Inventory replenishment planning of a distribution system with storage capacity constraints and multi-channel order fulfilment

Abstract

In this paper, an inventory replenishment planning problem in a two-echelon distribution system of Alibaba with a central distribution centre (CDC) and multiple front distribution centers (FDCs) is studied. In the system, the CDC replenishes its inventories of multiple products from external suppliers, while each FDC replenishes its inventories of the products from the CDC. These products are jointly replenished at each stock. This problem arises when Alibaba prepares its annual “double 11” promotion. Facing stochastic demands of the products in the promotion period, the objective of the problem is to optimally determine the inventory replenishment quantities of the products for each stock before the promotion so that the expected total profit of the system is maximized, subject to the storage capacity constraint of each stock. During the promotion, customer orders may be fulfilled through multiple channels, that is, a customer order may be fulfilled by its local FDC, other FDCs, or the CDC. This stochastic optimization problem is formulated as a convex nonlinear programming model and solved optimally by a piecewise linear approximation approach. The effectiveness of the model and the approach is demonstrated by numerical experiments on instances generated based on data of Alibaba. The results show that our model can lead to a significantly higher expected total profit compared with a deterministic planning model.