Turnpike Sets in Optimal Stochastic Production Planning Problems

摘要

This paper considers an infinite horizon stochastic production planning problem with demand assumed to be a continuous-time Markov processs. The problems with control (production) and state (inventory) constraints are treated. It is shown that a unique optimal feedback solution exists. The solution is characterized in terms of a turnpike set, toward which the optimal inventory level approach monotonically over time. Moreover, for nondeterministic demand the optimal inventory level reaches the turnpike set almost surely in a finite time and, thereafter, it wanders inside the set in respone to the randomly fluctuating demand. Keywords: Stochastic optimal control. (Author)