Supplement to 'A Simple Heuristic Policy for Stochastic Distribution Inventory Systems with Fixed Shipment Costs'

As a supplement to Zhu et al. (2020), this document consists of five parts. First, it provides technical proofs of some theoretical results in Zhu et al. (2020). Second, it introduces some preliminary results on stochastic distribution systems with fixed shipment costs. Third, it provides some examples and illustrations on the modified echelon (r,Q) policies (and some related concepts) studied in Zhu et al. (2020). Fourth, it presents some explicit performance bounds that depends on system primitives for the modified echelon (r,Q) policies in stochastic distribution systems. Finally, extensive numerical experiments are conducted to test the effectiveness of the modified echelon (r,Q) policies. Specifically, the numerical studies show that the modified echelon (r,Q) policies perform well with an average gap of about 5% above the cost lower bound, 2) outperform the echelon-stock (r, Q) policy used in Chen and Zheng (1997), and 3) have robust performances with respect to the allocation rule at the warehouse.