Abstract
The paper addresses the optimal production control problems for an unreliable manufacturing system that produces items that can be regarded as conforming or non conforming. Two cases ares considered: (i) The ratio between conforming and non conforming parts is fixed at all times, (ii) the production of defective parts is respectively initiated and stopped at the random entrance times to and departure times from a defective production state. Case (i) is treated as an extension of the Bielecki-Kumar single machine optimality theory, while a new stochastic hybrid-state Markovian model is introduced to analyze case (ii). The intricate piecewise deterministic dynamics of the model are studied, and the associated Kolmogorov equations are developed under the suboptimal class of hedging policies.
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