Borrowing Strength Across Stores: Transfer Learning for Choice-Based Revenue Management
Authors: Recep Yusuf Bekci, Stefanus Jasin, Joline Uichanco
Organizations: Department of Management Science and Engineering, University of Waterloo, Waterloo, Ontario, Canada · Stephen M. Ross School of Business, University of Michigan, Ann Arbor, Michigan, USA · Department of Technology Management and Innovation, Tandon School of Engineering, New York University, Brooklyn, New York, USA
Large retail chains must tailor assortment and pricing decisions to local customer preferences, yet even retailers with extensive sales records often have limited data for estimating demand at the store or local market level, particularly in product categories with short selling windows. Local estimation (fitting a demand model for each store on its own) can therefore be unreliable, while pooling data across stores improves estimation precision at the cost of ignoring local demand heterogeneity. We study how retailers can balance these competing effects through transfer learning under a multinomial logit (MNL) demand model. We propose a shrinkage estimator that combines store-specific demand estimates with information pooled from other stores. Unlike the linear or quadratic settings underlying much of the existing theoretical literature on information transfer in operations, the nonlinear MNL likelihood does not admit a straightforward bias-variance decomposition. By exploiting its self-concordant-like properties, we establish finite-sample performance guarantees that characterize when information transfer improves demand estimation and how the appropriate degree of shrinkage depends on local sample size, feature dimensionality, and cross-store heterogeneity. We further derive regret bounds for downstream assortment and pricing decisions. Numerical experiments demonstrate the operational benefits of shrinkage across different data environments. An empirical study using data from several hundred stores of a European apparel retailer shows that shrinkage improves out-of-sample product prioritization and revenue capture relative to both local estimation and full pooling. Our findings demonstrate how retailers can leverage information across their store networks to improve revenue management decisions while preserving local demand differences.
Figures & tables
Figure 1: Reduction in expected excess risk that Theorem 5.5 guarantees for shrinkage relative to local estimation, over cross-store heterogeneity Δ and the local sample ratio nk/d . Blue marks where shrinkage is guaranteed to improve on local estimation, and red where the bound gives no such guarantee.
Figure 2: Percentage Regret for assortment (left) and pricing (right) decisions as cross-store heterogeneity Δ varies.
Figure 3: Percentage regret for assortment (left) and pricing (right) decisions as the local sample size nk varies.
Category
# Stores
# Products
Total Observations
Total Units Sold
Blazers
365
790
622,642
173,471
Dresses
371
4,182
1,669,206
781,011
Leggings
361
255
193,958
79,181
Trousers
372
3,394
1,552,620
614,147
T-shirts
375
3,984
2,783,502
1,894,169
Table 1: Dataset dimensions by product category.
Category
Avg. # products per store
Avg. assortment size per store-week
Avg. units sold per store-week
Blazers
178.7
9.7
4.7
Dresses
493.9
39.2
24.9
Leggings
48.8
5.5
3.8
Trousers
447.5
31.4
18.6
T-shirts
754.5
101.9
69.6
Table 2: Average store- and store-week-level scale by category.
Figure 4: Out-of-sample revenue capture across the five apparel categories, evaluated at a m=20% budget constraint. Store-level predictive performance is disaggregated by historical sales volume into Lower Volume stores (left), Medium Volume stores (center), and Higher Volume stores (right). Error bars represent standard errors.
Δstore vs. Store MLE
Δpool vs. Pooled MLE
Group
Mean lift (pp)
95% CI
Win rate
Mean lift (pp)
95% CI
Win rate
Overall
2.64
[2.17, 3.10]
86.6%
3.11
[2.55, 3.68]
83.6%
Category: Blazers
1.59
[-0.04, 3.20]
91.0%
4.21
[2.85, 5.58]
93.2%
Category: Dresses
1.44
[1.00, 1.95]
85.4%
3.13
[1.98, 4.23]
80.7%
Category: Leggings
7.53
[5.69, 9.66]
93.9%
4.15
[2.46, 5.81]
94.3%
Category: Trousers
2.48
[1.66, 3.27]
85.3%
2.41
[1.37, 3.39]
82.2%
Table 3: Mean lift from Shrinkage CV at m=20% . Lifts are reported in percentage points. Confidence intervals are clustered-bootstrap intervals resampling stores, and win rates report the fraction of store-weeks in which Shrinkage CV outperforms the corresponding benchmark.
Figure 5: Revenue capture by product category and local-information tercile at display budget m=10% .
Figure 6: Revenue capture by product category and local-information tercile at display budget m=30% .
Figure 7: Validation-selected shrinkage weights by category and local-information bucket.
Figure 8: Sensitivity of assortment (left) and pricing (right) regret to the number of nonprice features d−2 . In this sweep, nonprice features are rescaled by 1/d−2 so that the variance of the linear predictor remains approximately constant as dimension grows. The heterogeneity radius Δ is held fixed, so increasing d spreads a fixed amount of cross-store mismatch over more coordinates.