Inventory Management under Storage and Order Restrictions
Bibliographic record
Abstract
Inventory management in most practical settings faces challenges due to various restrictions on storage and replenishment of products. These restrictions may be posed by budget availability, different production/supply schedules for different products, and limited storage space shared by a number of products—very common in retail, food, and the pharmaceutical industry. Motivated by this, we investigate in this study how simultaneous restrictions on shared storage capacity and product‐specific order capacities impact optimal replenishments in a multi‐product system. We formulate the inventory replenishment problem as a multi‐period stochastic dynamic program, where products face stochastic demand with general distributions and excess demand is lost or fulfilled by emergency orders. We first fully characterize the optimal replenishment policy for two‐product systems, and provide a methodology to compute optimal replenishment quantities, which can be described as a dynamic priority‐based replenishment rule. Our results show that for each product, the optimal replenishment priority as well as quantity depends on the inventory levels of both products and all available capacities. More interestingly, the results show that capacity restrictions can flip the stocking priorities of products. Based on the optimal policy for two‐product systems, we develop a heuristic for multi‐product systems whose complexity scales linearly with the number of products. Under moderate storage capacities, our heuristic significantly outperforms the naive heuristics that ignore dynamic priority assignment, and closely captures the benefits of the optimal policy for systems with large number of products.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 teacher head, 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".