Inventory Allocation Under the Greedy Fulfillment Policy: The (Potential) Perils of the Hindsight Approach
Bibliographic record
Abstract
We study the inventory allocation problem for an online retailer with multiple warehouses and geographically dispersed demand. The retailer fulfills customer orders using a greedy policy (i.e., ship from the cheapest available warehouse), and determines inventory allocation using the widely adopted hindsight or stochastic programming approach. While this approach is popular in both academia and practice, its limitations remain poorly understood. We show that the hindsight solution coincides with the optimal allocation under the greedy policy, but for a misspecified demand sequence that assumes an overly optimistic realization. This optimism can sometimes be harmless, but it can also lead to substantial inefficiencies. In particular, we identify three conditions under which the hindsight solution is asymptotically optimal as the lost-sales cost becomes large: (i) identical ordering costs across warehouses, (ii) unbounded warehouse capacities, and (iii) independence of demand across locations. Violating any of these may cause the hindsight solution to perform arbitrarily worse than the true optimum under the greedy policy. Surprisingly, we further show that even if the retailer were to pair the hindsight-based allocation with the best-possible fulfillment policy (not necessarily greedy), the resulting total cost can still be arbitrarily suboptimal. The significant sub-optimality extends beyond the asymptotic limiting regime. These findings reveal fundamental limitations of the hindsight approach and highlight the need for more robust allocation strategies in practice.
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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 | 0.018 | 0.038 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".