Large-scale optimization in online-retail inventory management

Abstract

This thesis studies the related decisions of inventory placement and inventory replenishment in online retail. The placement decision focuses on the selection of fulfillment centers in which to place items, while the replenishment decision concerns the amount of inventory to order for each item. In contrast with traditional retail, a distinctive feature of online retail is the flexibility to ship items to customers from different fulfillment centers. This creates interdependence between fulfillment centers and poses new challenges in inventory management. The placement decision can be formulated as a mixed-integer program. The objective is to minimize the sum of outbound shipping and fixed costs for all the items, while satisfying demand and capacity constraints. The large scale of the problem is due to the size of the fulfillment center network and the number of items. We propose a large-scale solution scheme that aggregates the items, solves a column-based reformulation of the aggregated problem using column generation, and then disaggregates the solution into placement plans for the individual items. The replenishment decision for a single item can be formulated as a dynamic program, in which the objective is to minimize the long-term average of outbound shipping, stockout and holding costs. Its scale and complexity arises from demand stochasticity, inventory dynamics, non-identical fulfillment center lead times, and the integrality of inventory units. We propose approximation schemes that employ simulation to evaluate and optimize parameterized policies. In particular, we design the simulation to estimate gradient-like information, and use the information to enhance the efficiency a random search method. For both problems, realistic numerical examples demonstrate that the large-scale optimization methods produce low-cost solutions in a relatively short amount of time, compared to simple heuristics that do not involve much optimization. We also study the properties of solutions in order to obtain managerial insights on the impact of key factors, including cost parameters, capacity constraints, and lead times.