Inventory Models for Substitutable Products: Optimal Policies and Heuristics
Bibliographic record
Abstract
In this paper, we examine the nature of optimal inventory policies in a system where a retailer manages substitutable products. We first consider a system with two products 1 and 2 whose total demand is D and individual demands are negatively correlated. A fixed proportion of the unsatisfied customers for an item will purchase the other item if it is available in inventory. For the single-period case, we show that the optimal inventory levels of the two items can be computed easily and follow what we refer to as “partially decoupled” policies, i.e., base stock policies that are not state dependent, in certain critical regions of interest both when D is known and random. Furthermore, we show that such a partially decoupled base-stock policy is optimal even in a multiperiod version of the problem for known D for a wide range of parameter values and in an N-product single-period model under some restrictive conditions. Using a numerical study, we show that heuristics based on the decoupled inventory policy perform well in conditions more general than the ones assumed to obtain the analytical results. The analytical and numerical results suggest that the approach presented here is most valuable in retail settings for product categories where the level of substitution between items in a category is not high, demand variation at the aggregate level is not high, and service levels or newsvendor ratios are high.
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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 | 0.006 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".