Joint dynamic pricing and inventory control policy for a stochastic inventory system with perishable products

Abstract

This paper considers the joint dynamic pricing and inventory control policy for a stochastic inventory system with perishable products. The inventory system, with random disturbance, is modelled as a continuous-time stochastic differential equation. Combined dynamic pricing and production control, a stochastic dynamic optimisation problem that maximises the total discounted profit is developed. By applying the stochastic optimal control method, we formulate the problem of finding the optimal joint dynamic pricing and production schedule as the problem of solving a Hamilton–Jacobi–Bellman (HJB) equation. It is shown that the optimal dynamic pricing and production rate take the linear feedback form of the inventory level, which allows the decision-maker to effectively adjust the strategies as time evolves. In addition, to highlight the advantage of the joint dynamic pricing and production strategy, the case of the optimal production with static price is considered. Numerical examples are given to illustrate the validness of the theoretical results.

Keywords:

• production
• dynamic pricing
• perishable products
• stochastic optimal control
• Hamilton–Jacobi–Bellman (HJB) equation

Acknowledgements

The authors thank the anonymous referees for their valuable comments and suggestions.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant numbers 61473204, grant number 71401007]; the Program for New Century Excellent Talents in the Universities of China [grant number NCET-11-0377]; and the Beijing Natural Science Foundation [grant number 9144031].