Joint pricing and inventory control with a Markovian demand model

Abstract

We consider the joint pricing and inventory control problem for a single product with a finite horizon and periodic review. The demand distribution in each period is determined by an exogenous Markov chain. Pricing and ordering decisions are made at the beginning of each period and all shortages are backlogged. The surplus costs as well as fixed and variable costs are state dependent. We show the existence of an optimal (s, S, p)-type feedback policy for the additive demand model. We extend the model to the case of emergency orders and also incorporate capacity and service level constraints. We compute the optimal policy for a class of Markovian demand and illustrate the benefits of dynamic pricing over fixed pricing strategies through numerical examples. The results indicate that it is more beneficial to implement the dynamic pricing strategy in a Markovian demand environment with a high fixed ordering cost or with high demand uncertainty.

Low price guarantee in inventory systems coordinated with pricing strategy

“…There exist some literature on the optimality of (s,S)-type policy. Yin and Rajaram (2005) extend the results of Chen and Simchi-Levi (2004a) to Markovian environments. Polatoglu and Sahin (2000) consider a model with lost sales.…”

Dynamic pricing in the newsvendor problem with yield risks

“…Research in pricing policy can also be categorised into various demand methods (Yin and Rajaram, 2007).…”

Continuous (s, S) policy with MMPP correlated demand

“…In addition, Lee and Chew (2005) consider a dynamic replenishment policy for different products that are auto-correlated but independent of each other. In the context of correlated Markovian demand, Yin and Rajaram (2007) consider a setting where pricing and ordering decisions are made at the start of each period, and they illustrate the benefits of dynamic pricing. None of these works consider the effect of correlation on the performance of different (heuristic and optimal) ordering policies under MMPP demand, as we do in this paper.…”

“…The literature on (s, S) policies with fluctuating demand assumes periodic review and utilizes a dynamic programming approach to obtain the optimal policy, Yin and Rajaram (2007), Sethi and Cheng (1997). Yin and Rajaram (2007) consider a periodic review model over a finite time horizon.…”

“…Yin and Rajaram (2007) consider a periodic review model over a finite time horizon. Sethi and Cheng (1997) consider periodic review (s, S) policies for finite and infinite horizon nonstationary systems and assume no lead time.…”