On-line Non-stationary Inventory Control using Champion Competition
  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. 
Jianfeng Mao
math.OC