Prescriptive Fragility in Retail Multiproduct Pricing: When Well-Performing Demand Models Lead to Different Optimal Prices

This paper investigates whether demand models with comparable holdout predictive performance can induce materially different optimal prices in retail multiproduct pricing. A controlled daily dataset with three products over 18 weeks is used. For each product, linear-in-level and log-log demand specifications are estimated over 455 training samples formed by selecting 12 of the first 15 weeks; weeks 16--18 are reserved for holdout evaluation. Models are ranked within each product--family cell using MAE plus absolute bias, with RMSE as a secondary diagnostic. Retaining the five highest-ranked models from each family yields 30 product-level models and 1,000 admissible multiproduct demand systems. Each system is embedded in the same bounded nonlinear gross-margin pricing problem and solved through a multistart procedure.

The results reveal heterogeneous prescriptive fragility. The optimal price of product 1 spans the full feasible interval, from 24.291 to 37.389, with a standard deviation of 3.966. The price of product 2 reaches its upper bound in 815 systems, whereas the price of product 3 reaches its lower bound in all 1,000 systems. Optimal gross margin ranges from 2,000.042 to 2,473.025. A numerical diagnostic shows that dispersion across demand systems is substantially greater than variation across starting points within the same system.

Predictive screening therefore does not eliminate decision-relevant uncertainty. Prescriptive fragility is product-specific, and apparent price stability may reflect an active bound rather than genuine agreement among demand models. Demand models used for pricing should be evaluated not only by forecast accuracy, but also by the stability of the decisions they induce.