The theory of semi-Markov decision processes was used for the mathematical description and solution of the problem. A model of a decision-making process over an infinite time horizon was used.1. INTRODUCTION
Semi-Markov decision (controlled) processes constitute a convenient mathematical apparatus for formulating and solving decision-making problems related to the operation of objects.
The literature on semi-Markov decision processes is extensive. Key works include those by Jewell [6], Howard [5], Mine and Osaki [9], and Gercbakh [2]. Semi-Markov decision processes were also discussed in [3].
A semi-Markov decision process is an SM process { X (t ) : t ≥ 0} whose realization depends on decisions made at the initial moment
τ 1 ,…,τ n ,… .
The decision at the moment
τn, when
τ
and at the moments of state changes
X (τ n ) = i , is denoted by the symbol d i (τ n ) .
We assume that the set of decisions in each state i is finite. We denote this set by the symbol Di . (…)
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Source: Logistyka Magazine