A robust (r, Q) policy for a simple VMI system with inventory inaccuracy and time-delay

Inventory record inaccuracy has significant negative impacts on the performance of inventory management. For example, it usually leads to high holding cost or large backlog penalty. To hedge against it, we investigate the robust replenishment problem for a one-vendor-and-one-retailer vendor managed inventory (VMI) system with inventory inaccuracy. The objective of this research is to minimize the average cost of the retailer, including the transportation cost, the inventory holding cost and the backlog penalty. First, we show how to compute the probability distribution of the physical inventory level in the future periods. Based on this probability distribution, the expected inventory cost (EIC) of the retailer is defined. Then a robust (r, Q) policy that is insensitive to inventory inaccuracy is proposed. Finally, numerical experiments are conducted to examine the performance of the proposed robust policy for hedging against inventory inaccuracy; and sensitivity analysis is carried out to study how the parameters of the system affect the average cost.