Pricing a Finite Inventory of Substitutable Products with Show-All Constraint

Maximizing Retail Revenue When Hiding Products Isn’t an Option Retailers often face a difficult balancing act: how to dynamically price a limited inventory of substitutable goods when business rules dictate that all available items must remain on display. Finding computationally tractable algorithms for pricing under this strict "show-all constraint" has remained an open problem. In "Pricing a Finite Inventory of Substitutable Products with Show-All Constraint," Vineet Goyal, Garud Iyengar, and Rajan Udwani solve this open problem within the large inventory regime. The authors successfully derive an asymptotically optimal pricing policy for the multinomial logit (MNL) choice model, proving that optimal product prices must monotonically increase over time. Furthermore, they provide a generalized approximation framework applicable to any weakly rational and monotone choice model. These findings offer practical algorithmic strategies for maximizing revenue while maintaining comprehensive product visibility.