A Kronecker Algebra Formulation for Markov Activity Networks with Phase-Type Distributions

Alessio Angius, András Horváth and Marcello Urgo
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Alessio Angius: Enerbrain, 10132 Turin, Italy
András Horváth: Computer Science Department, University of Turin, 10149 Turin, Italy
Marcello Urgo: Mechanical Engineering Department, Polytechnic University of Milan, 20133 Milan, Italy

Mathematics, 2021, vol. 9, issue 12, 1-22

Abstract: The application of theoretical scheduling approaches to the real world quite often crashes into the need to cope with uncertain events and incomplete information. Stochastic scheduling approaches exploiting Markov models have been proposed for this class of problems with the limitation to exponential durations. Phase-type approximations provide a tool to overcome this limitation. This paper proposes a general approach for using phase-type distributions to model the execution of a network of activities with generally distributed durations through a Markov chain. An analytical representation of the infinitesimal generator of the Markov chain in terms of Kronecker algebra is proposed, providing a general formulation for this class of problems and supporting more efficient computation methods. This entails the capability to address stochastic scheduling in terms of the estimation of the distribution of common objective functions (i.e., makespan, lateness), enabling the use of risk measures to address robustness.

Keywords: stochastic makespan; markov activity network; phase-type distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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