The Value of the Stochastic Solution in a Two-Stage Assembly-to-Order Problem

We consider a simple assembly to order problem, where components must be manufactured under demand uncertainty and end items are assembled only after demand is realized. The problem can be naturally cast as a two-stage stochastic linear program with recourse, and possibly generalized to multiple stages. We investigate the two-stage case not only because it make sense, e.g., in specific newsvendor-like applications, but also because it allows a thorough investigation of relevant issues. In this paper we investigate the conditions under which using a stochastic programming approach yields significant advantages over a straightforward deterministic model based on the expected value of demand. The analysis is carried out on the basis of a large number of out-of-sample scenarios, assessing the so-called value of the stochastic solution. We study the impact of problem features such as demand variability, skewness and multimodality, number of specific components, profit margin, and capacity tightness. Furthermore, we compare the behavior of standard two-stage stochastic programming against linear decision rules.