Optimal Dynamic Pricing Strategy for Inventory with Reference Price Effects

10.6186/IJIMS.202103_32(1).0005

Xiao-Hong Zhang

Dynamic pricing ； Inventory ； Reference price effects ； Pontryagin's maximum ； principle

International Journal of Information and Management Sciences

32卷1期（2021 / 03 / 01）

77 - 100

英文

A dynamic pricing model of a retailer selling a kind of fixed quantity of items with shelf life under reference price effects is investigated. An optimal control model is established to maximize the retailer's total profit, where the demand is time-varying and depends on price and reference price. The continuous time dynamic optimal pricing policy with reference price effects are obtained for both finite and infinite planning horizon by Pontryagin's maximum principle. Numerical experiments are account for the impacts of the key system parameters. The theoretical and numerical analysis shows that: (1) in finite planning horizon, the optimal price is increasing in the initial reference price and reference price coefficient, and is concave in memory effect coefficient and discount rate, while the optimal inventory level decreases with these parameters. (2) in infinite planning horizon, the retailer makes a choice between price skimming and price penetration based on the difference between the consumers' initial reference price and the steady state price. Further, the steady state price increases with memory effect coefficient and discount rate, and decreases with reference price coefficient. Finally, some managerial inspiration and implication that retailer may adopt to formulate its pricing policy are obtained.

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