also discussed. Finally a hybrid method based on the Successive Over-Relaxation (SOR) method and the evolutionary algorithm was developed for solving system of linear equations. It was then used to compute the steady state probability of queueing systems whose generator matrices do not have a near-Toeplitz structure. The fast convergence rate of the proposed method was demonstrated by the numerical examples of different queueing systems.
Bibliographical Information:

School:The University of Hong Kong

School Location:China - Hong Kong SAR

Source Type:Master's Thesis

Keywords:remanufacturing mathematical models

ISBN:

Date of Publication:01/01/2004