We study production systems with non-stationary stochastic demand, perishable inventory, and abandonment of backorders. In addition to inventory-related (holding, perishment) and demand-related (waiting, abandonment) costs, we consider a cost that penalizes rapid fluctuations of production rates. We formulate a finite-time production rate planning problem to minimize the overall costs. A crucial challenge from the nonstationary demand is how to effectively capture both the time variability and stochastic variability of the systems into the optimal decision processes. In response, we develop a novel two-stage optimal control method that takes advantage of the fluid control problem’s capability of capturing the system’s time variability and the diffusion control problem’s capability of capturing stochastic variability under the associated FCP solutions. The proposed method expands the scope of existing stochastic control methods from the Brownian control problems, because the critically loaded condition can be bypassed. Such a feature is crucial in nonstationary systems because the system inevitably experiences significant periods of overloading and underloading.
Dr. Xin (Sophie) Liu is an assistant professor in the Department of Mathematical Sciences at Clemson. Her research focuses on the study of various queuing models, stochastic epidemic models, rare event simulations, and time series. She holds a Ph.D. in Statistics and Operations Research from the University of North Carolina at Chapel Hill, and a B.S. in Mathematics from the University of Science and Technology of China.