A Two-Stage Stochastic Model for Distribution Logistics with Transshipment and Backordering: Stochastic Versus Deterministic Solutions

We present a two-stage stochastic program for a distribution logistic system with transshipment and backordering under stochastic demand and we first argue that it is NP-hard. Then, we perform a computational analysis based on a distribution network. In the case with two retailers, we show that modeling uncertainty with a stochastic program leads to better solutions with respect to the ones provided by the deterministic program, especially if limited recourse actions are admitted. Although there are special cases in which the deterministic and the stochastic solutions select the same retailers towards which sending items, in general, the deterministic solution cannot be upgraded in order to find the optimal solution of the stochastic program. Finally, in the case with four retailers, transshipment can provide more flexibility and better results.