  The commonly adopted assumption of stationary demands cannot actually reflect
fluctuating demands and will weaken solution effectiveness in real practice. We
consider an On-line Non-stationary Inventory Control Problem (ONICP), in which
no specific assumption is imposed on demands and their probability
distributions are allowed to vary over periods and correlate with each other.
The nature of non-stationary demands disables the optimality of static (s,S)
policies and the applicability of its corresponding algorithms. The ONICP
becomes computationally intractable by using general Simulation-based
Optimization (SO) methods, especially under an on-line decision-making
environment with no luxury of time and computing resources to afford the huge
computational burden. We develop a new SO method, termed "Champion Competition"
(CC), which provides a different framework and bypasses the time-consuming
sample average routine adopted in general SO methods. An alternate type of
optimal solution, termed "Champion Solution", is pursued in the CC framework,
which coincides the traditional optimality sense under certain conditions and
serves as a near-optimal solution for general cases. The CC can reduce the
complexity of general SO methods by orders of magnitude in solving a class of
SO problems, including the ONICP. A polynomial algorithm, termed "Renewal Cycle
Algorithm" (RCA), is further developed to fulfill an important procedure of the
CC framework in solving this ONICP. Numerical examples are included to
demonstrate the performance of the CC framework with the RCA embedded.
