Buffer allocation and preventive maintenance optimization in unreliable production lines

In this paper, we consider a serial production line consisting of n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document} unreliable machines with n-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n-1$$\end{document} buffers. The objective is to determine the optimal preventive maintenance policy and the optimal buffer allocation that will minimize the total system cost subject to a given system throughput level. We assume that the mean time between failure of all machines will be increased after performing periodic preventive maintenance. An analytical decomposition-type approximation is used to estimate the production line throughput. The optimal design problem is formulated as a combinatorial optimization one where the decision variables are buffer levels and times between preventive maintenance. To solve this problem, the extended great deluge algorithm is proposed. Illustrative numerical examples are presented to illustrate the model.