We consider lot sizing policies in multi-stage serial production systems with machines prone to failure. The production rates are finite; failure and restoration of unreliable machines follow some stochastic processes with known probability distributions. The total production cost includes order or procurement cost, machine setup cost, restoration cost, and inventory carrying costs for raw material, Work-In-Process (WIP), and finished product. The expected production cost per unit time is minimized by stochastic models. The contributions of this paper are twofold. We analyze the general model for the two-stage lot sizing problem; and analytic formulae are derived for the special production structure. It has been shown that lot sizing policies in the unreliable systems can be smaller or larger than the ones in the classical model. Numerical experiments also indicate that lot sizing decisions in these systems can be counterintuitive, due to the interaction of machine breakdown and repair, and inventory carrying effects. Computational findings also give insight for the operational planning and control of unreliable production systems.
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