The routed inventory pooling problem with multiple lateral transshipments

We consider a single item, single-period inventory problem with two identical retailers who can pool stocks at multiple predetermined points in time. Since routing decisions are often taken at the multi-item level in practice, we use a predetermined route for redistribution at the single-item level. The objective is to determine order-up-to levels and transshipment decisions that minimise the sum of inventory holding, backorder and fixed as well as variable transshipment costs. We present a Dynamic Programming formulation to solve the problem and we compare the performance of our routed pooling policy to situations without pooling and with complete pooling in an extensive numerical study. The results reveal when routed pooling performs well and when multiple pooling moments provide significant benefits.