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We investigate the problem of choosing optimal lot sizes in assembly systems when component manufacturing or procurement yields, and possibly assembly yields, are random. For a single-period setting, we analyze two models. The first has components with identical yield distributions and costs, random demand and an imperfect assembly stage. We analyze this two-stage problem, and highlight the implications of the results for the single-stage case where the final product is just a set of good components. The second model is a single-stage system where components have non-identical yield distributions and costs. We analyze a two-component system with known demand, identify conditions for concavity, and derive the optimality conditions.
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