The optimal control of production-inventory system

Author

Fu Yi ; Bian Baojun ; Zhang Jizhou

Author_Institution

Dept. of Math., Tongji Univ., Shanghai, China

fYear

2013

fDate

25-27 May 2013

Firstpage

4571

Lastpage

4576

Abstract

In this paper, we study the optimal production strategy of a production-inventory system with stochastic demand rate. This strategy is called a target level strategy, since it determines an optimal target inventory level and production rate level in the time period. The value function for developing the optimal production strategy is established, and the corresponding equation which is a fully nonlinear equation is derived using the dynamic programming principle (DPP). The uniqueness and comparison principle of the viscosity solutions of related Hamilton-Jacobi-Bellman (HJB) equation are proved. Finally, the numerical illustrative examples are discussed.

Keywords

dynamic programming; inventory management; nonlinear equations; optimal control; partial differential equations; DPP; Hamilton-Jacobi-Bellman equation; dynamic programming principle; nonlinear equation; optimal control; optimal production strategy; optimal target inventory level; production rate level; production-inventory system; stochastic demand rate; time period; value function; viscosity solutions; Equations; Mathematical model; Optimal control; Planning; Production; Stochastic processes; Viscosity; Hamilton-Jacobi-Bellman equation; Production-Inventory System; Viscosity Solution;

fLanguage

English

Publisher

ieee

Conference_Titel

Control and Decision Conference (CCDC), 2013 25th Chinese

Conference_Location

Guiyang

Print_ISBN

978-1-4673-5533-9

Type

conf

DOI

10.1109/CCDC.2013.6561760

Filename

6561760