Rolling horizon policies for multi-stage stochastic assemble-to-order problems

Assemble-to-order production approaches deal with randomness in the demand for end items by producing components under uncertainty, but assembling them only after demand is observed. Such planning problems can be tackled by stochastic programming, but true multistage models are computationally challenging and few studies apply them to production planning. Solutions based on two-stage models are often short-sighted and unable to effectively deal with non-stationary demand. A further complication may be the scarcity of available data, especially in the case of correlated distributions and seasonal patterns. In this paper, we compare different scenario tree structures. In particular, we enrich a two-stage formulation by introducing a piecewise linear approximation of the value of the terminal inventory, to mitigate the two-stage myopic behavior. We compare the out-of-sample performance of the resulting models by rolling horizon simulations, within a data-driven setting, characterized by seasonality, bimodality, and correlations in the distribution of end item demand. Computational experiments suggest the potential benefit of adding a terminal value function and illustrate interesting patterns arising from demand correlations and the level of manufacturing capacity available. An open-source library for multistage ATO problems is available for the replication of experiments and further extensions.