Properties of the multiple lot-sizing problem with rigid demands and general yield distributions

We study the structural properties of the multiple lot-sizing problem with a rigid demand and a generally distributed yield. This problem arises in unreliable production systems and is formulated as a stochastic dynamic program. We obtain partial characterizations of the optimal cost function and the optimal run size, and show that the monotonicity of the optimal run size is related to the monotonicity of a conditional yield distribution. We also consider the computational aspect for solving the multiple lot-sizing problem and provide upper bounds on the optimal cost and optimal run size, which are used to reduce the search ranges in a numerical solution procedure.