Data-Driven Modeling and Optimization of the Order Consolidation Problem in E-Warehousing

Abstract

We analyze data emanating from a major e-commerce warehouse and provided by a third-party warehouse logistics management company to replicate flow diagrams, assess order fulfillment efficiency, identify bottlenecks, and suggest improvement strategies. Without access to actual layouts and process-flow diagrams and purely based on data, we are able to describe the processes in detail and prescribe changes. By investigating the characteristics of orders, the wave-sorting operation, and the order-preparation process, we find that products from different orders are picked in batches for efficiency. Similar products are picked in small containers called totes. Totes are then stored in a buffer area and routed to be emptied of their contents at induction lines. Orders are then consolidated at the put wall, where each order is accumulated in a cubby. This order consolidation process depends on the sequence in which totes are processed and has a huge impact on order-completion time. We, therefore, present a generalization of the parallel machine–scheduling problem that we call the order consolidation problem to determine the tote-processing sequence that minimizes total order completion time. We provide mathematical formulations and devise heuristic and exact solution methods. We propose a fast simulated annealing metaheuristic and a branch-and-price approach in which the subproblems are variants of the single machine-scheduling problem and are solved using dynamic programming. We also devise a new branching rule, compare it against the literature, and test it on randomly generated and industry data. Applied to the data and the warehouse under study, optimizing the order consolidation is found to decrease the completion time of 75.66% of orders and achieve average improvements of up to 28.77% in order consolidation time and 21.92% in cubby usage.