Asymptotic Optimality of (r,Q) Inventory System in a stochastic parallel processing environment
Abstract
We consider a single-item continuous-review (r, q) inventory system with i.i.d. stochastic leadtimes. Using stationary marked point process and a heavy traffic limit, we prove a previous conjecture that inventory position and inventory on-order are asymptotically independent. We also establish closed-form expressions for the optimal policy parameters and system cost in heavy traffic limit, the first of their kind to our knowledge. These expressions sharpen our understanding on the joint effect of lead time variance and lot size. For instance, they demonstrate that the well-known square root relationship between the optimal order quantity and demand rate under a sequential processing environment is replaced by the power of 1/3 under a stochastic parallel processing environment. We further extend the study to periodic-review (S,T) systems with constant leadtimes.