On-line inventory control in single-echelon systems with time-dependent environment over multiple periods

We consider an on-line inventory control in single-echelon systems with time-dependent environment over multiple periods, in which full backlogging and average cost function are adopted. We seek to control order quantity for each period so as to minimize a cost function involving maintenance cost and setup cost for each order. Most of state-of-art inventory control methods require the assumption that demands are independent and identically distributed over multiple periods which could result in a stationary optimal (s; S) or (Q;R) or base stock policy throughout the whole process. The assumption is not quite realistic in practice, especially when we face those disruptive events in supply chain systems. To consider this time-dependent demands, we develop a novel on-line inventory control algorithm to directly obtain the optimal order quantity for the current stage instead of the computation of those optimal policies like (s; S). A “best solution in probability” is introduced, which leads to a high-performance inventory system and can be efficiently obtained by solving a series of corresponding off-line inventory control problems. Numerical examples are included to illustrate our results and show substantial performance improvements over off-line analysis.