Promotion Optimization for Multiple Items in Supermarkets
Bibliographic record
Abstract
Promotions are a critical decision for supermarket managers, who must decide the price promotions for a large number of items. Retailers often use promotions to boost the sales of the different items by leveraging the cross-item effects. We formulate the promotion optimization problem for multiple items as a nonlinear integer program. Our formulation includes several business rules as constraints. Our demand models can be estimated from data and capture the postpromotion dip effect and cross-item effects (substitution and complementarity). Because demand functions are typically nonlinear, the exact formulation is intractable. To address this issue, we propose a general class of integer programming approximations. For demand models with additive cross-item effects, we prove that it is sufficient to account for unilateral and pairwise contributions and derive parametric bounds on the performance of the approximation. We also show that the unconstrained problem can be solved efficiently via a linear program when items are substitutable and the price set has two values. For more general cases, we develop efficient rounding schemes to obtain an integer solution. We conclude by testing our method on realistic instances and convey the potential practical impact for retailers. This paper was accepted by Yinyu Ye, optimization.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 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".