Constrained Inventory Optimization on Complex Warehouse Networks

Abstract

Online retailers increasingly face the problem of optimizing the inventory allocation of various products across a large network of warehouses. In most practical cases, the demand for these products is unknown, and product-level inventory available for distribution across the different warehouses is very limited.

We first consider the problem of inventory allocation of multiple products, across a network of warehouses. This is a problem commonly faced by large fashion e-retailers. The objective is to minimize the overall shipment cost and to speed up deliveries to customers accounting for inventory constraints on the various products and capacity constraints of warehouses. We propose a multi-period, multi-product newsvendor formulation as well as an efficient solution algorithm that balances the tradeoff between overage and underage costs across time periods. We also establish the rate of convergence of the algorithm. Furthermore, and in collaboration with a fashion e-tailer, we perform a case study showing a reduction of 9% in inventory costs relative to the retailer’s current method.

We then turn our attention to inventory optimization across a network with cross-fulfillment. Optimizing this problem in such networks is an intractable problem. We resolve this by introducing a tractable algorithm. We introduce the concept of Fulfillment Rules in order to capture the fulfillment priorities of the retailer while at the same time allowing for a tractable approach to the inventory allocation problem that works for both continuous and discrete demand distributions.

In the final chapter of the thesis, we tackle the issue of high dimensional data in the context of classification settings. We develop a new dimensionality reduction algorithm called Supervised Approach for Feature Engineering (SAFE), which is an alternative to Principal Component Analysis (PCA). SAFE finds uncorrelated, lower dimensional features in order to best explain differences among classes. This allows us to improve the speed and accuracy of the classification task.