Data-Driven Modeling and Optimization of the Order Consolidation Problem in E-Warehousing
Bibliographic record
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".