Optimal Allocation Problem in the Machine Repairman System with Heterogeneous Servers

A controllable repairman model consists of L machines subject to failures and two repair servers working at different speeds. The problem of optimal allocation of failed machines between the servers is examined. The optimal control policy is calculated versus cost structures. As a result the optimal...

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Bibliographic Details
Published inInformation Technologies and Mathematical Modelling Vol. 487; pp. 113 - 122
Main Authors Efrosinin, Dmitry, Spannring, Christopher, Sztrik, Janos
Format Book Chapter
LanguageEnglish
Published Switzerland Springer International Publishing AG 2014
Springer International Publishing
SeriesCommunications in Computer and Information Science
Subjects
dynamic-programming
hysteretic policy
Machine repairman system
Maths for computer scientists
optimal allocation
performance analysis
Probability & statistics
Systems analysis & design
threshold policy
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Summary:A controllable repairman model consists of L machines subject to failures and two repair servers working at different speeds. The problem of optimal allocation of failed machines between the servers is examined. The optimal control policy is calculated versus cost structures. As a result the optimal policy can be of threshold type, hysteretic type or have more complicated form. It is shown that the corresponding Markov process for hysteretic control policy belongs to the class of the Quasi-Birth-and-Death processes (QBD) with three diagonal block infinitesimal matrix. The stationary characteristics in this case are derived in matrix analytic form. Some numerical results are used to illustrate a number of features of the controlled model under study.
ISBN:9783319136707
3319136704
ISSN:1865-0929
1865-0937
DOI:10.1007/978-3-319-13671-4_14