Optimal Joint Replenishment and Transshipment Policies in a Multi-Period Inventory System with Lost Sales
Bibliographic record
Abstract
Mismatch between supply and demand when the uncertainty of the demand is high and the supply lead time is relatively long, such as seasonal good markets, can result in high overstocking and understocking costs. In this paper we propose transshipment as a powerful mechanism to mitigate the mismatch between the supply and demand. We consider a finite horizon multi-period inventory system where in each period two retailers have the option to replenish their inventory from a supplier (if there is any supply) or via transshipment from the other retailer. Each retailer observes nonnegative stochastic demand with general distribution in each period and incurs overstocking/understocking costs as well as costs for replenishment and transshipment that may be time dependent. We study a stochastic control problem where the objective is to determine the optimal joint replenishment and transshipment policies so as to minimize the total expected cost over the season. We characterize the structure of the optimal policy and show that unlike the known order-up-to level inventory policy, the optimal ordering policy in each period is determined based on two switching curves. Similarly, the optimal transshipment policy is also identified by two switching curves. These four curves together partition the optimal joint ordering and transshipment polices to eight regions where in each region the optimal policy is an order-up-to-curve policy. We demonstrate that the structure of the optimal policy holds for any known sequence and combination of ordering and transshipment over time.
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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) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 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".