A best-choice problem for a production system which deteriorates at a disorder time (Q2762678)

The paper is devoted to a model of production systems. A controller observes output of a production system one by one sequentially over time. If the system is in the `good' state during one period, there is a constant probability that it will deteriorate and be in the `bad' state during the next period. When system reaches the `bad' state it remains there. The true state of the system is unknown and can only be inferred from the observed quality of output. The distribution of the quality of the output \(X\) in each state is given. Two available actions are `Continue' or `Stop' production. The objective is to maximize the expected net value of the output \(X_\tau\) at the stopping time \(\tau\) under assumption that horizon \(n\) is finite. NEWLINENEWLINENEWLINEIt is shown that for uniform distributions of observations the optimal policy is of control-limit type. The optimal expected net value for the problem becomes larger as the decision maker's opinion, that the unknown true state of the system is \(0\), increases. The model discussed in the paper has many applications and it is closely related to those considered by \textit{A. Grosfeld-Nir} [Oper. Res. 44, 458-463 (1996; Zbl 0864.90052)] and \textit{M. Sakaguchi} [Math. Jap. 51, 471-478 2000; Zbl 0964.62083)].