Lot Sizing in Assembly Systems With Random Component Yields

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.