## Abstract

We study the following fundamental joint pricing and inventory management problem. We consider an infinite horizon, continuous review, stochastic inventory system. Demand arrives according to a Poisson process, where the customers purchase only if their valuation exceeds the current price. The seller can replenish inventory for a fixed cost, and also incurs holding and backlogging costs. The optimal policy to maximize profit under this setting is known to be an (s, S, 𝒑) policy: when the inventory level drops to s units, the seller immediately places an order to replenish the inventory to S units. Specifically, the optimal pricing policy 𝒑 has a different price for every inventory state. However, such inventory-based pricing policies are difficult to implement for sellers and may lead to strategic customer behavior or perceptions of unfairness. In this work, we prove that simple policies where only a small number of prices are offered are near-optimal, compared to the optimal policy which requires S-s prices.

We first consider the case where customer valuations follow a monotone hazard rate (MHR) distribution. When no backlogging is allowed (lost sales model) we show that there exists a static, single price policy that garners at least as much revenue as the optimal dynamic policy while incurring at most √ (1+㏑ S) times the cost of the optimal dynamic policy. For the classic case where valuations are uniform (linear demand), we improve the cost ratio to 1.225. When backlogging is allowed, we show that a three price policy can be used to achieve similar guarantees. In numerical experiments, we show that our simple policies capture a large fraction of the profit in most cases, with the performance improving as the profit margin increases.

We first consider the case where customer valuations follow a monotone hazard rate (MHR) distribution. When no backlogging is allowed (lost sales model) we show that there exists a static, single price policy that garners at least as much revenue as the optimal dynamic policy while incurring at most √ (1+㏑ S) times the cost of the optimal dynamic policy. For the classic case where valuations are uniform (linear demand), we improve the cost ratio to 1.225. When backlogging is allowed, we show that a three price policy can be used to achieve similar guarantees. In numerical experiments, we show that our simple policies capture a large fraction of the profit in most cases, with the performance improving as the profit margin increases.

Original language | English |
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DOIs | |

Publication status | E-pub ahead of print - 16 Jun 2023 |

Externally published | Yes |