Managing inventory with cash register information: Sales recorded but not demands

This study considers inventory systems where sales are recorded but unmet demand is unobserved. It develops a dynamic model that updates beliefs about inventory and demand using sales and stockout information and characterizes effective replenishment policies.

Alain Bensoussan, Metin Çakanyıldırım, Meng Li, Suresh P. Sethi (2016). Managing inventory with cash register information: Sales recorded but not demands. Production and Operations Management 25(1), 9–21.