Comparing Markov chains: aggregation and precedence relations applied to sets of states, with applications to assemble-to-order systems

A. Busic, Ingrid Vliegen, A. Scheller-Wolf

Research output: Contribution to journalArticleAcademicpeer-review

8 Citations (Scopus)

Abstract

Solving Markov chains is, in general, difficult if the state space of the chain is very large (or infinite) and lacking a simple repeating structure. One alternative to solving such chains is to construct models that are simple to analyze and provide bounds for a reward function of interest. We present a new bounding method for Markov chains inspired by Markov reward theory: Our method constructs bounds by redirecting selected sets of transitions, facilitating an intuitive interpretation of the modifications of the original system. We show that our method is compatible with strong aggregation of Markov chains; thus we can obtain bounds for an initial chain by analyzing a much smaller chain. We illustrate our method by using it to prove monotonicity results and bounds for assemble-to-order systems.
Original languageEnglish
Article number2
Pages (from-to)259-287
Number of pages37
JournalMathematics of operations research
Volume37
Issue number2
DOIs
Publication statusPublished - 2012

Keywords

  • METIS-286868
  • IR-80767

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