Leveraging the Newsvendor for Inventory Distribution at a Large Fashion E-Retailer With Depth and Capacity Constraints

Abstract

Problem definition:We consider the problem of inventory allocation of multiple products, across a network of warehouses, faced by a large fashion e-retailer. The objective is to minimize overall shipment costs and to speed up deliveries to customers accounting for inventory constraints on products and capacity constraints of warehouses.

Academic / Practical Relevance: Online retailers increasingly face the problem of optimizing inventory allocation for a wide variety of products, across a large network of warehouses. In most practical cases, demand of these products is unknown, and product level inventory available for distribution across the warehouses is very limited. Nevertheless, to the best of our knowledge, inventory allocation with both capacity and depth constraints has not been previously studied.

Methodology: We formulate the inventory allocation problem as a Multi-Product, Multi-Warehouse Newsvendor (MPMWN) problem that balances overage and underage costs across products and warehouses. We then use Lagrangian duality to propose an efficient allocation algorithm (Optimal Distribution Algorithm (ODA)). ODA breaks the central MPMWN problem into two subproblems with either depth or capacity constraints. We show that these subproblems can be efficiently solved using binary search, due to the separability of the objective function and monotonicity of the constraints with respect to the dual variables.

Results: Analytically, we show that the inventory allocation from the proposed algorithm converges to the optimal solution of the MPMWN problem. Furthermore, we analyze the rate of convergence of the algorithm to show fast convergence. Numerically, in collaboration with a large fashion retailer, we perform a large-scale real data study to show that the proposed algorithm, combined with a state-of-the-art demand prediction method can reduce inventory costs by as much as 7% and increase In-Class-Fulfillment (ICF) up to 10%. This improvement is also robust to changes in the demand distribution and the overage to underage cost ratio. Hence, the proposed method leads to considerable cost reduction and service improvement, both very important for the retailer.

Managerial Implications: E-Retailers increasingly face the task of managing a very wide variety of products across a large network. Adding both capacity and depth constraints to the classical newsvendor problem poses computational challenges that make the current inventory optimization methods either impractical or inapplicable. We solve this problem by proposing an efficient and practical algorithm that combines transaction data for efficient inventory allocation.

Keywords: Newsvendor problem, Inventory Management, Data-Driven Operations