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A branch and bound algorithm for computing optimal replacement policies in consecutive k ‐out‐of‐ n ‐systems
Author(s) -
Flynn James,
Chung ChiaShin
Publication year - 2002
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/nav.10017
Subject(s) - component (thermodynamics) , computer science , branch and bound , set (abstract data type) , binary number , algorithm , function (biology) , mathematical optimization , time horizon , upper and lower bounds , dynamic programming , mathematics , arithmetic , mathematical analysis , physics , evolutionary biology , biology , thermodynamics , programming language
This paper presents a branch and bound algorithm for computing optimal replacement policies in a discrete‐time, infinite‐horizon, dynamic programming model of a binary coherent system with n statistically independent components, and then specializes the algorithm to consecutive k ‐out‐of‐ n systems. The objective is to minimize the long‐run expected average undiscounted cost per period. (Costs arise when the system fails and when failed components are replaced.) An earlier paper established the optimality of following a critical component policy (CCP), i.e., a policy specified by a critical component set and the rule: Replace a component if and only if it is failed and in the critical component set. Computing an optimal CCP is a optimization problem with n binary variables and a nonlinear objective function. Our branch and bound algorithm for solving this problem has memory storage requirement O ( n ) for consecutive k ‐out‐of‐ n systems. Extensive computational experiments on such systems involving over 350,000 test problems with n ranging from 10 to 150 find this algorithm to be effective when n ≤ 40 or k is near n . © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 288–302, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10017

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