Item Aggregation and Column Generation for Online-Retail Inventory Placement

Problem definition: This paper studies an online retailer’s problem of choosing fulfillment centers in which to place items. We formulate the problem as a mixed-integer program that models thousands or millions of items to be placed in dozens of fulfillment centers and shipped to dozens of customer regions. The objective is to minimize the sum of shipping and fixed costs over one planning period. Academic/practical relevance: A good placement plan can significantly reduce the operational cost, which is crucial for online-retail businesses because they often have a low profit margin. The placement problem can be difficult to solve with existing techniques or off-the-shelf software because of the large number of items and the fulfillment center fixed costs and capacity constraints. Methodology: We propose a large-scale optimization framework that aggregates items into clusters, solves the cluster-level problem with column generation, and disaggregates the solution into item-level placement plans. We develop an a priori bound on the optimality gap, and we also apply the framework to a numerical example that consists of 1,000,000 items. Results: The a priori bound provides insights on how to select the appropriate aggregation criteria. For the numerical example, our framework produces a near-optimal solution in a few hours, significantly outperforming a sequential placement heuristic that approximates the status quo. Managerial implications: Our study provides a computationally efficient approach for solving online-retail inventory placement as well as similar large-scale optimization problems in practice.