Computational experiments with stochastic models for the assembly-to-order system under demand uncertainty

Computational experiments with stochastic models for the assembly-to-order system under demand uncertainty We consider an assembly-to-order problem, whereby components must be manufactured under demand uncertainty, and end items are assembled only after the demand is realized, in order to maximize profit. We analyze the impact of problem features such as demand variability and skewness, number of specific versus common components, profit margin, and capacity tightness. In the first part of the work, we use a sampled scenario tree for the demand to build a two-stage stochastic linear programming model, the associated expected value problem, and a model based on linear decision rules. The performances of these models are investigated based on out-of-sample scenarios, assessing the value of the stochastic solution. We find that, for our problem instances, when uncertainty is modelled, a reasonably limited number of scenarios allows to significantly improve expected profit with respect to the deterministic model; however, the amount of improvement depends strongly on the problem features. We develop also robust counterparts of the precedent models and we analyze how expected profit and return are traded off against a reduction in risk, which is quantified by variability measures. Then, we extend our discussion to a multi-period setting and build a multi-stage stochastic linear programming model and a model based on decision rules. Here the focus is on both performance and computational issues, in the light of the exponential growth of complexity in multistage stochastic optimization. Results show that decision rules become a good alternative to the classical multi-stage stochastic linear problem when the horizon increases. Finally, following a dynamic programming logic, we look for a continuation value to be assigned to the not assembled components (final inventory) of the two-stage models which allows evaluating these models in the multi-stage framework. We compare this approach with a heuristic based on multi-stage decision rules and with a two-stage multi-period model. Results show that, in the end, all these approaches are almost equivalent in computational terms, while the heuristic seems to perform slightly worse in economic terms.