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Optimal dynamic pricing of inventories with stochastic demand and discounted criterion |
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| Authors: | Ping Cao Hong Yan |
| Affiliation: | a MADIS and National Center for Mathematics and Interdisciplinary Sciences, Academy of Mathematics and Systems Science, CAS, Beijing 100190, China b School of Management, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China c Department of Logistics and Maritime Studies, Hong Kong Polytechnic University, Hung Hom, Hong Kong |
| Abstract: | We consider a continuous time dynamic pricing problem for selling a given number of items over a finite or infinite time horizon. The demand is price sensitive and follows a non-homogeneous Poisson process. We formulate this problem as to maximize the expected discounted revenue and obtain the structural properties of the optimal revenue function and optimal price policy by the Hamilton-Jacobi-Bellman (HJB) equation. Moreover, we study the impact of the discount rate on the optimal revenue function and the optimal price. Further, we extend the problem to the case with discounting and time-varying demand, the infinite time horizon problem. Numerical examples are used to illustrate our analytical results. |
| Keywords: | Revenue management HJB equation Optimal pricing Discounted criterion |
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