Inventory control policy for a periodic review system with expediting

In this work, we examine a single stage, periodic review inventory system where two modes, namely regular mode and expediting mode are available for a firm to obtain its replenishment. The firm can choose expediting mode with shorter lead time at a higher cost when necessary. A two-replenishment-mode model, with random expediting points is established and an innovative ordering policy (S, e) which replenishes the inventory level to S in every cycle and expedites a part of the order using fast mode when the inventory level drops to or below a certain level e, is proposed. A simulation-based optimization approach is employed to solve the problem. To be specific, an infinitesimal perturbation analysis (IPA) method is applied to estimate the gradients of the objective function and a gradient search algorithm is then used to find the best (S, e). Numerical experiments have validated the IPA estimate of (S, e) and shown that our new (S, e) policy outperforms the pure order-up-to policy and two single review moment policies. Sensitivity analysis has been conducted to evaluate the impact of system parameters of interest and managerial insights have been drawn.