Lead Time Independent Joint Inventory and Pricing Control for Lost Sales System with Poisson Demand

We consider the problem of joint inventory and pricing control in a finite-horizon setting with Poisson demand, positive lead time, and lost sales. We study the performance of a lead time independent heuristic control, which we call Dynamic Batch Pricing (DBP), and show that it is asymptotically optimal when the annual expected demand is large. Moreover, with a proper tuning of the control parameters, we also show that DBP has a robust performance with respect to the magnitude of lost sales cost, which is important in applications such as retails where the targeted service level is very high (equivalently, the lost sales cost is very large). Our result for the lost sales system complements the recent result of Chen et al. (2019), who show that a lead time independent heuristic can be near optimal in the backorder system with a large lead time. Together, both our result and Chen et al. (2019) reinforce the message that simple lead time independent heuristics can perform sufficiently well, at least in some practically relevant cases if not in all cases. This insight is important given that the task of solving the joint inventory and pricing problem (under either backorder or lost sales system) with positive lead time for the most general model remains very challenging