# Case Study Results

This directory contains the outputs for the Case Study (Section 5), including estimation results (Table 2) and optimization plots (Figures 1-5).

## Important Note on Data Source
Due to confidentiality agreements with the company we collaborated with, **we cannot release the raw transaction data** used in the paper. 

Instead, this replication script utilizes a **Synthetic Dataset**. This dataset was generated to mimic the structure of the original data but contains simulated consumer choices based on a choice model with **history-dependent effects** estimated using the original data. Specifically, we selected one month of assortment data (25 workdays) to generate synthetic data, maintaining a repeat customer ratio consistent with the original data. The choices were simulated using our $M=3$ model.

Consequently, the synthetic data differs from the real data in three key ways: it covers only 34 products over one month (vs. 53 products over six months), has lower price variation due to the shorter time window, and contains strictly i.i.d. Gumbel noise rather than the richer unobserved heterogeneity present in real-world data.


## Expected Differences from the Paper
Because the input data differs from that used in the paper, the estimation results and optimal solutions will naturally differ. Below is a guide on what differences to expect and why they occur.

### 1. Estimation Results (Table 2)
* **Estimators:** You may observe minor differences between the estimators obtained from our replication and those reported in the original paper due to data differences. 
*   **Chi-Square & Log-Likelihood:** You may observe **smaller Chi-square values and larger log-likelihood values** (better fit) and **larger improvement percentages** compared to the paper. Since the synthetic data contains cleaner, stronger satiation effects, our model recovers the underlying choice structure more accurately on synthetic data, yielding larger improvements (19%–44%) than on real data (4%–5%), where noise and model misspecification naturally dampen gains.
* **Variance of Estimators** The larger standard deviation of the estimated price sensitivity parameter ($\theta$) is likely due to differences between the original and synthetic datasets, including the smaller number of products and narrower range of normalized prices in the synthetic data. Since MNL/logit standard errors depend on many aspects of the data (e.g., choice probability, offering sets), we view this difference as a consequence of using synthetic rather than original transaction data.


### 2. Optimization Results (Figures 1 & 2)
*   **Normalized Revenue:** In Figure 1 (Left Panel), our model and the MNL model may exhibit **higher normalized revenue**  than in the paper. The "Normalized Revenue" is calculated relative to a "Practice Menu" benchmark. This benchmark was derived from historical practice. On this specific synthetic dataset with strong satiation effects, the benchmark performs poorly. A lower benchmark revenue leads to a higher normalized ratio for our model and the MNL model.
*   **Optimal Assortment Size:** You may observe different optimal sizes. Different estimators (from Table 2) lead to a different optimal solution structure.  

### 3. Assortment Structures (Figure 4)
*   **Menu Composition:** The specific products included in the optimal menus (Plots a-d) and the specific attraction values (Plot f) will differ from those in the paper. However, the **general trend** and the comparative performance (Figure 5) between models remain consistent with the paper's conclusions.