Stochastic optimization models with substitution as a result of price differences and stockouts
Bibliographic record
Abstract
Abstract Many firms produce a variety of products that are subject to demand uncertainty and are substitutable by customers where the potential for product substitution affects the firm's pricing and production decisions. Two common reasons for product substitution are stockouts (or inventory‐driven substitution), when a customer will substitute a product that is out of stock with a similar product, and price‐driven substitution where customers respond to price differences by substituting a lower priced product for a similar but higher priced product. In this paper, we include the potential for demand to move from one product or market segment to another into the demand model of the firm and present a series of single‐period stochastic models for finding optimal solutions for production quantity and product prices separately, as well as investigating the joint pricing and production decision model. We derive the optimal solution with and without a total production capacity limit and consider both inventory‐driven and price‐driven substitutions. We investigate how the firm should modify pricing and production decisions to take into account both price‐driven and inventory‐driven substitution and examine changes in the optimal prices and supply quantities with and without an aggregate supply limit. Our results demonstrate that both forms of substitution provide a revenue or profit opportunity if the firm is able to recognize the potential for substitution and respond in advance using an optimal pricing and/or ordering strategy. The contribution of this research is to present theoretical results that demonstrate the value of more complex demand models that include the possibility of stockouts and customer “leakage” from higher priced market segments to lower priced segments. Insights derived from these models lead to modified pricing and ordering strategies that will increase firm revenues and/or profitability.
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.003 | 0.002 |
| 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".