Decentralized Online Order Fulfillment in Omni-Channel Retailers
Bibliographic record
Abstract
We consider an order fulfillment problem of an omni-channel retailer that ships online orders from its distribution center (DC) and brick-and-mortar stores. Stores use their local information, not observed by the retailer, that can lead them to accept or reject fulfillment requests of items in an online order. We investigate the problem of sequencing requests to stores and inventory rationing decisions at the DC to minimize expected costs under uncertain store acceptance behavior and when items are indistinguishable in terms of shipping. First, under the scenario that stores are used only when the DC has insufficient inventory, we propose a Markov Decision Process formulation and analyze the performance of myopic policies that are preferable because of their interpretability. We show that the performance rate of a myopic approach that orders stores by cost only depends on the number of items in an order, which is small in practice. We also determine conditions for the range of acceptance probabilities for the myopic policy to be optimal for small-sized orders. Using optimality conditions for a special case of the problem, we develop an adaptive variant of the myopic policy, and propose a new degree-based strategy that balances shipping costs and acceptance probabilities. Numerical testing suggests that the best-performing sequencing policy is within 1% of optimality on average. Moreover, using two years of data from a large omni-channel retailer in North America, we observe that adaptive policies, albeit more complex, are beneficial in reducing costs and split deliveries if acceptance rates can be estimated accurately. Second, we determine when the retailer should ship from stores or ration the inventory at the DC. We show that for single-item orders, the optimal policy has a threshold structure, where, remarkably, the highest priority region is also subject to rationing. We then consider the novel multi-unit-single-item rationing problem, and leverage the structure of the single-unit model to develop a heuristic. We numerically establish the efficacy of rationing models and our heuristic.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".