Optimal management of the machine repair problem with working vacation: Newton's method
type: Item
instance of: scholarly article
title: Optimal management of the machine repair problem with working vacation: Newton's method
zbMATH Open document ID: 1180.90098
author: Kuo-Hsiung Wang
author: Wei-Lun Chen
author: Dong-Yuh Yang
published in: Journal of Computational and Applied Mathematics
publication date: 2009-10-09T00:00:00Z
review text: According to authors' abstract the paper ``studies the M/M/1 machine repair problem with working vacation in which the server works with different repair rates rather than completely terminating the repair during a vacation period. We assume that the server begins the working vacation when the system is empty. The failure times, repair times, and vacation times are all assumed to be exponentially distributed. We use the MAPLE software to compute steady-state probabilities and several system performance measures. A cost model is derived to determine the optimal values of the number of operating machines and two different repair rates simultaneously, and maintain the system availability at a certain level. We use the direct search method and Newton's method for unconstrained optimization to repeatedly find the global minimum value until the system availability constraint is satisfied. Some numerical examples are provided to illustrate Newton's method''. The paper can be interested to students and scientists working in the area of optimal management of the machine repair problems.
reviewed by: Stefan Jendo
Mathematics Subject Classification ID: 90B25
Mathematics Subject Classification ID: 90C53
zbMATH DE Number: 5612613
zbMATH Keywords: cost
zbMATH Keywords: optimization
zbMATH Keywords: working vacation
zbMATH Keywords: Newton's method
describes a project that uses: Maple
MaRDI profile type: Publication
full work available at URL: j.cam.2009.07.043
OpenAlex ID: W2000306236
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DOI: 10.1016/J.CAM.2009.07.043
description: scientific article; zbMATH DE number 5612613